stau.space
Permutation matrices research.
ci: Ignore correct files in jupyter notebooks.
The .gitignore had `src/jupyter/.ipynb_checkpoints/` instead of `__pycache__`.
+4660
-1
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-1
.gitignore
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-1
.gitignore
src/jupyter/.ipynb_checkpoints/costas_13x13-checkpoint.gif
src/jupyter/.ipynb_checkpoints/costas_13x13-checkpoint.gif
This is a binary file and will not be displayed.
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src/jupyter/.ipynb_checkpoints/gif-checkpoint.jl
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src/jupyter/.ipynb_checkpoints/gif-checkpoint.jl
···
1
+
import Pkg
2
+
import Serialization
3
+
Pkg.add("Combinatorics")
4
+
Pkg.add("Primes")
5
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Pkg.add("BenchmarkTools")
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+
Pkg.add("Transducers")
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Pkg.add("Plots")
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using Combinatorics
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using Primes
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using BenchmarkTools
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using Transducers
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using Plots
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include("header.jl")
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+
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import Base.Iterators
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savevar(file_path::String, a) = Serialization.serialize(file_path, a)
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loadvar(file_path::String) = Serialization.deserialize(file_path)
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+
21
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for n in 1:10
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# out = 1:n |> permutations |> Filter(iscostas) |> tcollect
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file_path = "costas_$(n)x$(n).dat"
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out = loadvar(file_path)
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#savevar(file_path, out)
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println("$(file_path) has $(length(out)) arrays.")
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+
end
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costas_1x1 = loadvar("costas_1x1.dat")
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costas_2x2 = loadvar("costas_2x2.dat")
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costas_3x3 = loadvar("costas_3x3.dat")
32
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costas_4x4 = loadvar("costas_4x4.dat")
33
+
costas_5x5 = loadvar("costas_5x5.dat")
34
+
costas_6x6 = loadvar("costas_6x6.dat")
35
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costas_7x7 = loadvar("costas_7x7.dat")
36
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costas_8x8 = loadvar("costas_8x8.dat")
37
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costas_9x9 = loadvar("costas_9x9.dat")
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costas_10x10 = loadvar("costas_10x10.dat")
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costas_11x11 = loadvar("costas_11x11.dat")
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println("costas_11x11 has $(length(costas_11x11)) arrays.")
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costas_12x12 = loadvar("costas_12x12.dat")
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println("costas_12x12 has $(length(costas_12x12)) arrays.")
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costas_13x13 = loadvar("costas_13x13.dat")
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println("costas_13x13 has $(length(costas_13x13)) arrays.")
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+
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ize = 10
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last = costas_10x10[1][1:size - 3]
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inputs = []
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arr = []
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for l in costas_13x13
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if last != l[1:size - 3]
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push!(inputs, arr)
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last = l[1:size - 3]
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arr = []
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end
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push!(arr, (l[size - 2], l[size - 1], l[size]))
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end
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println(length(inputs))
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inputs
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+4152
src/jupyter/.ipynb_checkpoints/julia-checkpoint.ipynb
+4152
src/jupyter/.ipynb_checkpoints/julia-checkpoint.ipynb
···
1
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "eb80a7fb-7fb8-4117-898e-967f179749f5",
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"metadata": {},
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"outputs": [
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{
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+
"name": "stderr",
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"output_type": "stream",
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+
"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
14
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
15
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
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+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
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+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
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+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
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+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
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+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
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+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n"
28
+
]
29
+
},
30
+
{
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+
"data": {
32
+
"text/plain": [
33
+
"loadvar (generic function with 1 method)"
34
+
]
35
+
},
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+
"execution_count": 8,
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+
"metadata": {},
38
+
"output_type": "execute_result"
39
+
}
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+
],
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+
"source": [
42
+
"import Pkg\n",
43
+
"import Serialization\n",
44
+
"Pkg.add(\"Combinatorics\")\n",
45
+
"Pkg.add(\"Primes\")\n",
46
+
"Pkg.add(\"BenchmarkTools\")\n",
47
+
"Pkg.add(\"Transducers\")\n",
48
+
"Pkg.add(\"Plots\")\n",
49
+
"using Combinatorics\n",
50
+
"using Primes\n",
51
+
"using BenchmarkTools\n",
52
+
"using Transducers\n",
53
+
"using Plots\n",
54
+
"\n",
55
+
"include(\"header.jl\")\n",
56
+
"\n",
57
+
"import Base.Iterators\n",
58
+
"\n",
59
+
"savevar(file_path::String, a) = Serialization.serialize(file_path, a)\n",
60
+
"loadvar(file_path::String) = Serialization.deserialize(file_path)"
61
+
]
62
+
},
63
+
{
64
+
"cell_type": "code",
65
+
"execution_count": 9,
66
+
"id": "a9926a33-dc1c-4bd0-a26e-50e96184c3a0",
67
+
"metadata": {},
68
+
"outputs": [
69
+
{
70
+
"name": "stdout",
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+
"output_type": "stream",
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+
"text": [
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+
"false\n",
74
+
"true\n",
75
+
"true\n",
76
+
"false\n"
77
+
]
78
+
}
79
+
],
80
+
"source": [
81
+
"println(iscostas([1,2,3]))\n",
82
+
"println(iscostas([1,2]))\n",
83
+
"println(iscostas([1,2,4,3]))\n",
84
+
"println(iscostas([4,2,3,1]))"
85
+
]
86
+
},
87
+
{
88
+
"cell_type": "code",
89
+
"execution_count": 10,
90
+
"id": "903347cf-2f5f-4c3d-87cd-832347941bcc",
91
+
"metadata": {},
92
+
"outputs": [
93
+
{
94
+
"data": {
95
+
"text/plain": [
96
+
"4-element Vector{Vector{Integer}}:\n",
97
+
" [2, 4, 8, 5, 10, 9, 7, 3, 6, 1]\n",
98
+
" [6, 3, 7, 9, 10, 5, 8, 4, 2, 1]\n",
99
+
" [7, 5, 2, 3, 10, 4, 6, 9, 8, 1]\n",
100
+
" [8, 9, 6, 4, 10, 3, 2, 5, 7, 1]"
101
+
]
102
+
},
103
+
"execution_count": 10,
104
+
"metadata": {},
105
+
"output_type": "execute_result"
106
+
}
107
+
],
108
+
"source": [
109
+
"welch(11)"
110
+
]
111
+
},
112
+
{
113
+
"cell_type": "code",
114
+
"execution_count": 11,
115
+
"id": "2bd42ccd-f652-4887-babc-ac2a1de2a0e0",
116
+
"metadata": {},
117
+
"outputs": [
118
+
{
119
+
"data": {
120
+
"text/plain": [
121
+
"4-element Vector{Vector{Integer}}:\n",
122
+
" [5, 3, 2, 7, 1, 8, 4, 6, 9]\n",
123
+
" [1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
124
+
" [2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
125
+
" [4, 6, 3, 1, 7, 2, 5, 9, 8]"
126
+
]
127
+
},
128
+
"execution_count": 11,
129
+
"metadata": {},
130
+
"output_type": "execute_result"
131
+
}
132
+
],
133
+
"source": [
134
+
"lempel(11)"
135
+
]
136
+
},
137
+
{
138
+
"cell_type": "code",
139
+
"execution_count": 12,
140
+
"id": "fd67b6f4-2954-4521-a993-68a839c158ab",
141
+
"metadata": {},
142
+
"outputs": [
143
+
{
144
+
"data": {
145
+
"text/plain": [
146
+
"4-element Vector{Vector{Integer}}:\n",
147
+
" [5, 3, 2, 7, 1, 8, 4, 6, 9]\n",
148
+
" [1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
149
+
" [2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
150
+
" [4, 6, 3, 1, 7, 2, 5, 9, 8]"
151
+
]
152
+
},
153
+
"execution_count": 12,
154
+
"metadata": {},
155
+
"output_type": "execute_result"
156
+
}
157
+
],
158
+
"source": [
159
+
"lempel(11) |> Filter(iscostas) |> collect"
160
+
]
161
+
},
162
+
{
163
+
"cell_type": "code",
164
+
"execution_count": 13,
165
+
"id": "f9f95fc7-0f77-49c8-855c-061f4c971022",
166
+
"metadata": {},
167
+
"outputs": [
168
+
{
169
+
"name": "stdout",
170
+
"output_type": "stream",
171
+
"text": [
172
+
"costas_1x1.dat has 1 arrays.\n",
173
+
"costas_2x2.dat has 2 arrays.\n",
174
+
"costas_3x3.dat has 4 arrays.\n",
175
+
"costas_4x4.dat has 12 arrays.\n",
176
+
"costas_5x5.dat has 40 arrays.\n",
177
+
"costas_6x6.dat has 116 arrays.\n",
178
+
"costas_7x7.dat has 200 arrays.\n",
179
+
"costas_8x8.dat has 444 arrays.\n",
180
+
"costas_9x9.dat has 760 arrays.\n",
181
+
"costas_10x10.dat has 2160 arrays.\n",
182
+
"costas_11x11 has 4367 arrays.\n",
183
+
"costas_12x12 has 7852 arrays.\n",
184
+
"costas_13x13 has 12828 arrays.\n"
185
+
]
186
+
}
187
+
],
188
+
"source": [
189
+
"for n in 1:10\n",
190
+
" # out = 1:n |> permutations |> Filter(iscostas) |> tcollect\n",
191
+
" file_path = \"costas_$(n)x$(n).dat\"\n",
192
+
" out = loadvar(file_path)\n",
193
+
" #savevar(file_path, out)\n",
194
+
" println(\"$(file_path) has $(length(out)) arrays.\")\n",
195
+
"end\n",
196
+
"\n",
197
+
"costas_1x1 = loadvar(\"costas_1x1.dat\")\n",
198
+
"costas_2x2 = loadvar(\"costas_2x2.dat\")\n",
199
+
"costas_3x3 = loadvar(\"costas_3x3.dat\")\n",
200
+
"costas_4x4 = loadvar(\"costas_4x4.dat\")\n",
201
+
"costas_5x5 = loadvar(\"costas_5x5.dat\")\n",
202
+
"costas_6x6 = loadvar(\"costas_6x6.dat\")\n",
203
+
"costas_7x7 = loadvar(\"costas_7x7.dat\")\n",
204
+
"costas_8x8 = loadvar(\"costas_8x8.dat\")\n",
205
+
"costas_9x9 = loadvar(\"costas_9x9.dat\")\n",
206
+
"costas_10x10 = loadvar(\"costas_10x10.dat\")\n",
207
+
"costas_11x11 = loadvar(\"costas_11x11.dat\")\n",
208
+
"println(\"costas_11x11 has $(length(costas_11x11)) arrays.\")\n",
209
+
"costas_12x12 = loadvar(\"costas_12x12.dat\")\n",
210
+
"println(\"costas_12x12 has $(length(costas_12x12)) arrays.\")\n",
211
+
"costas_13x13 = loadvar(\"costas_13x13.dat\")\n",
212
+
"println(\"costas_13x13 has $(length(costas_13x13)) arrays.\")"
213
+
]
214
+
},
215
+
{
216
+
"cell_type": "code",
217
+
"execution_count": 7,
218
+
"id": "239e70bf-e41a-4d74-9935-ad5343195031",
219
+
"metadata": {},
220
+
"outputs": [
221
+
{
222
+
"name": "stdout",
223
+
"output_type": "stream",
224
+
"text": [
225
+
"costas_1x2.dat has 1 arrays.\n",
226
+
"costas_2x3.dat has 1 arrays.\n",
227
+
"costas_3x4.dat has 2 arrays.\n",
228
+
"costas_4x5.dat has 4 arrays.\n",
229
+
"costas_5x6.dat has 12 arrays.\n",
230
+
"costas_6x7.dat has 40 arrays.\n",
231
+
"costas_7x8.dat has 116 arrays.\n",
232
+
"costas_8x9.dat has 200 arrays.\n",
233
+
"costas_9x10.dat has 444 arrays.\n",
234
+
"costas_10x11.dat has 760 arrays.\n"
235
+
]
236
+
},
237
+
{
238
+
"data": {
239
+
"text/plain": [
240
+
"760-element Vector{Vector{Int64}}:\n",
241
+
" [2, 3, 7, 5, 10, 9, 6, 8, 4]\n",
242
+
" [2, 3, 7, 9, 6, 4, 10, 5, 8]\n",
243
+
" [2, 3, 7, 9, 6, 5, 10, 8, 4]\n",
244
+
" [2, 3, 7, 10, 6, 4, 9, 8, 5]\n",
245
+
" [2, 3, 8, 6, 10, 7, 9, 5, 4]\n",
246
+
" [2, 3, 8, 7, 10, 5, 9, 6, 4]\n",
247
+
" [2, 3, 9, 5, 10, 8, 7, 4, 6]\n",
248
+
" [2, 3, 10, 5, 8, 4, 9, 7, 6]\n",
249
+
" [2, 3, 10, 7, 6, 4, 9, 5, 8]\n",
250
+
" [2, 3, 10, 7, 9, 5, 4, 8, 6]\n",
251
+
" [2, 3, 10, 9, 5, 7, 4, 8, 6]\n",
252
+
" [2, 4, 8, 5, 10, 9, 7, 3, 6]\n",
253
+
" [2, 4, 9, 8, 3, 10, 6, 7, 5]\n",
254
+
" ⋮\n",
255
+
" [10, 8, 4, 7, 2, 3, 5, 9, 6]\n",
256
+
" [10, 9, 2, 3, 7, 5, 8, 4, 6]\n",
257
+
" [10, 9, 2, 5, 3, 7, 8, 4, 6]\n",
258
+
" [10, 9, 2, 5, 6, 8, 3, 7, 4]\n",
259
+
" [10, 9, 2, 7, 4, 8, 3, 5, 6]\n",
260
+
" [10, 9, 3, 7, 2, 4, 5, 8, 6]\n",
261
+
" [10, 9, 4, 5, 2, 7, 3, 6, 8]\n",
262
+
" [10, 9, 4, 6, 2, 5, 3, 7, 8]\n",
263
+
" [10, 9, 5, 2, 6, 8, 3, 4, 7]\n",
264
+
" [10, 9, 5, 3, 6, 7, 2, 4, 8]\n",
265
+
" [10, 9, 5, 3, 6, 8, 2, 7, 4]\n",
266
+
" [10, 9, 5, 7, 2, 3, 6, 4, 8]"
267
+
]
268
+
},
269
+
"execution_count": 7,
270
+
"metadata": {},
271
+
"output_type": "execute_result"
272
+
}
273
+
],
274
+
"source": [
275
+
"for n in 1:10\n",
276
+
" out = 2:n |> permutations |> Filter(Base.Fix2(iscostas, asterisk_predicate)) |> tcollect\n",
277
+
" file_path = \"costas_$(n)x$(n + 1).dat\"\n",
278
+
" #savevar(file_path, out)\n",
279
+
" println(\"$(file_path) has $(size(out, 1)) arrays.\")\n",
280
+
"end\n",
281
+
"\n",
282
+
"costas_1x2 = loadvar(\"costas_1x2.dat\")\n",
283
+
"costas_2x3 = loadvar(\"costas_2x3.dat\")\n",
284
+
"costas_3x4 = loadvar(\"costas_3x4.dat\")\n",
285
+
"costas_4x5 = loadvar(\"costas_4x5.dat\")\n",
286
+
"costas_5x6 = loadvar(\"costas_5x6.dat\")\n",
287
+
"costas_6x7 = loadvar(\"costas_6x7.dat\")\n",
288
+
"costas_7x8 = loadvar(\"costas_7x8.dat\")\n",
289
+
"costas_8x9 = loadvar(\"costas_8x9.dat\")\n",
290
+
"costas_9x10 = loadvar(\"costas_9x10.dat\")\n",
291
+
"costas_10x11 = loadvar(\"costas_10x11.dat\")"
292
+
]
293
+
},
294
+
{
295
+
"cell_type": "code",
296
+
"execution_count": 12,
297
+
"id": "230e7196-78a9-4119-8a03-d61997345038",
298
+
"metadata": {},
299
+
"outputs": [
300
+
{
301
+
"name": "stdout",
302
+
"output_type": "stream",
303
+
"text": [
304
+
"12684\n"
305
+
]
306
+
},
307
+
{
308
+
"data": {
309
+
"text/plain": [
310
+
"12684-element Vector{Any}:\n",
311
+
" Any[]\n",
312
+
" Any[(11, 7, 5)]\n",
313
+
" Any[(3, 12, 6)]\n",
314
+
" Any[(5, 11, 3)]\n",
315
+
" Any[(11, 3, 6)]\n",
316
+
" Any[(12, 6, 11)]\n",
317
+
" Any[(3, 10, 9)]\n",
318
+
" Any[(4, 11, 3)]\n",
319
+
" Any[(13, 4, 3)]\n",
320
+
" Any[(3, 10, 9)]\n",
321
+
" Any[(4, 10, 13)]\n",
322
+
" Any[(12, 11, 3)]\n",
323
+
" Any[(5, 13, 4)]\n",
324
+
" ⋮\n",
325
+
" Any[(9, 10, 2)]\n",
326
+
" Any[(9, 1, 10)]\n",
327
+
" Any[(2, 3, 11)]\n",
328
+
" Any[(10, 4, 1)]\n",
329
+
" Any[(11, 4, 5)]\n",
330
+
" Any[(1, 10, 11)]\n",
331
+
" Any[(10, 3, 11)]\n",
332
+
" Any[(11, 4, 5)]\n",
333
+
" Any[(2, 8, 3)]\n",
334
+
" Any[(3, 11, 8)]\n",
335
+
" Any[(9, 3, 11)]\n",
336
+
" Any[(11, 2, 8)]"
337
+
]
338
+
},
339
+
"execution_count": 12,
340
+
"metadata": {},
341
+
"output_type": "execute_result"
342
+
}
343
+
],
344
+
"source": [
345
+
"size = 10\n",
346
+
"last = costas_10x10[1][1:size - 3]\n",
347
+
"inputs = []\n",
348
+
"arr = []\n",
349
+
"for l in costas_13x13\n",
350
+
" if last != l[1:size - 3]\n",
351
+
" push!(inputs, arr)\n",
352
+
" last = l[1:size - 3]\n",
353
+
" arr = []\n",
354
+
" end\n",
355
+
" push!(arr, (l[size - 2], l[size - 1], l[size]))\n",
356
+
"end\n",
357
+
"println(length(inputs))\n",
358
+
"inputs"
359
+
]
360
+
},
361
+
{
362
+
"cell_type": "code",
363
+
"execution_count": null,
364
+
"id": "f2a63de1-5fb5-45ed-9113-240ccc6fb22f",
365
+
"metadata": {},
366
+
"outputs": [],
367
+
"source": [
368
+
"kw = (proj_type = :ortho, legend = false, aspect_ratio = :equal, xlimits = (0,10), ylimits = (0,10), zlimits = (0,10))\n",
369
+
"limit = length(inputs)\n",
370
+
"colors = palette([:orange, :blue], limit + 2)\n",
371
+
"@gif for i in 45:135\n",
372
+
" idx = 1\n",
373
+
" for pts in inputs\n",
374
+
" x = pts .|> a -> a[1]\n",
375
+
" y = pts .|> a -> a[2]\n",
376
+
" z = pts .|> a -> a[3]\n",
377
+
" idx += 1\n",
378
+
" scatter!(x, y, z; markercolor = colors[idx], camera = (i, round(atand(1 / √2); digits = 3)), kw...)\n",
379
+
" end\n",
380
+
"end"
381
+
]
382
+
},
383
+
{
384
+
"cell_type": "code",
385
+
"execution_count": 15,
386
+
"id": "88a92f2b-1325-4742-90b0-407dbed6a93a",
387
+
"metadata": {},
388
+
"outputs": [
389
+
{
390
+
"name": "stdout",
391
+
"output_type": "stream",
392
+
"text": [
393
+
"From costas_1x2:\n",
394
+
"Any[1, '*']\n",
395
+
"Any['*', 1]\n",
396
+
"From costas_3x4:\n",
397
+
"Any[1, 2, '*', 3]\n",
398
+
"Any[1, 3, 2, '*']\n",
399
+
"Any[2, 1, 3, '*']\n",
400
+
"Any[2, '*', 1, 3]\n",
401
+
"Any[3, 1, '*', 2]\n",
402
+
"Any[3, '*', 2, 1]\n",
403
+
"Any['*', 2, 3, 1]\n",
404
+
"Any['*', 3, 1, 2]\n",
405
+
"From costas_5x6:\n",
406
+
"Any[2, 3, 5, '*', 1, 4]\n",
407
+
"Any[3, 1, '*', 5, 2, 4]\n",
408
+
"Any[4, 1, '*', 5, 3, 2]\n",
409
+
"Any[4, 2, 5, '*', 1, 3]\n",
410
+
"Any[5, 2, 4, 3, 1, '*']\n",
411
+
"Any[5, 3, 2, 4, 1, '*']\n",
412
+
"Any['*', 1, 3, 4, 2, 5]\n",
413
+
"Any['*', 1, 4, 2, 3, 5]\n",
414
+
"From costas_9x10:\n",
415
+
"Any[1, 4, 6, 2, 9, 3, 8, 7, 5, '*']\n",
416
+
"Any[1, 7, 2, 3, 5, '*', 9, 6, 4, 8]\n",
417
+
"Any[2, 1, 5, 8, 3, 9, 7, 4, 6, '*']\n",
418
+
"Any[2, 5, 9, 8, '*', 4, 6, 3, 1, 7]\n",
419
+
"Any[3, 8, 5, 1, 2, '*', 6, 4, 7, 9]\n",
420
+
"Any[3, 8, 7, 5, '*', 1, 4, 6, 2, 9]\n",
421
+
"Any[4, 6, 3, 1, 7, 2, 5, 9, 8, '*']\n",
422
+
"Any[5, 3, 2, 7, 1, 8, 4, 6, 9, '*']\n",
423
+
"Any[7, 1, 3, 6, 4, '*', 8, 9, 5, 2]\n",
424
+
"Any[8, 4, 6, 9, '*', 5, 3, 2, 7, 1]\n",
425
+
"Any[9, 2, 6, 4, 1, '*', 5, 7, 8, 3]\n",
426
+
"Any[9, 7, 4, 6, '*', 2, 1, 5, 8, 3]\n",
427
+
"Any['*', 5, 7, 8, 3, 9, 2, 6, 4, 1]\n",
428
+
"Any['*', 6, 4, 7, 9, 3, 8, 5, 1, 2]\n",
429
+
"Any['*', 8, 9, 5, 2, 7, 1, 3, 6, 4]\n",
430
+
"Any['*', 9, 6, 4, 8, 1, 7, 2, 3, 5]\n"
431
+
]
432
+
}
433
+
],
434
+
"source": [
435
+
"println(\"From costas_1x2:\")\n",
436
+
"checklempel(costas_1x2,3)\n",
437
+
"println(\"From costas_3x4:\")\n",
438
+
"checklempel(costas_3x4,5)\n",
439
+
"println(\"From costas_5x6:\")\n",
440
+
"checklempel(costas_5x6,7)\n",
441
+
"println(\"From costas_9x10:\")\n",
442
+
"checklempel(costas_9x10,11)"
443
+
]
444
+
},
445
+
{
446
+
"cell_type": "code",
447
+
"execution_count": 16,
448
+
"id": "e3cf4111-f655-4075-9b90-3cc7faf77320",
449
+
"metadata": {},
450
+
"outputs": [
451
+
{
452
+
"data": {
453
+
"text/plain": [
454
+
"checkwelch (generic function with 1 method)"
455
+
]
456
+
},
457
+
"execution_count": 16,
458
+
"metadata": {},
459
+
"output_type": "execute_result"
460
+
}
461
+
],
462
+
"source": [
463
+
"function checkwelch(costas::Vector{Vector{Integer}}, prime::Integer)\n",
464
+
" all(all(w == lst || isrotated(w, lst) || isrotated(w, reverse(lst)) for w in welch(prime)) for lst in costas)\n",
465
+
"end"
466
+
]
467
+
},
468
+
{
469
+
"cell_type": "code",
470
+
"execution_count": 17,
471
+
"id": "d4e6119c-a191-4be4-8d07-14506117c7a5",
472
+
"metadata": {},
473
+
"outputs": [
474
+
{
475
+
"ename": "LoadError",
476
+
"evalue": "MethodError: no method matching checkwelch(::Vector{Vector{Int64}}, ::Int64)\n\n\u001b[0mClosest candidates are:\n\u001b[0m checkwelch(\u001b[91m::Vector{Vector{Integer}}\u001b[39m, ::Integer)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[16]:1\u001b[24m\u001b[39m\n",
477
+
"output_type": "error",
478
+
"traceback": [
479
+
"MethodError: no method matching checkwelch(::Vector{Vector{Int64}}, ::Int64)\n\n\u001b[0mClosest candidates are:\n\u001b[0m checkwelch(\u001b[91m::Vector{Vector{Integer}}\u001b[39m, ::Integer)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[16]:1\u001b[24m\u001b[39m\n",
480
+
"",
481
+
"Stacktrace:",
482
+
" [1] top-level scope",
483
+
" @ In[17]:1"
484
+
]
485
+
}
486
+
],
487
+
"source": [
488
+
"println(\"From costas_2x2:\", checkwelch(costas_2x2,3))\n",
489
+
"println(\"From costas_4x4:\", checkwelch(costas_4x4,5))\n",
490
+
"println(\"From costas_6x6:\", checkwelch(costas_6x6,7))\n",
491
+
"println(\"From costas_10x10:\", checkwelch(costas_10x10,11))"
492
+
]
493
+
},
494
+
{
495
+
"cell_type": "code",
496
+
"execution_count": 59,
497
+
"id": "ae2a139b-caeb-4d29-b1d2-c4e2009f118c",
498
+
"metadata": {},
499
+
"outputs": [
500
+
{
501
+
"data": {
502
+
"text/plain": [
503
+
"4-element Vector{Vector{Int64}}:\n",
504
+
" [1, 4, 2, 3]\n",
505
+
" [2, 3, 1, 4]\n",
506
+
" [3, 2, 4, 1]\n",
507
+
" [4, 1, 3, 2]"
508
+
]
509
+
},
510
+
"execution_count": 59,
511
+
"metadata": {},
512
+
"output_type": "execute_result"
513
+
}
514
+
],
515
+
"source": [
516
+
"function filterwelchs(costas, prime)\n",
517
+
" filter(lst -> all(!isrotated(lst, w) && !isrotated(lst, reverse(w)) for w in welch(prime)), costas)\n",
518
+
"end\n",
519
+
"filterwelchs(costas_4x4, 5)"
520
+
]
521
+
},
522
+
{
523
+
"cell_type": "code",
524
+
"execution_count": 61,
525
+
"id": "5431bf61-e169-48aa-90c7-e15d669cf625",
526
+
"metadata": {},
527
+
"outputs": [
528
+
{
529
+
"data": {
530
+
"text/plain": [
531
+
"issubarray (generic function with 2 methods)"
532
+
]
533
+
},
534
+
"execution_count": 61,
535
+
"metadata": {},
536
+
"output_type": "execute_result"
537
+
}
538
+
],
539
+
"source": [
540
+
"function issubarray(lhs::Vector, rhs::Vector)::Bool\n",
541
+
" lhs .|> Base.Fix1(findindex, rhs) |> issorted\n",
542
+
"end"
543
+
]
544
+
},
545
+
{
546
+
"cell_type": "code",
547
+
"execution_count": 64,
548
+
"id": "cee27363-a468-4a91-b379-5515b0bf9d21",
549
+
"metadata": {},
550
+
"outputs": [
551
+
{
552
+
"name": "stdout",
553
+
"output_type": "stream",
554
+
"text": [
555
+
"Integer[1, 4, 6, 2, 9, 3, 8, 7, 5] [10, 1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
556
+
"Integer[2, 1, 5, 8, 3, 9, 7, 4, 6] [10, 2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
557
+
"Integer[4, 6, 3, 1, 7, 2, 5, 9, 8] [10, 4, 6, 3, 1, 7, 2, 5, 9, 8]\n",
558
+
"Integer[5, 3, 2, 7, 1, 8, 4, 6, 9] [10, 5, 3, 2, 7, 1, 8, 4, 6, 9]\n"
559
+
]
560
+
}
561
+
],
562
+
"source": [
563
+
"for arr in filterwelchs(costas_10x10, 11)\n",
564
+
" for l in lempel(11)\n",
565
+
" if issubarray(l, arr)\n",
566
+
" println(\"$l $arr\")\n",
567
+
" end\n",
568
+
" end\n",
569
+
"end"
570
+
]
571
+
},
572
+
{
573
+
"cell_type": "code",
574
+
"execution_count": 65,
575
+
"id": "db8b3c90-2dd1-45d1-9739-ee3ee0bdf74c",
576
+
"metadata": {},
577
+
"outputs": [
578
+
{
579
+
"data": {
580
+
"text/plain": [
581
+
"2144"
582
+
]
583
+
},
584
+
"execution_count": 65,
585
+
"metadata": {},
586
+
"output_type": "execute_result"
587
+
}
588
+
],
589
+
"source": [
590
+
"length(filterwelchs(costas_10x10, 11))"
591
+
]
592
+
},
593
+
{
594
+
"cell_type": "code",
595
+
"execution_count": 25,
596
+
"id": "0753c6e2-8dd3-4bd9-8233-4b090eaaac68",
597
+
"metadata": {},
598
+
"outputs": [
599
+
{
600
+
"data": {
601
+
"text/plain": [
602
+
"buildallnaive (generic function with 1 method)"
603
+
]
604
+
},
605
+
"execution_count": 25,
606
+
"metadata": {},
607
+
"output_type": "execute_result"
608
+
}
609
+
],
610
+
"source": [
611
+
"# /*\n",
612
+
"# * Complexity: O(n^3)\n",
613
+
"# */\n",
614
+
"# template <class T> fn build_all_naive(Vec<T> const& vec, T x) -> Vec<Vec<T>> {\n",
615
+
"# var out = Vec<Vec<T>>();\n",
616
+
"# for (Size i = 0; i < vec.size(); ++i) {\n",
617
+
"# var lst2 = vec;\n",
618
+
"# lst2.insert(lst2.begin() + i, x);\n",
619
+
"# if (is_costas(lst2))\n",
620
+
"# out.push_back(lst2);\n",
621
+
"# }\n",
622
+
"# return out;\n",
623
+
"# }\n",
624
+
"\n",
625
+
"function buildallnaive(vec::Vector{T}, x::T)::Vector{Vector{T}} where T\n",
626
+
" out = []\n",
627
+
" for i in 1:length(vec)\n",
628
+
" lst2 = copy(vec)\n",
629
+
" insert!(lst2, i, x)\n",
630
+
" if iscostas(lst2)\n",
631
+
" push!(out,lst2)\n",
632
+
" end\n",
633
+
" end\n",
634
+
" out\n",
635
+
"end"
636
+
]
637
+
},
638
+
{
639
+
"cell_type": "code",
640
+
"execution_count": 63,
641
+
"id": "31fcaf99-c20b-4cf6-850f-a117ea166376",
642
+
"metadata": {},
643
+
"outputs": [
644
+
{
645
+
"name": "stdout",
646
+
"output_type": "stream",
647
+
"text": [
648
+
"Vector{Integer}[]\n",
649
+
"Vector{Integer}[]\n",
650
+
"Vector{Integer}[]\n",
651
+
"Vector{Integer}[]\n",
652
+
"Vector{Integer}[]\n",
653
+
"Vector{Integer}[]\n",
654
+
"Vector{Integer}[]\n",
655
+
"Vector{Integer}[]\n"
656
+
]
657
+
}
658
+
],
659
+
"source": [
660
+
"for v in welch(17)\n",
661
+
" println(buildallnaive(v,17))\n",
662
+
"end"
663
+
]
664
+
},
665
+
{
666
+
"cell_type": "code",
667
+
"execution_count": 57,
668
+
"id": "fb16e912-f3a8-467f-99f1-b5ab331efacc",
669
+
"metadata": {},
670
+
"outputs": [
671
+
{
672
+
"data": {
673
+
"text/plain": [
674
+
"12-element Vector{Int64}:\n",
675
+
" 2\n",
676
+
" 3\n",
677
+
" 5\n",
678
+
" 7\n",
679
+
" 11\n",
680
+
" 13\n",
681
+
" 17\n",
682
+
" 19\n",
683
+
" 23\n",
684
+
" 29\n",
685
+
" 31\n",
686
+
" 37"
687
+
]
688
+
},
689
+
"execution_count": 57,
690
+
"metadata": {},
691
+
"output_type": "execute_result"
692
+
}
693
+
],
694
+
"source": [
695
+
"primes(40)"
696
+
]
697
+
},
698
+
{
699
+
"cell_type": "code",
700
+
"execution_count": 34,
701
+
"id": "a42393e3-afc5-49a5-8abc-9c52b39f4326",
702
+
"metadata": {},
703
+
"outputs": [
704
+
{
705
+
"name": "stdout",
706
+
"output_type": "stream",
707
+
"text": [
708
+
"[3, 1, 2]\n",
709
+
"[1, 3, 2]\n",
710
+
"[2, 3, 1]\n",
711
+
"[[3, 1, 2, 1, 3, 2], [2, 3, 1]]\n",
712
+
"[2, 4, 3, 1]\n",
713
+
"[Int64[], [2, 4, 3, 1]]\n",
714
+
"[5, 2, 4, 3, 1]\n",
715
+
"[Int64[], [5, 2, 4, 3, 1]]\n",
716
+
"[5, 2, 4, 3, 6, 1]\n",
717
+
"[Int64[], [5, 2, 4, 3, 6, 1]]\n",
718
+
"[Int64[], Int64[]]\n",
719
+
"[Int64[], Int64[]]\n",
720
+
"[Int64[], Int64[]]\n",
721
+
"[Int64[], Int64[]]\n",
722
+
"[Int64[], Int64[]]\n",
723
+
"[Int64[], Int64[]]\n",
724
+
"[Int64[], Int64[]]\n",
725
+
"[Int64[], Int64[]]\n",
726
+
"[Int64[], Int64[]]\n",
727
+
"[Int64[], Int64[]]\n",
728
+
"[Int64[], Int64[]]\n",
729
+
"[Int64[], Int64[]]\n",
730
+
"[Int64[], Int64[]]\n",
731
+
"[Int64[], Int64[]]\n"
732
+
]
733
+
}
734
+
],
735
+
"source": [
736
+
"out = [[1,2],[2,1]]\n",
737
+
"for i ∈ 3:20\n",
738
+
" out = [buildallnaive(vec,i) |> flatten for vec in out]\n",
739
+
" println(out)\n",
740
+
"end"
741
+
]
742
+
},
743
+
{
744
+
"cell_type": "code",
745
+
"execution_count": 31,
746
+
"id": "0dc1ee17-2b26-49f5-841f-aee998ee3dc6",
747
+
"metadata": {},
748
+
"outputs": [
749
+
{
750
+
"data": {
751
+
"text/plain": [
752
+
"flatten (generic function with 1 method)"
753
+
]
754
+
},
755
+
"execution_count": 31,
756
+
"metadata": {},
757
+
"output_type": "execute_result"
758
+
}
759
+
],
760
+
"source": [
761
+
"function flatten(vec::Vector{Vector{T}})::Vector{T} where T\n",
762
+
" out = []\n",
763
+
" for v in vec\n",
764
+
" println(v)\n",
765
+
" out = vcat(out,v)\n",
766
+
" end\n",
767
+
" out\n",
768
+
"end"
769
+
]
770
+
},
771
+
{
772
+
"cell_type": "code",
773
+
"execution_count": 32,
774
+
"id": "13065e83-3e9b-4df9-b96e-b6459cb3b460",
775
+
"metadata": {},
776
+
"outputs": [
777
+
{
778
+
"name": "stdout",
779
+
"output_type": "stream",
780
+
"text": [
781
+
"[1, 2]\n",
782
+
"[2, 3]\n"
783
+
]
784
+
},
785
+
{
786
+
"data": {
787
+
"text/plain": [
788
+
"4-element Vector{Int64}:\n",
789
+
" 1\n",
790
+
" 2\n",
791
+
" 2\n",
792
+
" 3"
793
+
]
794
+
},
795
+
"execution_count": 32,
796
+
"metadata": {},
797
+
"output_type": "execute_result"
798
+
}
799
+
],
800
+
"source": [
801
+
"flatten([[1,2],[2,3]])"
802
+
]
803
+
},
804
+
{
805
+
"cell_type": "code",
806
+
"execution_count": 89,
807
+
"id": "3d7728a1-c5f8-4abe-a99f-c1effcd4bd75",
808
+
"metadata": {},
809
+
"outputs": [
810
+
{
811
+
"name": "stdout",
812
+
"output_type": "stream",
813
+
"text": [
814
+
" 12.701 ms (369811 allocations: 34.37 MiB)\n",
815
+
" 13.263 ms (369822 allocations: 35.17 MiB)\n"
816
+
]
817
+
},
818
+
{
819
+
"data": {
820
+
"text/plain": [
821
+
"444-element Vector{Vector{Int64}}:\n",
822
+
" [1, 2, 5, 7, 6, 4, 8, 3]\n",
823
+
" [1, 2, 8, 6, 3, 5, 4, 7]\n",
824
+
" [1, 3, 6, 2, 7, 8, 5, 4]\n",
825
+
" [1, 3, 6, 7, 5, 2, 8, 4]\n",
826
+
" [1, 3, 6, 7, 5, 4, 8, 2]\n",
827
+
" [1, 3, 8, 6, 7, 2, 5, 4]\n",
828
+
" [1, 4, 2, 8, 7, 3, 5, 6]\n",
829
+
" [1, 4, 5, 3, 7, 6, 8, 2]\n",
830
+
" [1, 4, 5, 7, 6, 3, 8, 2]\n",
831
+
" [1, 5, 3, 8, 7, 4, 6, 2]\n",
832
+
" [1, 5, 4, 7, 2, 8, 6, 3]\n",
833
+
" [1, 5, 6, 3, 8, 7, 2, 4]\n",
834
+
" [1, 5, 6, 8, 3, 2, 7, 4]\n",
835
+
" ⋮\n",
836
+
" [8, 4, 3, 6, 1, 2, 7, 5]\n",
837
+
" [8, 4, 5, 2, 7, 1, 3, 6]\n",
838
+
" [8, 4, 6, 1, 2, 5, 3, 7]\n",
839
+
" [8, 5, 4, 2, 3, 6, 1, 7]\n",
840
+
" [8, 5, 4, 6, 2, 3, 1, 7]\n",
841
+
" [8, 5, 7, 1, 2, 6, 4, 3]\n",
842
+
" [8, 6, 1, 3, 2, 7, 4, 5]\n",
843
+
" [8, 6, 3, 2, 4, 5, 1, 7]\n",
844
+
" [8, 6, 3, 2, 4, 7, 1, 5]\n",
845
+
" [8, 6, 3, 7, 2, 1, 4, 5]\n",
846
+
" [8, 7, 1, 3, 6, 4, 5, 2]\n",
847
+
" [8, 7, 4, 2, 3, 5, 1, 6]"
848
+
]
849
+
},
850
+
"execution_count": 89,
851
+
"metadata": {},
852
+
"output_type": "execute_result"
853
+
}
854
+
],
855
+
"source": [
856
+
"@btime 1:8 |> permutations |> Filter(iscostas) |> tcollect\n",
857
+
"@btime 1:8 |> permutations |> tcollect |> Filter(iscostas) |> tcollect"
858
+
]
859
+
},
860
+
{
861
+
"cell_type": "code",
862
+
"execution_count": 12,
863
+
"id": "b8d572c5-71c5-4157-8f00-b28b6f6a5c86",
864
+
"metadata": {},
865
+
"outputs": [
866
+
{
867
+
"data": {
868
+
"text/plain": [
869
+
"push! (generic function with 27 methods)"
870
+
]
871
+
},
872
+
"execution_count": 12,
873
+
"metadata": {},
874
+
"output_type": "execute_result"
875
+
}
876
+
],
877
+
"source": [
878
+
"push!"
879
+
]
880
+
},
881
+
{
882
+
"cell_type": "code",
883
+
"execution_count": 74,
884
+
"id": "bc84dea7-abbf-4391-b7ca-bc3ef042b5f6",
885
+
"metadata": {},
886
+
"outputs": [
887
+
{
888
+
"data": {
889
+
"text/plain": [
890
+
"iscostashelper2 (generic function with 1 method)"
891
+
]
892
+
},
893
+
"execution_count": 74,
894
+
"metadata": {},
895
+
"output_type": "execute_result"
896
+
}
897
+
],
898
+
"source": [
899
+
"function iscostashelper2(lst::Vector{T}, f::Function, n::Integer)::Bool where T\n",
900
+
" all(begin\n",
901
+
" seen::Vector{Bool} = zeros(Bool, 2 * n)\n",
902
+
" all(begin\n",
903
+
" result = f(lst[i+k],lst[i],n)\n",
904
+
" prev = seen[result]\n",
905
+
" seen[result] = true\n",
906
+
" !prev\n",
907
+
" end for i ∈ 1:(n - k))\n",
908
+
" end for k ∈ 1:n)\n",
909
+
"end"
910
+
]
911
+
},
912
+
{
913
+
"cell_type": "code",
914
+
"execution_count": 76,
915
+
"id": "f23c7781-a45e-4eb8-b826-75195d85f4a2",
916
+
"metadata": {},
917
+
"outputs": [
918
+
{
919
+
"data": {
920
+
"text/plain": [
921
+
"false"
922
+
]
923
+
},
924
+
"execution_count": 76,
925
+
"metadata": {},
926
+
"output_type": "execute_result"
927
+
}
928
+
],
929
+
"source": [
930
+
"iscostashelper2([1,2,3], (x,y,n) -> x - y + n, 3)"
931
+
]
932
+
},
933
+
{
934
+
"cell_type": "code",
935
+
"execution_count": 87,
936
+
"id": "6b4fc3f1-add6-4062-88f4-40e2aeb365e7",
937
+
"metadata": {},
938
+
"outputs": [
939
+
{
940
+
"data": {
941
+
"text/plain": [
942
+
"8-element Vector{Int64}:\n",
943
+
" 1\n",
944
+
" 2\n",
945
+
" 3\n",
946
+
" 4\n",
947
+
" 5\n",
948
+
" 6\n",
949
+
" 7\n",
950
+
" 8"
951
+
]
952
+
},
953
+
"execution_count": 87,
954
+
"metadata": {},
955
+
"output_type": "execute_result"
956
+
}
957
+
],
958
+
"source": [
959
+
"1:8 |> collect"
960
+
]
961
+
},
962
+
{
963
+
"cell_type": "code",
964
+
"execution_count": 85,
965
+
"id": "a4342391-7c28-4871-b69f-7f5d746e7f87",
966
+
"metadata": {},
967
+
"outputs": [
968
+
{
969
+
"data": {
970
+
"text/plain": [
971
+
"6-element Vector{Vector{Any}}:\n",
972
+
" [1, 2, '*']\n",
973
+
" [1, '*', 2]\n",
974
+
" [2, 1, '*']\n",
975
+
" [2, '*', 1]\n",
976
+
" ['*', 1, 2]\n",
977
+
" ['*', 2, 1]"
978
+
]
979
+
},
980
+
"execution_count": 85,
981
+
"metadata": {},
982
+
"output_type": "execute_result"
983
+
}
984
+
],
985
+
"source": [
986
+
"costas_2x3"
987
+
]
988
+
},
989
+
{
990
+
"cell_type": "code",
991
+
"execution_count": 4,
992
+
"id": "a23e4d3d-1e0f-4956-a7ae-fe60b4296675",
993
+
"metadata": {},
994
+
"outputs": [
995
+
{
996
+
"data": {
997
+
"text/plain": [
998
+
"12-element Vector{Vector{Int64}}:\n",
999
+
" [1, 2, 4, 3]\n",
1000
+
" [1, 3, 4, 2]\n",
1001
+
" [1, 4, 2, 3]\n",
1002
+
" [2, 1, 3, 4]\n",
1003
+
" [2, 3, 1, 4]\n",
1004
+
" [2, 4, 3, 1]\n",
1005
+
" [3, 1, 2, 4]\n",
1006
+
" [3, 2, 4, 1]\n",
1007
+
" [3, 4, 2, 1]\n",
1008
+
" [4, 1, 3, 2]\n",
1009
+
" [4, 2, 1, 3]\n",
1010
+
" [4, 3, 1, 2]"
1011
+
]
1012
+
},
1013
+
"execution_count": 4,
1014
+
"metadata": {},
1015
+
"output_type": "execute_result"
1016
+
}
1017
+
],
1018
+
"source": [
1019
+
"costas_4x4"
1020
+
]
1021
+
},
1022
+
{
1023
+
"cell_type": "code",
1024
+
"execution_count": 6,
1025
+
"id": "85b4de41-4ba6-49a6-9bc8-4e52b68c760b",
1026
+
"metadata": {},
1027
+
"outputs": [
1028
+
{
1029
+
"data": {
1030
+
"text/plain": [
1031
+
"12-element Vector{Vector{Int64}}:\n",
1032
+
" [1, 2, 4, 3]\n",
1033
+
" [1, 3, 4, 2]\n",
1034
+
" [1, 4, 2, 3]\n",
1035
+
" [2, 1, 3, 4]\n",
1036
+
" [2, 3, 1, 4]\n",
1037
+
" [2, 4, 3, 1]\n",
1038
+
" [3, 1, 2, 4]\n",
1039
+
" [3, 2, 4, 1]\n",
1040
+
" [3, 4, 2, 1]\n",
1041
+
" [4, 1, 3, 2]\n",
1042
+
" [4, 2, 1, 3]\n",
1043
+
" [4, 3, 1, 2]"
1044
+
]
1045
+
},
1046
+
"execution_count": 6,
1047
+
"metadata": {},
1048
+
"output_type": "execute_result"
1049
+
}
1050
+
],
1051
+
"source": [
1052
+
"lst = copy(costas_4x4)"
1053
+
]
1054
+
},
1055
+
{
1056
+
"cell_type": "code",
1057
+
"execution_count": 8,
1058
+
"id": "024f14ce-bbad-4b3c-a038-56e9e7e0b801",
1059
+
"metadata": {},
1060
+
"outputs": [
1061
+
{
1062
+
"data": {
1063
+
"text/plain": [
1064
+
"13-element Vector{Vector{Int64}}:\n",
1065
+
" [1, 2, 4, 3]\n",
1066
+
" [1, 3, 4, 2]\n",
1067
+
" [1, 4, 2, 3]\n",
1068
+
" [2, 1, 3, 4]\n",
1069
+
" [2, 3, 1, 4]\n",
1070
+
" [2, 4, 3, 1]\n",
1071
+
" [3, 1, 2, 4]\n",
1072
+
" [3, 2, 4, 1]\n",
1073
+
" [3, 4, 2, 1]\n",
1074
+
" [4, 1, 3, 2]\n",
1075
+
" [4, 2, 1, 3]\n",
1076
+
" [4, 3, 1, 2]\n",
1077
+
" [3]"
1078
+
]
1079
+
},
1080
+
"execution_count": 8,
1081
+
"metadata": {},
1082
+
"output_type": "execute_result"
1083
+
}
1084
+
],
1085
+
"source": [
1086
+
"push!(lst,[3])"
1087
+
]
1088
+
},
1089
+
{
1090
+
"cell_type": "code",
1091
+
"execution_count": 9,
1092
+
"id": "b6984319-851e-41aa-a023-4fb222c248bc",
1093
+
"metadata": {},
1094
+
"outputs": [
1095
+
{
1096
+
"data": {
1097
+
"text/plain": [
1098
+
"12-element Vector{Vector{Int64}}:\n",
1099
+
" [1, 2, 4, 3]\n",
1100
+
" [1, 3, 4, 2]\n",
1101
+
" [1, 4, 2, 3]\n",
1102
+
" [2, 1, 3, 4]\n",
1103
+
" [2, 3, 1, 4]\n",
1104
+
" [2, 4, 3, 1]\n",
1105
+
" [3, 1, 2, 4]\n",
1106
+
" [3, 2, 4, 1]\n",
1107
+
" [3, 4, 2, 1]\n",
1108
+
" [4, 1, 3, 2]\n",
1109
+
" [4, 2, 1, 3]\n",
1110
+
" [4, 3, 1, 2]"
1111
+
]
1112
+
},
1113
+
"execution_count": 9,
1114
+
"metadata": {},
1115
+
"output_type": "execute_result"
1116
+
}
1117
+
],
1118
+
"source": [
1119
+
"costas_4x4"
1120
+
]
1121
+
},
1122
+
{
1123
+
"cell_type": "code",
1124
+
"execution_count": 27,
1125
+
"id": "ea43d891-12c2-48df-9187-d7a72d84e31f",
1126
+
"metadata": {},
1127
+
"outputs": [
1128
+
{
1129
+
"data": {
1130
+
"text/plain": [
1131
+
"29-element Vector{Integer}:\n",
1132
+
" 9\n",
1133
+
" 27\n",
1134
+
" 20\n",
1135
+
" 11\n",
1136
+
" 25\n",
1137
+
" 6\n",
1138
+
" 21\n",
1139
+
" 19\n",
1140
+
" 1\n",
1141
+
" 28\n",
1142
+
" 4\n",
1143
+
" 13\n",
1144
+
" 12\n",
1145
+
" ⋮\n",
1146
+
" 16\n",
1147
+
" 8\n",
1148
+
" 3\n",
1149
+
" 7\n",
1150
+
" 26\n",
1151
+
" 29\n",
1152
+
" 15\n",
1153
+
" 5\n",
1154
+
" 22\n",
1155
+
" 2\n",
1156
+
" 10\n",
1157
+
" 23"
1158
+
]
1159
+
},
1160
+
"execution_count": 27,
1161
+
"metadata": {},
1162
+
"output_type": "execute_result"
1163
+
}
1164
+
],
1165
+
"source": [
1166
+
"lst = lempel(31)[1]"
1167
+
]
1168
+
},
1169
+
{
1170
+
"cell_type": "code",
1171
+
"execution_count": 28,
1172
+
"id": "d5168b88-2176-48c7-a9c9-11fe3237767e",
1173
+
"metadata": {},
1174
+
"outputs": [
1175
+
{
1176
+
"name": "stdout",
1177
+
"output_type": "stream",
1178
+
"text": [
1179
+
"6 6\n"
1180
+
]
1181
+
}
1182
+
],
1183
+
"source": [
1184
+
"for i in 1:length(lst)\n",
1185
+
" if lst[i] == i\n",
1186
+
" println(lst[i], ' ', i)\n",
1187
+
" end\n",
1188
+
"end"
1189
+
]
1190
+
},
1191
+
{
1192
+
"cell_type": "code",
1193
+
"execution_count": 25,
1194
+
"id": "5840c9f4-ff21-4c25-b142-e27d0a01dc20",
1195
+
"metadata": {},
1196
+
"outputs": [
1197
+
{
1198
+
"data": {
1199
+
"text/plain": [
1200
+
"30-element Vector{Integer}:\n",
1201
+
" 9\n",
1202
+
" 27\n",
1203
+
" 20\n",
1204
+
" 11\n",
1205
+
" 25\n",
1206
+
" 6\n",
1207
+
" 21\n",
1208
+
" 19\n",
1209
+
" 1\n",
1210
+
" 28\n",
1211
+
" 4\n",
1212
+
" 13\n",
1213
+
" 12\n",
1214
+
" ⋮\n",
1215
+
" 8\n",
1216
+
" 3\n",
1217
+
" 7\n",
1218
+
" 26\n",
1219
+
" 29\n",
1220
+
" 15\n",
1221
+
" 5\n",
1222
+
" 22\n",
1223
+
" 2\n",
1224
+
" 10\n",
1225
+
" 23\n",
1226
+
" 30"
1227
+
]
1228
+
},
1229
+
"execution_count": 25,
1230
+
"metadata": {},
1231
+
"output_type": "execute_result"
1232
+
}
1233
+
],
1234
+
"source": [
1235
+
"\n",
1236
+
"push!(lst, 30)"
1237
+
]
1238
+
},
1239
+
{
1240
+
"cell_type": "code",
1241
+
"execution_count": 30,
1242
+
"id": "9887c630-5b65-4105-b39f-80daf59d8fe6",
1243
+
"metadata": {},
1244
+
"outputs": [
1245
+
{
1246
+
"data": {
1247
+
"text/plain": [
1248
+
"false"
1249
+
]
1250
+
},
1251
+
"execution_count": 30,
1252
+
"metadata": {},
1253
+
"output_type": "execute_result"
1254
+
}
1255
+
],
1256
+
"source": [
1257
+
"iscostas([4,5,3,1,2])"
1258
+
]
1259
+
},
1260
+
{
1261
+
"cell_type": "code",
1262
+
"execution_count": 32,
1263
+
"id": "60afa128-2bd5-4d24-b324-847db1c86426",
1264
+
"metadata": {},
1265
+
"outputs": [
1266
+
{
1267
+
"data": {
1268
+
"text/plain": [
1269
+
"12-element Vector{Int64}:\n",
1270
+
" 2\n",
1271
+
" 3\n",
1272
+
" 5\n",
1273
+
" 7\n",
1274
+
" 11\n",
1275
+
" 13\n",
1276
+
" 17\n",
1277
+
" 19\n",
1278
+
" 23\n",
1279
+
" 29\n",
1280
+
" 31\n",
1281
+
" 37"
1282
+
]
1283
+
},
1284
+
"execution_count": 32,
1285
+
"metadata": {},
1286
+
"output_type": "execute_result"
1287
+
}
1288
+
],
1289
+
"source": [
1290
+
"primes(40)"
1291
+
]
1292
+
},
1293
+
{
1294
+
"cell_type": "code",
1295
+
"execution_count": 36,
1296
+
"id": "7ba9a47b-889f-47db-81cd-59f4cf0ffc33",
1297
+
"metadata": {},
1298
+
"outputs": [
1299
+
{
1300
+
"data": {
1301
+
"text/plain": [
1302
+
"35-element Vector{Integer}:\n",
1303
+
" 18\n",
1304
+
" 8\n",
1305
+
" 14\n",
1306
+
" 31\n",
1307
+
" 27\n",
1308
+
" 30\n",
1309
+
" 22\n",
1310
+
" 2\n",
1311
+
" 32\n",
1312
+
" 11\n",
1313
+
" 10\n",
1314
+
" 28\n",
1315
+
" 15\n",
1316
+
" ⋮\n",
1317
+
" 34\n",
1318
+
" 17\n",
1319
+
" 19\n",
1320
+
" 5\n",
1321
+
" 12\n",
1322
+
" 33\n",
1323
+
" 6\n",
1324
+
" 4\n",
1325
+
" 9\n",
1326
+
" 29\n",
1327
+
" 24\n",
1328
+
" 35"
1329
+
]
1330
+
},
1331
+
"execution_count": 36,
1332
+
"metadata": {},
1333
+
"output_type": "execute_result"
1334
+
}
1335
+
],
1336
+
"source": [
1337
+
"lst = lempel(37)[1]"
1338
+
]
1339
+
},
1340
+
{
1341
+
"cell_type": "code",
1342
+
"execution_count": 44,
1343
+
"id": "1ba968f1-e5fe-44a0-bea5-8631e9594024",
1344
+
"metadata": {},
1345
+
"outputs": [
1346
+
{
1347
+
"data": {
1348
+
"text/plain": [
1349
+
"false"
1350
+
]
1351
+
},
1352
+
"execution_count": 44,
1353
+
"metadata": {},
1354
+
"output_type": "execute_result"
1355
+
}
1356
+
],
1357
+
"source": [
1358
+
"lst = lempel(37)[1]\n",
1359
+
"lst = [lst[i] for i in 1:(length(lst) - 1)]\n",
1360
+
"lst[24] = lst[34]\n",
1361
+
"lst = [lst[i] for i in 1:(length(lst) - 1)]\n",
1362
+
"lst[29] = lst[33]\n",
1363
+
"lst = [lst[i] for i in 1:(length(lst) - 1)]\n",
1364
+
"iscostas(lst)"
1365
+
]
1366
+
},
1367
+
{
1368
+
"cell_type": "code",
1369
+
"execution_count": 46,
1370
+
"id": "a137ecde-01da-434c-81b1-d9609acc37ef",
1371
+
"metadata": {},
1372
+
"outputs": [
1373
+
{
1374
+
"name": "stdout",
1375
+
"output_type": "stream",
1376
+
"text": [
1377
+
"2: 1\n",
1378
+
"3: 1\n",
1379
+
"5: 2\n",
1380
+
"7: 2\n",
1381
+
"11: 4\n",
1382
+
"13: 4\n",
1383
+
"17: 8\n",
1384
+
"19: 6\n",
1385
+
"23: 10\n",
1386
+
"29: 12\n",
1387
+
"31: 8\n",
1388
+
"37: 12\n",
1389
+
"41: 16\n",
1390
+
"43: 12\n",
1391
+
"47: 22\n",
1392
+
"53: 24\n",
1393
+
"59: 28\n",
1394
+
"61: 16\n",
1395
+
"67: 20\n"
1396
+
]
1397
+
}
1398
+
],
1399
+
"source": [
1400
+
"for p in primes(70)\n",
1401
+
" println(\"$p: $(length(lempel(p)))\")\n",
1402
+
"end"
1403
+
]
1404
+
},
1405
+
{
1406
+
"cell_type": "code",
1407
+
"execution_count": 2,
1408
+
"id": "f1185f41-b5db-4d0c-b278-f069c8755df6",
1409
+
"metadata": {},
1410
+
"outputs": [
1411
+
{
1412
+
"data": {
1413
+
"text/plain": [
1414
+
"telephone (generic function with 1 method)"
1415
+
]
1416
+
},
1417
+
"execution_count": 2,
1418
+
"metadata": {},
1419
+
"output_type": "execute_result"
1420
+
}
1421
+
],
1422
+
"source": [
1423
+
"function telephone(n)\n",
1424
+
" n <= 1 ? 1 : telephone(n-1) + (n - 1) * telephone(n - 2)\n",
1425
+
"end"
1426
+
]
1427
+
},
1428
+
{
1429
+
"cell_type": "code",
1430
+
"execution_count": 48,
1431
+
"id": "e1163acd-0287-4b86-b4ff-0aa56c87aa89",
1432
+
"metadata": {},
1433
+
"outputs": [
1434
+
{
1435
+
"data": {
1436
+
"text/plain": [
1437
+
"4034315351021199616"
1438
+
]
1439
+
},
1440
+
"execution_count": 48,
1441
+
"metadata": {},
1442
+
"output_type": "execute_result"
1443
+
}
1444
+
],
1445
+
"source": [
1446
+
"telephone(32)"
1447
+
]
1448
+
},
1449
+
{
1450
+
"cell_type": "code",
1451
+
"execution_count": 4,
1452
+
"id": "fed2bc43-df75-421b-8a41-5b4519183103",
1453
+
"metadata": {},
1454
+
"outputs": [
1455
+
{
1456
+
"name": "stdout",
1457
+
"output_type": "stream",
1458
+
"text": [
1459
+
"1\n",
1460
+
"2\n",
1461
+
"4\n",
1462
+
"10\n",
1463
+
"26\n",
1464
+
"76\n",
1465
+
"232\n",
1466
+
"764\n",
1467
+
"2620\n",
1468
+
"9496\n"
1469
+
]
1470
+
}
1471
+
],
1472
+
"source": [
1473
+
"for i ∈ 1:10\n",
1474
+
" println(telephone(i))\n",
1475
+
"end"
1476
+
]
1477
+
},
1478
+
{
1479
+
"cell_type": "code",
1480
+
"execution_count": 8,
1481
+
"id": "add0d34d-16c7-464b-9827-0b0deb904541",
1482
+
"metadata": {},
1483
+
"outputs": [
1484
+
{
1485
+
"data": {
1486
+
"text/plain": [
1487
+
"12-element Vector{Vector{Integer}}:\n",
1488
+
" [2, 4, 8, 16, 32, 27, 17, 34, 31, 25 … 6, 12, 24, 11, 22, 7, 14, 28, 19, 1]\n",
1489
+
" [5, 25, 14, 33, 17, 11, 18, 16, 6, 30 … 31, 7, 35, 27, 24, 9, 8, 3, 15, 1]\n",
1490
+
" [13, 21, 14, 34, 35, 11, 32, 9, 6, 4 … 31, 33, 22, 27, 18, 12, 8, 30, 20, 1]\n",
1491
+
" [15, 3, 8, 9, 24, 27, 35, 7, 31, 21 … 6, 16, 18, 11, 17, 33, 14, 25, 5, 1]\n",
1492
+
" [17, 30, 29, 12, 19, 27, 15, 33, 6, 28 … 31, 9, 5, 11, 2, 34, 23, 21, 24, 1]\n",
1493
+
" [18, 28, 23, 7, 15, 11, 13, 12, 31, 3 … 6, 34, 20, 27, 5, 16, 29, 4, 35, 1]\n",
1494
+
" [19, 28, 14, 7, 22, 11, 24, 12, 6, 3 … 31, 34, 17, 27, 32, 16, 8, 4, 2, 1]\n",
1495
+
" [20, 30, 8, 12, 18, 27, 22, 33, 31, 28 … 6, 9, 32, 11, 35, 34, 14, 21, 13, 1]\n",
1496
+
" [22, 3, 29, 9, 13, 27, 2, 7, 6, 21 … 31, 16, 19, 11, 20, 33, 23, 25, 32, 1]\n",
1497
+
" [24, 21, 23, 34, 2, 11, 5, 9, 31, 4 … 6, 33, 15, 27, 19, 12, 29, 30, 17, 1]\n",
1498
+
" [32, 25, 23, 33, 20, 11, 19, 16, 31, 30 … 6, 7, 2, 27, 13, 9, 29, 3, 22, 1]\n",
1499
+
" [35, 4, 29, 16, 5, 27, 20, 34, 6, 25 … 31, 12, 13, 11, 15, 7, 23, 28, 18, 1]"
1500
+
]
1501
+
},
1502
+
"execution_count": 8,
1503
+
"metadata": {},
1504
+
"output_type": "execute_result"
1505
+
}
1506
+
],
1507
+
"source": [
1508
+
"welch(37)"
1509
+
]
1510
+
},
1511
+
{
1512
+
"cell_type": "code",
1513
+
"execution_count": 9,
1514
+
"id": "e20cf1f6-44ae-4117-802e-31480d09752e",
1515
+
"metadata": {},
1516
+
"outputs": [
1517
+
{
1518
+
"data": {
1519
+
"text/plain": [
1520
+
"true"
1521
+
]
1522
+
},
1523
+
"execution_count": 9,
1524
+
"metadata": {},
1525
+
"output_type": "execute_result"
1526
+
}
1527
+
],
1528
+
"source": [
1529
+
"iscostas([4,6,7,2,8,1,5,3])"
1530
+
]
1531
+
},
1532
+
{
1533
+
"cell_type": "code",
1534
+
"execution_count": 46,
1535
+
"id": "75a8b103-a13b-4ad1-a1fd-48fd509aad79",
1536
+
"metadata": {},
1537
+
"outputs": [
1538
+
{
1539
+
"data": {
1540
+
"text/plain": [
1541
+
"ts (generic function with 1 method)"
1542
+
]
1543
+
},
1544
+
"execution_count": 46,
1545
+
"metadata": {},
1546
+
"output_type": "execute_result"
1547
+
}
1548
+
],
1549
+
"source": [
1550
+
"function ts(n::Integer)::Vector{Vector{Integer}}\n",
1551
+
" out = [[1]]\n",
1552
+
" for i ∈ 1:n\n",
1553
+
" new_out = []\n",
1554
+
" for vec ∈ out\n",
1555
+
" println(vec)\n",
1556
+
" verts = findverts(vec)\n",
1557
+
" println(verts)\n",
1558
+
" for vert ∈ verts\n",
1559
+
" c = swapidx([copy(vec);[i+1]], vert, i)\n",
1560
+
" push!(new_out, c)\n",
1561
+
" println(\"$new_out, $i\")\n",
1562
+
" end\n",
1563
+
" push!(new_out, [copy(vec);[i+1]])\n",
1564
+
" end\n",
1565
+
" new_out\n",
1566
+
" out = new_out\n",
1567
+
" end\n",
1568
+
" out\n",
1569
+
"end"
1570
+
]
1571
+
},
1572
+
{
1573
+
"cell_type": "code",
1574
+
"execution_count": 47,
1575
+
"id": "8c7d4ef8-5a4b-455a-b434-7bb4c58d629d",
1576
+
"metadata": {},
1577
+
"outputs": [
1578
+
{
1579
+
"name": "stdout",
1580
+
"output_type": "stream",
1581
+
"text": [
1582
+
"[1]\n",
1583
+
"Any[1]\n",
1584
+
"Any[[1, 2]], 1\n",
1585
+
"[1, 2]\n",
1586
+
"Any[1, 2]\n",
1587
+
"Any[[2, 1, 3]], 2\n",
1588
+
"Any[[2, 1, 3], [1, 2, 3]], 2\n",
1589
+
"[1, 2]\n",
1590
+
"Any[1, 2]\n",
1591
+
"Any[[2, 1, 3], [1, 2, 3], [1, 2, 3], [2, 1, 3]], 2\n",
1592
+
"Any[[2, 1, 3], [1, 2, 3], [1, 2, 3], [2, 1, 3], [1, 2, 3]], 2\n"
1593
+
]
1594
+
},
1595
+
{
1596
+
"data": {
1597
+
"text/plain": [
1598
+
"6-element Vector{Vector{Integer}}:\n",
1599
+
" [2, 1, 3]\n",
1600
+
" [1, 2, 3]\n",
1601
+
" [1, 2, 3]\n",
1602
+
" [2, 1, 3]\n",
1603
+
" [1, 2, 3]\n",
1604
+
" [1, 2, 3]"
1605
+
]
1606
+
},
1607
+
"execution_count": 47,
1608
+
"metadata": {},
1609
+
"output_type": "execute_result"
1610
+
}
1611
+
],
1612
+
"source": [
1613
+
"ts(2)"
1614
+
]
1615
+
},
1616
+
{
1617
+
"cell_type": "code",
1618
+
"execution_count": 38,
1619
+
"id": "e2708920-52cd-4189-a1ea-ed60d6b0c82d",
1620
+
"metadata": {},
1621
+
"outputs": [
1622
+
{
1623
+
"data": {
1624
+
"text/plain": [
1625
+
"4-element Vector{Int64}:\n",
1626
+
" 2\n",
1627
+
" 1\n",
1628
+
" 3\n",
1629
+
" 4"
1630
+
]
1631
+
},
1632
+
"execution_count": 38,
1633
+
"metadata": {},
1634
+
"output_type": "execute_result"
1635
+
}
1636
+
],
1637
+
"source": [
1638
+
"[1]\n",
1639
+
"\n",
1640
+
"[1,2]\n",
1641
+
"[2,1]\n",
1642
+
"\n",
1643
+
"[1,2,3]\n",
1644
+
"[3,2,1]\n",
1645
+
"[1,3,2]\n",
1646
+
"[2,1,3]\n",
1647
+
"\n",
1648
+
"[4,2,3,1]\n",
1649
+
"[1,4,3,2]\n",
1650
+
"[1,2,4,3]\n",
1651
+
"[1,2,3,4]\n",
1652
+
"[3,4,1,2]\n",
1653
+
"[3,2,1,4]\n",
1654
+
"[4,3,2,1]\n",
1655
+
"[1,3,2,4]\n",
1656
+
"[2,1,4,3]\n",
1657
+
"[2,1,3,4]"
1658
+
]
1659
+
},
1660
+
{
1661
+
"cell_type": "code",
1662
+
"execution_count": 18,
1663
+
"id": "b82ed301-bf08-4d21-8d01-f9861de83fca",
1664
+
"metadata": {},
1665
+
"outputs": [
1666
+
{
1667
+
"data": {
1668
+
"text/plain": [
1669
+
"findverts (generic function with 2 methods)"
1670
+
]
1671
+
},
1672
+
"execution_count": 18,
1673
+
"metadata": {},
1674
+
"output_type": "execute_result"
1675
+
}
1676
+
],
1677
+
"source": [
1678
+
"function findverts(vec::Vector)::Vector\n",
1679
+
" out = []\n",
1680
+
" for i in 1:length(vec)\n",
1681
+
" if vec[i] == i\n",
1682
+
" push!(out, i)\n",
1683
+
" end\n",
1684
+
" end\n",
1685
+
" out\n",
1686
+
"end"
1687
+
]
1688
+
},
1689
+
{
1690
+
"cell_type": "code",
1691
+
"execution_count": 12,
1692
+
"id": "b224b927-2c2b-4734-9899-e2ffc5ec868f",
1693
+
"metadata": {},
1694
+
"outputs": [
1695
+
{
1696
+
"data": {
1697
+
"text/plain": [
1698
+
"swapidx (generic function with 1 method)"
1699
+
]
1700
+
},
1701
+
"execution_count": 12,
1702
+
"metadata": {},
1703
+
"output_type": "execute_result"
1704
+
}
1705
+
],
1706
+
"source": [
1707
+
"function swapidx(vec::Vector{T}, i::Integer, j::Integer)::Vector{T} where T\n",
1708
+
" tmp = vec[i]\n",
1709
+
" vec[i] = vec[j]\n",
1710
+
" vec[j] = tmp\n",
1711
+
" vec\n",
1712
+
"end"
1713
+
]
1714
+
},
1715
+
{
1716
+
"cell_type": "code",
1717
+
"execution_count": 32,
1718
+
"id": "f7473e8c-2e80-420f-95f6-8ea32640bb3a",
1719
+
"metadata": {},
1720
+
"outputs": [
1721
+
{
1722
+
"data": {
1723
+
"text/plain": [
1724
+
"3-element Vector{Int64}:\n",
1725
+
" 2\n",
1726
+
" 1\n",
1727
+
" 3"
1728
+
]
1729
+
},
1730
+
"execution_count": 32,
1731
+
"metadata": {},
1732
+
"output_type": "execute_result"
1733
+
}
1734
+
],
1735
+
"source": [
1736
+
"swapidx([1,2,3],1,2)"
1737
+
]
1738
+
},
1739
+
{
1740
+
"cell_type": "code",
1741
+
"execution_count": 33,
1742
+
"id": "6c3f104f-2ff0-489d-84ea-1602e7adf9f2",
1743
+
"metadata": {},
1744
+
"outputs": [
1745
+
{
1746
+
"data": {
1747
+
"text/plain": [
1748
+
"6-element Vector{Int64}:\n",
1749
+
" 1\n",
1750
+
" 2\n",
1751
+
" 3\n",
1752
+
" 4\n",
1753
+
" 5\n",
1754
+
" 6"
1755
+
]
1756
+
},
1757
+
"execution_count": 33,
1758
+
"metadata": {},
1759
+
"output_type": "execute_result"
1760
+
}
1761
+
],
1762
+
"source": [
1763
+
"a = [1,2,3]\n",
1764
+
"b = [4,5,6]\n",
1765
+
"[a;b]"
1766
+
]
1767
+
},
1768
+
{
1769
+
"cell_type": "code",
1770
+
"execution_count": 49,
1771
+
"id": "5067937c-7e15-4991-b1db-47ccab9864ee",
1772
+
"metadata": {},
1773
+
"outputs": [
1774
+
{
1775
+
"data": {
1776
+
"text/plain": [
1777
+
"4-element Vector{Vector{Integer}}:\n",
1778
+
" [2, 4, 8, 5, 10, 9, 7, 3, 6, 1]\n",
1779
+
" [6, 3, 7, 9, 10, 5, 8, 4, 2, 1]\n",
1780
+
" [7, 5, 2, 3, 10, 4, 6, 9, 8, 1]\n",
1781
+
" [8, 9, 6, 4, 10, 3, 2, 5, 7, 1]"
1782
+
]
1783
+
},
1784
+
"execution_count": 49,
1785
+
"metadata": {},
1786
+
"output_type": "execute_result"
1787
+
}
1788
+
],
1789
+
"source": [
1790
+
"welch(11)"
1791
+
]
1792
+
},
1793
+
{
1794
+
"cell_type": "code",
1795
+
"execution_count": 22,
1796
+
"id": "bce5e8c4-a9ae-43ce-8a39-47d8531ff169",
1797
+
"metadata": {},
1798
+
"outputs": [
1799
+
{
1800
+
"data": {
1801
+
"text/plain": [
1802
+
"2-element Vector{Vector{Integer}}:\n",
1803
+
" [3, 2, 6, 4, 5, 1]\n",
1804
+
" [5, 4, 6, 2, 3, 1]"
1805
+
]
1806
+
},
1807
+
"execution_count": 22,
1808
+
"metadata": {},
1809
+
"output_type": "execute_result"
1810
+
}
1811
+
],
1812
+
"source": [
1813
+
"welch(7)"
1814
+
]
1815
+
},
1816
+
{
1817
+
"cell_type": "code",
1818
+
"execution_count": 7,
1819
+
"id": "f95381ee-d182-4ae7-a96c-457502509933",
1820
+
"metadata": {},
1821
+
"outputs": [
1822
+
{
1823
+
"data": {
1824
+
"text/plain": [
1825
+
"true"
1826
+
]
1827
+
},
1828
+
"execution_count": 7,
1829
+
"metadata": {},
1830
+
"output_type": "execute_result"
1831
+
}
1832
+
],
1833
+
"source": [
1834
+
"iscostas([6,2,1,4,5,3])"
1835
+
]
1836
+
},
1837
+
{
1838
+
"cell_type": "code",
1839
+
"execution_count": 8,
1840
+
"id": "9f08cdc1-d944-4037-b13f-0e77893aa9dd",
1841
+
"metadata": {},
1842
+
"outputs": [
1843
+
{
1844
+
"data": {
1845
+
"text/plain": [
1846
+
"4-element Vector{Vector{Integer}}:\n",
1847
+
" [5, 3, 2, 7, 1, 8, 4, 6, 9]\n",
1848
+
" [1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
1849
+
" [2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
1850
+
" [4, 6, 3, 1, 7, 2, 5, 9, 8]"
1851
+
]
1852
+
},
1853
+
"execution_count": 8,
1854
+
"metadata": {},
1855
+
"output_type": "execute_result"
1856
+
}
1857
+
],
1858
+
"source": [
1859
+
"lempel(11)"
1860
+
]
1861
+
},
1862
+
{
1863
+
"cell_type": "code",
1864
+
"execution_count": 15,
1865
+
"id": "3a764240-e578-42f4-bd3f-ffb0d08e6f37",
1866
+
"metadata": {},
1867
+
"outputs": [
1868
+
{
1869
+
"data": {
1870
+
"text/plain": [
1871
+
"false"
1872
+
]
1873
+
},
1874
+
"execution_count": 15,
1875
+
"metadata": {},
1876
+
"output_type": "execute_result"
1877
+
}
1878
+
],
1879
+
"source": [
1880
+
"iscostas([10,3,4,6,2,7,1,9,8,5,10,3,4,6,2,7,1,9,8,5])"
1881
+
]
1882
+
},
1883
+
{
1884
+
"cell_type": "code",
1885
+
"execution_count": 19,
1886
+
"id": "4eef15ae-22e6-4924-8fbb-a519f8a98a22",
1887
+
"metadata": {},
1888
+
"outputs": [
1889
+
{
1890
+
"data": {
1891
+
"text/plain": [
1892
+
"false"
1893
+
]
1894
+
},
1895
+
"execution_count": 19,
1896
+
"metadata": {},
1897
+
"output_type": "execute_result"
1898
+
}
1899
+
],
1900
+
"source": [
1901
+
"iscostas([5, 3, 2, 7, 1, 8, 4, 6, 9, '*', 5, 3, 2, 7, 1, 8, 4, 6, 9], asterisk_predicate)"
1902
+
]
1903
+
},
1904
+
{
1905
+
"cell_type": "code",
1906
+
"execution_count": 21,
1907
+
"id": "c19f8e0d-b80f-4e70-ba6c-6be69f082872",
1908
+
"metadata": {},
1909
+
"outputs": [
1910
+
{
1911
+
"data": {
1912
+
"text/plain": [
1913
+
"false"
1914
+
]
1915
+
},
1916
+
"execution_count": 21,
1917
+
"metadata": {},
1918
+
"output_type": "execute_result"
1919
+
}
1920
+
],
1921
+
"source": [
1922
+
"iscostas([2,4,3,5])"
1923
+
]
1924
+
},
1925
+
{
1926
+
"cell_type": "code",
1927
+
"execution_count": 25,
1928
+
"id": "9dcb0b72-9f2d-4d4a-b9d0-8a25beeb8f9b",
1929
+
"metadata": {},
1930
+
"outputs": [
1931
+
{
1932
+
"name": "stdout",
1933
+
"output_type": "stream",
1934
+
"text": [
1935
+
"1 1 1 1 1 1 1 1 1 1 \n",
1936
+
"2 4 8 5 10 9 7 3 6 1 \n",
1937
+
"3 9 5 4 1 3 9 5 4 1 \n",
1938
+
"4 5 9 3 1 4 5 9 3 1 \n",
1939
+
"5 3 4 9 1 5 3 4 9 1 \n",
1940
+
"6 3 7 9 10 5 8 4 2 1 \n",
1941
+
"7 5 2 3 10 4 6 9 8 1 \n",
1942
+
"8 9 6 4 10 3 2 5 7 1 \n",
1943
+
"9 4 3 5 1 9 4 3 5 1 \n",
1944
+
"10 1 10 1 10 1 10 1 10 1 \n",
1945
+
"0 0 0 0 0 0 0 0 0 0 \n"
1946
+
]
1947
+
}
1948
+
],
1949
+
"source": [
1950
+
"for i in 1:11\n",
1951
+
" pow = i\n",
1952
+
" for _ in 1:10\n",
1953
+
" print(pow % 11, ' ')\n",
1954
+
" pow *= i\n",
1955
+
" end\n",
1956
+
" println()\n",
1957
+
"end"
1958
+
]
1959
+
},
1960
+
{
1961
+
"cell_type": "code",
1962
+
"execution_count": 3,
1963
+
"id": "f8dfb3a2-d636-4ef3-89c9-82c24b18d282",
1964
+
"metadata": {},
1965
+
"outputs": [
1966
+
{
1967
+
"data": {
1968
+
"text/plain": [
1969
+
"4-element Vector{Vector{Integer}}:\n",
1970
+
" [2, 4, 8, 5, 10, 9, 7, 3, 6, 1]\n",
1971
+
" [6, 3, 7, 9, 10, 5, 8, 4, 2, 1]\n",
1972
+
" [7, 5, 2, 3, 10, 4, 6, 9, 8, 1]\n",
1973
+
" [8, 9, 6, 4, 10, 3, 2, 5, 7, 1]"
1974
+
]
1975
+
},
1976
+
"execution_count": 3,
1977
+
"metadata": {},
1978
+
"output_type": "execute_result"
1979
+
}
1980
+
],
1981
+
"source": [
1982
+
"welch(11)"
1983
+
]
1984
+
},
1985
+
{
1986
+
"cell_type": "code",
1987
+
"execution_count": 2,
1988
+
"id": "12fc9576-c665-4db5-8742-613337dd0657",
1989
+
"metadata": {},
1990
+
"outputs": [
1991
+
{
1992
+
"data": {
1993
+
"text/plain": [
1994
+
"2-element Vector{Vector{Integer}}:\n",
1995
+
" [5, 3, 2, 4, 1]\n",
1996
+
" [5, 2, 4, 3, 1]"
1997
+
]
1998
+
},
1999
+
"execution_count": 2,
2000
+
"metadata": {},
2001
+
"output_type": "execute_result"
2002
+
}
2003
+
],
2004
+
"source": [
2005
+
"lempel(7)"
2006
+
]
2007
+
},
2008
+
{
2009
+
"cell_type": "code",
2010
+
"execution_count": 31,
2011
+
"id": "31389c6e-17b6-41a6-ba3e-d7be1891ffe0",
2012
+
"metadata": {},
2013
+
"outputs": [
2014
+
{
2015
+
"data": {
2016
+
"text/plain": [
2017
+
"2-element Vector{Vector{Integer}}:\n",
2018
+
" [5, 3, 2, 4, 1]\n",
2019
+
" [5, 2, 4, 3, 1]"
2020
+
]
2021
+
},
2022
+
"execution_count": 31,
2023
+
"metadata": {},
2024
+
"output_type": "execute_result"
2025
+
}
2026
+
],
2027
+
"source": [
2028
+
"lempel(7)"
2029
+
]
2030
+
},
2031
+
{
2032
+
"cell_type": "code",
2033
+
"execution_count": 30,
2034
+
"id": "c7e406e5-b73a-4152-b435-1a7e847071b7",
2035
+
"metadata": {},
2036
+
"outputs": [
2037
+
{
2038
+
"data": {
2039
+
"text/plain": [
2040
+
"true"
2041
+
]
2042
+
},
2043
+
"execution_count": 30,
2044
+
"metadata": {},
2045
+
"output_type": "execute_result"
2046
+
}
2047
+
],
2048
+
"source": [
2049
+
"iscostas([[6, 10, 5, 7, 3, 1, 4, 9, 8, 2, 11]; '*'], asterisk_predicate)"
2050
+
]
2051
+
},
2052
+
{
2053
+
"cell_type": "code",
2054
+
"execution_count": 22,
2055
+
"id": "64d4f5be-05da-47d5-9bef-ef0408ceb632",
2056
+
"metadata": {},
2057
+
"outputs": [
2058
+
{
2059
+
"data": {
2060
+
"text/plain": [
2061
+
"4-element Vector{Vector{Integer}}:\n",
2062
+
" [5, 3, 2, 7, 1, 8, 4, 6, 9]\n",
2063
+
" [1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
2064
+
" [2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
2065
+
" [4, 6, 3, 1, 7, 2, 5, 9, 8]"
2066
+
]
2067
+
},
2068
+
"execution_count": 22,
2069
+
"metadata": {},
2070
+
"output_type": "execute_result"
2071
+
}
2072
+
],
2073
+
"source": [
2074
+
"lempel(11)"
2075
+
]
2076
+
},
2077
+
{
2078
+
"cell_type": "code",
2079
+
"execution_count": 32,
2080
+
"id": "52989e6a-f04a-421c-8447-f49c652fab37",
2081
+
"metadata": {},
2082
+
"outputs": [
2083
+
{
2084
+
"data": {
2085
+
"text/plain": [
2086
+
"4-element Vector{Vector{Integer}}:\n",
2087
+
" [5, 3, 2, 7, 1, 8, 4, 6, 9]\n",
2088
+
" [1, 4, 6, 2, 9, 3, 8, 7, 5]\n",
2089
+
" [2, 1, 5, 8, 3, 9, 7, 4, 6]\n",
2090
+
" [4, 6, 3, 1, 7, 2, 5, 9, 8]"
2091
+
]
2092
+
},
2093
+
"execution_count": 32,
2094
+
"metadata": {},
2095
+
"output_type": "execute_result"
2096
+
}
2097
+
],
2098
+
"source": [
2099
+
"lempel(11)"
2100
+
]
2101
+
},
2102
+
{
2103
+
"cell_type": "code",
2104
+
"execution_count": 33,
2105
+
"id": "328b4c5b-d862-49cb-9d6b-dfb14aeb2a02",
2106
+
"metadata": {},
2107
+
"outputs": [
2108
+
{
2109
+
"data": {
2110
+
"text/plain": [
2111
+
"4-element Vector{Vector{Integer}}:\n",
2112
+
" [2, 4, 8, 5, 10, 9, 7, 3, 6, 1]\n",
2113
+
" [6, 3, 7, 9, 10, 5, 8, 4, 2, 1]\n",
2114
+
" [7, 5, 2, 3, 10, 4, 6, 9, 8, 1]\n",
2115
+
" [8, 9, 6, 4, 10, 3, 2, 5, 7, 1]"
2116
+
]
2117
+
},
2118
+
"execution_count": 33,
2119
+
"metadata": {},
2120
+
"output_type": "execute_result"
2121
+
}
2122
+
],
2123
+
"source": [
2124
+
"welch(11)"
2125
+
]
2126
+
},
2127
+
{
2128
+
"cell_type": "code",
2129
+
"execution_count": 35,
2130
+
"id": "c4b1a2ad-4968-46d8-a08d-fcbf4abfbd27",
2131
+
"metadata": {},
2132
+
"outputs": [
2133
+
{
2134
+
"data": {
2135
+
"text/plain": [
2136
+
"Vector{Integer}[]"
2137
+
]
2138
+
},
2139
+
"execution_count": 35,
2140
+
"metadata": {},
2141
+
"output_type": "execute_result"
2142
+
}
2143
+
],
2144
+
"source": [
2145
+
"welch(9)"
2146
+
]
2147
+
},
2148
+
{
2149
+
"cell_type": "code",
2150
+
"execution_count": 38,
2151
+
"id": "618899d2-09b8-49dd-8087-dd73b42adf41",
2152
+
"metadata": {},
2153
+
"outputs": [
2154
+
{
2155
+
"name": "stderr",
2156
+
"output_type": "stream",
2157
+
"text": [
2158
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
2159
+
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m CEnum ──────────────── v0.5.0\n",
2160
+
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m libcxxwrap_julia_jll ─ v0.13.2+0\n",
2161
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"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m z3_jll ─────────────── v4.13.3+0\n",
2162
+
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Z3 ─────────────────── v1.0.3\n",
2163
+
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
2164
+
" \u001b[90m[06b161dc] \u001b[39m\u001b[92m+ Z3 v1.0.3\u001b[39m\n",
2165
+
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
2166
+
" \u001b[90m[fa961155] \u001b[39m\u001b[92m+ CEnum v0.5.0\u001b[39m\n",
2167
+
" \u001b[90m[06b161dc] \u001b[39m\u001b[92m+ Z3 v1.0.3\u001b[39m\n",
2168
+
" \u001b[90m[3eaa8342] \u001b[39m\u001b[92m+ libcxxwrap_julia_jll v0.13.2+0\u001b[39m\n",
2169
+
" \u001b[90m[1bc4e1ec] \u001b[39m\u001b[92m+ z3_jll v4.13.3+0\u001b[39m\n",
2170
+
" \u001b[90m[781609d7] \u001b[39m\u001b[92m+ GMP_jll v6.2.1+6\u001b[39m\n",
2171
+
"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
2172
+
"\u001b[32m ✓ \u001b[39m\u001b[90mGMP_jll\u001b[39m\n",
2173
+
"\u001b[32m ✓ \u001b[39m\u001b[90mCEnum\u001b[39m\n",
2174
+
"\u001b[32m ✓ \u001b[39m\u001b[90mlibcxxwrap_julia_jll\u001b[39m\n",
2175
+
"\u001b[32m ✓ \u001b[39m\u001b[90mz3_jll\u001b[39m\n",
2176
+
"\u001b[32m ✓ \u001b[39mZ3\n",
2177
+
" 5 dependencies successfully precompiled in 2 seconds. 54 already precompiled.\n"
2178
+
]
2179
+
}
2180
+
],
2181
+
"source": [
2182
+
"Pkg.add(\"Z3\")"
2183
+
]
2184
+
},
2185
+
{
2186
+
"cell_type": "code",
2187
+
"execution_count": 50,
2188
+
"id": "4c9adcfb-1bfe-4891-923f-3d34130e124f",
2189
+
"metadata": {},
2190
+
"outputs": [
2191
+
{
2192
+
"ename": "LoadError",
2193
+
"evalue": "MethodError: no method matching FuncDecl()\n\n\u001b[0mClosest candidates are:\n\u001b[0m FuncDecl(\u001b[91m::Context\u001b[39m, \u001b[91m::Ptr{Z3.Libz3._Z3_func_decl}\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:150\u001b[24m\u001b[39m\n\u001b[0m FuncDecl(\u001b[91m::String\u001b[39m, \u001b[91m::Vector{Sort}\u001b[39m, \u001b[91m::Sort\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:174\u001b[24m\u001b[39m\n\u001b[0m FuncDecl(\u001b[91m::String\u001b[39m, \u001b[91m::Vector{Sort}\u001b[39m, \u001b[91m::Sort\u001b[39m, \u001b[91m::Any\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:174\u001b[24m\u001b[39m\n",
2194
+
"output_type": "error",
2195
+
"traceback": [
2196
+
"MethodError: no method matching FuncDecl()\n\n\u001b[0mClosest candidates are:\n\u001b[0m FuncDecl(\u001b[91m::Context\u001b[39m, \u001b[91m::Ptr{Z3.Libz3._Z3_func_decl}\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:150\u001b[24m\u001b[39m\n\u001b[0m FuncDecl(\u001b[91m::String\u001b[39m, \u001b[91m::Vector{Sort}\u001b[39m, \u001b[91m::Sort\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:174\u001b[24m\u001b[39m\n\u001b[0m FuncDecl(\u001b[91m::String\u001b[39m, \u001b[91m::Vector{Sort}\u001b[39m, \u001b[91m::Sort\u001b[39m, \u001b[91m::Any\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[33mZ3\u001b[39m \u001b[90m~/.julia/packages/Z3/L6TVj/src/\u001b[39m\u001b[90m\u001b[4mZ3.jl:174\u001b[24m\u001b[39m\n",
2197
+
"",
2198
+
"Stacktrace:",
2199
+
" [1] top-level scope",
2200
+
" @ In[50]:1"
2201
+
]
2202
+
}
2203
+
],
2204
+
"source": [
2205
+
"Z3.FuncDecl()"
2206
+
]
2207
+
},
2208
+
{
2209
+
"cell_type": "code",
2210
+
"execution_count": 12,
2211
+
"id": "49d55ff1-4346-4682-b41b-8fd6fde14ee0",
2212
+
"metadata": {},
2213
+
"outputs": [
2214
+
{
2215
+
"data": {
2216
+
"text/plain": [
2217
+
"#9 (generic function with 1 method)"
2218
+
]
2219
+
},
2220
+
"execution_count": 12,
2221
+
"metadata": {},
2222
+
"output_type": "execute_result"
2223
+
}
2224
+
],
2225
+
"source": [
2226
+
"f1 = Base.Fix1\n",
2227
+
"f2 = Base.Fix2\n",
2228
+
"p2 = x -> y -> (x, y)"
2229
+
]
2230
+
},
2231
+
{
2232
+
"cell_type": "code",
2233
+
"execution_count": 13,
2234
+
"id": "06a91f55-853e-45e6-8492-1856d37f48e1",
2235
+
"metadata": {},
2236
+
"outputs": [
2237
+
{
2238
+
"data": {
2239
+
"text/plain": [
2240
+
"isprimitiveroot (generic function with 1 method)"
2241
+
]
2242
+
},
2243
+
"execution_count": 13,
2244
+
"metadata": {},
2245
+
"output_type": "execute_result"
2246
+
}
2247
+
],
2248
+
"source": [
2249
+
"function isprimitiveroot(prime::Integer, alpha::Integer)::Bool \n",
2250
+
" not_one::Bool = all(powermod(alpha, i, prime) != prime - 1 for i in 1:((prime - 1) ÷ 2 - 1))\n",
2251
+
" last_one::Bool = powermod(alpha, (prime - 1) ÷ 2, prime) == prime - 1\n",
2252
+
" not_one && last_one\n",
2253
+
"end"
2254
+
]
2255
+
},
2256
+
{
2257
+
"cell_type": "code",
2258
+
"execution_count": 6,
2259
+
"id": "5fd3614c-db37-44e2-8dbb-aa0393113100",
2260
+
"metadata": {},
2261
+
"outputs": [
2262
+
{
2263
+
"data": {
2264
+
"text/plain": [
2265
+
"4-element Vector{Int64}:\n",
2266
+
" 2\n",
2267
+
" 6\n",
2268
+
" 7\n",
2269
+
" 11"
2270
+
]
2271
+
},
2272
+
"execution_count": 6,
2273
+
"metadata": {},
2274
+
"output_type": "execute_result"
2275
+
}
2276
+
],
2277
+
"source": [
2278
+
"filter(alpha -> isprimitiveroot(13, alpha), 2:13)"
2279
+
]
2280
+
},
2281
+
{
2282
+
"cell_type": "code",
2283
+
"execution_count": 2,
2284
+
"id": "95e22df0-0d20-4dac-aca3-cc8305702a58",
2285
+
"metadata": {},
2286
+
"outputs": [
2287
+
{
2288
+
"data": {
2289
+
"text/plain": [
2290
+
"iscostasdbg (generic function with 2 methods)"
2291
+
]
2292
+
},
2293
+
"execution_count": 2,
2294
+
"metadata": {},
2295
+
"output_type": "execute_result"
2296
+
}
2297
+
],
2298
+
"source": [
2299
+
"struct Unit\n",
2300
+
"end\n",
2301
+
"\n",
2302
+
"struct Pair{T, S}\n",
2303
+
" l::T\n",
2304
+
" r::S\n",
2305
+
" function fst()::T\n",
2306
+
" l\n",
2307
+
" end\n",
2308
+
" function snd()::S\n",
2309
+
" r\n",
2310
+
" end\n",
2311
+
"end\n",
2312
+
"\n",
2313
+
"# Check if a sequence is a Costas sequence with debug information\n",
2314
+
"function iscostasdbg(lst::Vector, f::Function = normal_predicate) #::Union{Unit, Tuple{Int64, Int64}}\n",
2315
+
" n::Integer = length(lst)\n",
2316
+
" for k in 1:n\n",
2317
+
" diffs = [(false, (-1,-1)) for _ in 1:2 * n]\n",
2318
+
" for i in 1:(n - k)\n",
2319
+
" a = lst[i + k]\n",
2320
+
" b = lst[i]\n",
2321
+
" result = f(a, b, n)\n",
2322
+
" if diffs[result][1]\n",
2323
+
" return ((i, i + k), diffs[result][2])\n",
2324
+
" elseif result != n\n",
2325
+
" diffs[result] = (true, (i, i + k))\n",
2326
+
" end\n",
2327
+
" end\n",
2328
+
" end\n",
2329
+
" return Unit()\n",
2330
+
"end"
2331
+
]
2332
+
},
2333
+
{
2334
+
"cell_type": "code",
2335
+
"execution_count": 5,
2336
+
"id": "365866e4-e7bf-4d63-8005-f9d2b7044434",
2337
+
"metadata": {},
2338
+
"outputs": [
2339
+
{
2340
+
"data": {
2341
+
"text/plain": [
2342
+
"searchdbg (generic function with 1 method)"
2343
+
]
2344
+
},
2345
+
"execution_count": 5,
2346
+
"metadata": {},
2347
+
"output_type": "execute_result"
2348
+
}
2349
+
],
2350
+
"source": [
2351
+
"using Base.Threads\n",
2352
+
"function searchdbg(n::Integer)::Vector{Vector{Integer}}\n",
2353
+
" p1 = 0\n",
2354
+
" p2 = 0\n",
2355
+
" p3 = 0\n",
2356
+
" p4 = 0\n",
2357
+
" i1 = 0\n",
2358
+
" i2 = 0\n",
2359
+
" i3 = 0\n",
2360
+
" i4 = 0\n",
2361
+
" acc::Vector{Vector{Vector{Integer}}} = [[] for _ in 1:nthreads()]\n",
2362
+
" \n",
2363
+
" @threads :static for i in 1:factorial(n)\n",
2364
+
" tid = threadid()\n",
2365
+
" lst = nthperm(1:n, i)\n",
2366
+
" if (i1 != 0 && p1 == lst[i1]) && (i2 != 0 && p2 == lst[i2]) && (i3 != 0 && p3 == lst[i3]) && (i4 != 0 && p4 == lst[i4])\n",
2367
+
" #println(\"miss: \", lst)\n",
2368
+
" continue\n",
2369
+
" end\n",
2370
+
" result = iscostasdbg(lst)\n",
2371
+
" if result isa Unit\n",
2372
+
" push!(acc[tid], lst)\n",
2373
+
" else\n",
2374
+
" #println(\"fail: \", lst, \"; \", result)\n",
2375
+
" (i1, i2), (i3, i4) = result\n",
2376
+
" p1, p2, p3, p4 = lst[i1], lst[i2], lst[i3], lst[i4]\n",
2377
+
" end\n",
2378
+
" end\n",
2379
+
" reduce(vcat, acc)\n",
2380
+
"end"
2381
+
]
2382
+
},
2383
+
{
2384
+
"cell_type": "code",
2385
+
"execution_count": 13,
2386
+
"id": "417662cf-6ccc-488b-95f3-bc42fd988f64",
2387
+
"metadata": {},
2388
+
"outputs": [
2389
+
{
2390
+
"name": "stderr",
2391
+
"output_type": "stream",
2392
+
"text": [
2393
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
2394
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
2395
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n"
2396
+
]
2397
+
}
2398
+
],
2399
+
"source": [
2400
+
"import Pkg; Pkg.add(\"StaticArrays\")\n",
2401
+
"using StaticArrays"
2402
+
]
2403
+
},
2404
+
{
2405
+
"cell_type": "code",
2406
+
"execution_count": 74,
2407
+
"id": "54cc4c58-ba59-47cc-865f-49c20cd27bfa",
2408
+
"metadata": {},
2409
+
"outputs": [
2410
+
{
2411
+
"data": {
2412
+
"text/plain": [
2413
+
"iscostas (generic function with 6 methods)"
2414
+
]
2415
+
},
2416
+
"execution_count": 74,
2417
+
"metadata": {},
2418
+
"output_type": "execute_result"
2419
+
}
2420
+
],
2421
+
"source": [
2422
+
"# Check if a sequence is a Costas sequence with debug information\n",
2423
+
"function iscostas(lst::SVector, f::Function = normal_predicate)::Union{Unit, Tuple{Tuple{Int64, Int64}, Tuple{Int64, Int64}}}\n",
2424
+
" n::Int64 = length(lst)\n",
2425
+
" for k in 1:n\n",
2426
+
" diffs::Vector{Tuple{Bool, Tuple{Int64, Int64}}} = [(false, (-1,-1)) for _ in 1:2 * n]\n",
2427
+
" for i in 1:(n - k)\n",
2428
+
" a = lst[i + k]\n",
2429
+
" b = lst[i]\n",
2430
+
" result = f(a, b, n)\n",
2431
+
" if diffs[result][1]\n",
2432
+
" return ((i, i + k), diffs[result][2])\n",
2433
+
" elseif result != n\n",
2434
+
" diffs[result] = (true, (i, i + k))\n",
2435
+
" end\n",
2436
+
" end\n",
2437
+
" end\n",
2438
+
" return Unit()\n",
2439
+
"end"
2440
+
]
2441
+
},
2442
+
{
2443
+
"cell_type": "code",
2444
+
"execution_count": 75,
2445
+
"id": "da9e3d3d-7bf7-48b3-9d3d-370590f06355",
2446
+
"metadata": {},
2447
+
"outputs": [
2448
+
{
2449
+
"data": {
2450
+
"text/plain": [
2451
+
"((2, 3), (1, 2))"
2452
+
]
2453
+
},
2454
+
"execution_count": 75,
2455
+
"metadata": {},
2456
+
"output_type": "execute_result"
2457
+
}
2458
+
],
2459
+
"source": [
2460
+
"iscostas(SA[1,2,3])"
2461
+
]
2462
+
},
2463
+
{
2464
+
"cell_type": "code",
2465
+
"execution_count": 78,
2466
+
"id": "db5561bb-56ee-4806-897d-b58d1ed37323",
2467
+
"metadata": {},
2468
+
"outputs": [
2469
+
{
2470
+
"data": {
2471
+
"text/plain": [
2472
+
"searchallt (generic function with 2 methods)"
2473
+
]
2474
+
},
2475
+
"execution_count": 78,
2476
+
"metadata": {},
2477
+
"output_type": "execute_result"
2478
+
}
2479
+
],
2480
+
"source": [
2481
+
"using Base.Threads\n",
2482
+
"function searchallt(n::Int64)::Vector{SVector{n, Int64}}\n",
2483
+
" p1::Int64 = 0\n",
2484
+
" p2::Int64 = 0\n",
2485
+
" p3::Int64 = 0\n",
2486
+
" p4::Int64 = 0\n",
2487
+
" i1::Int64 = 0\n",
2488
+
" i2::Int64 = 0\n",
2489
+
" i3::Int64 = 0\n",
2490
+
" i4::Int64 = 0\n",
2491
+
" acc::Vector{Vector{SVector{n, Integer}}} = [[] for _ in 1:nthreads()]\n",
2492
+
"\n",
2493
+
" @threads :static for i in 1:factorial(n)\n",
2494
+
" tid::Int64 = threadid()\n",
2495
+
" lst::SVector{n, Int64} = nthperm(1:n, i)\n",
2496
+
" if (i1 != 0 && p1 == lst[i1]) && (i2 != 0 && p2 == lst[i2]) && (i3 != 0 && p3 == lst[i3]) && (i4 != 0 && p4 == lst[i4])\n",
2497
+
" continue\n",
2498
+
" end\n",
2499
+
" result = iscostas(lst)\n",
2500
+
" if result isa Unit\n",
2501
+
" push!(acc[tid], lst)\n",
2502
+
" else\n",
2503
+
" (i1, i2), (i3, i4) = result\n",
2504
+
" p1, p2, p3, p4 = lst[i1], lst[i2], lst[i3], lst[i4]\n",
2505
+
" end\n",
2506
+
" end\n",
2507
+
" reduce(vcat, acc)\n",
2508
+
"end"
2509
+
]
2510
+
},
2511
+
{
2512
+
"cell_type": "code",
2513
+
"execution_count": 101,
2514
+
"id": "0cc33333-0bfe-49ef-af4b-15419d43a290",
2515
+
"metadata": {},
2516
+
"outputs": [
2517
+
{
2518
+
"name": "stdout",
2519
+
"output_type": "stream",
2520
+
"text": [
2521
+
"[1, 2, 3]\n",
2522
+
"[1, 3, 2]\n",
2523
+
"[2, 1, 3]\n",
2524
+
"[2, 3, 1]\n",
2525
+
"[3, 1, 2]\n",
2526
+
"[3, 2, 1]\n"
2527
+
]
2528
+
}
2529
+
],
2530
+
"source": [
2531
+
"for i in 1:6\n",
2532
+
" println(nthperm(1:3, i))\n",
2533
+
"end"
2534
+
]
2535
+
},
2536
+
{
2537
+
"cell_type": "code",
2538
+
"execution_count": 99,
2539
+
"id": "b9d236a0-28d7-4ad5-9385-a3fb2dbe13c6",
2540
+
"metadata": {},
2541
+
"outputs": [
2542
+
{
2543
+
"data": {
2544
+
"text/plain": [
2545
+
"searchall (generic function with 2 methods)"
2546
+
]
2547
+
},
2548
+
"execution_count": 99,
2549
+
"metadata": {},
2550
+
"output_type": "execute_result"
2551
+
}
2552
+
],
2553
+
"source": [
2554
+
"function searchall(n::Int64)::Set{Vector{Int64}}\n",
2555
+
" p1::Int64 = 0\n",
2556
+
" p2::Int64 = 0\n",
2557
+
" p3::Int64 = 0\n",
2558
+
" p4::Int64 = 0\n",
2559
+
" i1::Int64 = 0\n",
2560
+
" i2::Int64 = 0\n",
2561
+
" i3::Int64 = 0\n",
2562
+
" i4::Int64 = 0\n",
2563
+
" acc::Set{Vector{Int64}} = Set()\n",
2564
+
"\n",
2565
+
" for i in 1:(factorial(n) ÷ 2)\n",
2566
+
" lst::Vector{Int64} = nthperm(1:n, i)\n",
2567
+
" if (i1 != 0 && p1 == lst[i1]) && (i2 != 0 && p2 == lst[i2]) && (i3 != 0 && p3 == lst[i3]) && (i4 != 0 && p4 == lst[i4])\n",
2568
+
" continue\n",
2569
+
" end\n",
2570
+
" result = iscostas(lst)\n",
2571
+
" if result isa Unit\n",
2572
+
" push!(acc, lst)\n",
2573
+
" push!(acc, lst |> reverse)\n",
2574
+
" lst2 = lst .|> x -> (-x % n) + n\n",
2575
+
" #push!(acc, lst2)\n",
2576
+
" #push!(acc, lst2 |> reverse)\n",
2577
+
" else\n",
2578
+
" (i1, i2), (i3, i4) = result\n",
2579
+
" p1, p2, p3, p4 = lst[i1], lst[i2], lst[i3], lst[i4]\n",
2580
+
" end\n",
2581
+
" end\n",
2582
+
" acc\n",
2583
+
"end\n",
2584
+
"\n"
2585
+
]
2586
+
},
2587
+
{
2588
+
"cell_type": "code",
2589
+
"execution_count": 100,
2590
+
"id": "2552643c-d049-4cfe-b6f0-e57508f9fc46",
2591
+
"metadata": {},
2592
+
"outputs": [
2593
+
{
2594
+
"data": {
2595
+
"text/plain": [
2596
+
"Set{Vector{Int64}} with 32 elements:\n",
2597
+
" [1, 4, 5, 3, 2]\n",
2598
+
" [2, 3, 5, 4, 1]\n",
2599
+
" [2, 5, 4, 1, 3]\n",
2600
+
" [3, 1, 4, 5, 2]\n",
2601
+
" [4, 1, 5, 3, 2]\n",
2602
+
" [2, 4, 1, 5, 3]\n",
2603
+
" [2, 4, 3, 1, 5]\n",
2604
+
" [4, 3, 1, 5, 2]\n",
2605
+
" [1, 5, 4, 2, 3]\n",
2606
+
" [2, 3, 5, 1, 4]\n",
2607
+
" [5, 1, 3, 4, 2]\n",
2608
+
" [3, 5, 4, 1, 2]\n",
2609
+
" [5, 2, 4, 3, 1]\n",
2610
+
" [2, 5, 3, 4, 1]\n",
2611
+
" [3, 2, 4, 5, 1]\n",
2612
+
" [3, 1, 2, 5, 4]\n",
2613
+
" [4, 2, 5, 1, 3]\n",
2614
+
" [1, 3, 4, 2, 5]\n",
2615
+
" [1, 4, 3, 5, 2]\n",
2616
+
" [4, 3, 5, 1, 2]\n",
2617
+
" [1, 4, 2, 3, 5]\n",
2618
+
" [5, 3, 2, 4, 1]\n",
2619
+
" [1, 5, 3, 2, 4]\n",
2620
+
" [4, 5, 2, 1, 3]\n",
2621
+
" [3, 1, 5, 2, 4]\n",
2622
+
" ⋮ "
2623
+
]
2624
+
},
2625
+
"execution_count": 100,
2626
+
"metadata": {},
2627
+
"output_type": "execute_result"
2628
+
}
2629
+
],
2630
+
"source": [
2631
+
"Set(searchall(5))"
2632
+
]
2633
+
},
2634
+
{
2635
+
"cell_type": "code",
2636
+
"execution_count": 77,
2637
+
"id": "9d36bd50-373d-47fd-ad75-c9107f146128",
2638
+
"metadata": {},
2639
+
"outputs": [
2640
+
{
2641
+
"name": "stdout",
2642
+
"output_type": "stream",
2643
+
"text": [
2644
+
" 4.517 s (57459141 allocations: 4.25 GiB)\n"
2645
+
]
2646
+
},
2647
+
{
2648
+
"data": {
2649
+
"text/plain": [
2650
+
"2160-element Vector{SVector{10, Int64}}:\n",
2651
+
" [1, 2, 4, 8, 5, 10, 9, 7, 3, 6]\n",
2652
+
" [1, 2, 5, 7, 3, 10, 9, 6, 4, 8]\n",
2653
+
" [1, 2, 5, 9, 3, 8, 4, 10, 7, 6]\n",
2654
+
" [1, 2, 5, 9, 3, 10, 8, 7, 4, 6]\n",
2655
+
" [1, 2, 6, 9, 8, 5, 7, 3, 10, 4]\n",
2656
+
" [1, 2, 8, 5, 10, 4, 6, 9, 7, 3]\n",
2657
+
" [1, 2, 8, 10, 6, 3, 7, 5, 4, 9]\n",
2658
+
" [1, 2, 9, 3, 5, 10, 8, 4, 7, 6]\n",
2659
+
" [1, 2, 9, 6, 5, 7, 10, 4, 8, 3]\n",
2660
+
" [1, 2, 10, 6, 4, 7, 9, 3, 8, 5]\n",
2661
+
" [1, 2, 10, 8, 5, 4, 6, 9, 3, 7]\n",
2662
+
" [1, 3, 4, 9, 8, 6, 10, 7, 2, 5]\n",
2663
+
" [1, 3, 7, 10, 9, 4, 2, 8, 5, 6]\n",
2664
+
" ⋮\n",
2665
+
" [10, 8, 7, 2, 3, 5, 1, 4, 9, 6]\n",
2666
+
" [10, 9, 1, 3, 6, 7, 5, 2, 8, 4]\n",
2667
+
" [10, 9, 1, 5, 7, 4, 2, 8, 3, 6]\n",
2668
+
" [10, 9, 2, 5, 6, 4, 1, 7, 3, 8]\n",
2669
+
" [10, 9, 2, 8, 6, 1, 3, 7, 4, 5]\n",
2670
+
" [10, 9, 3, 1, 5, 8, 4, 6, 7, 2]\n",
2671
+
" [10, 9, 3, 6, 1, 7, 5, 2, 4, 8]\n",
2672
+
" [10, 9, 5, 2, 3, 6, 4, 8, 1, 7]\n",
2673
+
" [10, 9, 6, 2, 8, 1, 3, 4, 7, 5]\n",
2674
+
" [10, 9, 6, 2, 8, 3, 7, 1, 4, 5]\n",
2675
+
" [10, 9, 6, 4, 8, 1, 2, 5, 7, 3]\n",
2676
+
" [10, 9, 7, 3, 6, 1, 2, 4, 8, 5]"
2677
+
]
2678
+
},
2679
+
"execution_count": 77,
2680
+
"metadata": {},
2681
+
"output_type": "execute_result"
2682
+
}
2683
+
],
2684
+
"source": [
2685
+
"@btime searchall(10)"
2686
+
]
2687
+
},
2688
+
{
2689
+
"cell_type": "code",
2690
+
"execution_count": 126,
2691
+
"id": "27f43b7a-7998-4447-84b2-c2a5477721c7",
2692
+
"metadata": {},
2693
+
"outputs": [
2694
+
{
2695
+
"name": "stdout",
2696
+
"output_type": "stream",
2697
+
"text": [
2698
+
"[1, 2, 3]\n",
2699
+
"[1, 3, 2]\n",
2700
+
"[2, 1, 3]\n",
2701
+
"[2, 3, 1]\n",
2702
+
"[3, 1, 2]\n",
2703
+
"[3, 2, 1]\n"
2704
+
]
2705
+
}
2706
+
],
2707
+
"source": [
2708
+
"for i in 1:6\n",
2709
+
" println(nthperm([1,2,3], i))\n",
2710
+
"end"
2711
+
]
2712
+
},
2713
+
{
2714
+
"cell_type": "code",
2715
+
"execution_count": 139,
2716
+
"id": "5434992c-6060-4557-b806-8227c0aeaf35",
2717
+
"metadata": {},
2718
+
"outputs": [
2719
+
{
2720
+
"name": "stdout",
2721
+
"output_type": "stream",
2722
+
"text": [
2723
+
"[1, 2, 3]\n",
2724
+
"[1, 3, 2]\n",
2725
+
"[3, 1, 2]\n",
2726
+
"[1, 2, 3]\n",
2727
+
"[3, 1, 2]\n",
2728
+
"[2, 1, 3]\n"
2729
+
]
2730
+
}
2731
+
],
2732
+
"source": [
2733
+
"lst = [1,2,3]\n",
2734
+
"for i in 1:6\n",
2735
+
" nthperm!(lst, i)\n",
2736
+
" println(lst)\n",
2737
+
"end"
2738
+
]
2739
+
},
2740
+
{
2741
+
"cell_type": "code",
2742
+
"execution_count": 114,
2743
+
"id": "0785a658-ab45-48f1-b1f1-3f99375f3b1a",
2744
+
"metadata": {},
2745
+
"outputs": [
2746
+
{
2747
+
"data": {
2748
+
"text/plain": [
2749
+
"false"
2750
+
]
2751
+
},
2752
+
"execution_count": 114,
2753
+
"metadata": {},
2754
+
"output_type": "execute_result"
2755
+
}
2756
+
],
2757
+
"source": [
2758
+
"[3,2,4,1,5] in costas_5x5"
2759
+
]
2760
+
},
2761
+
{
2762
+
"cell_type": "code",
2763
+
"execution_count": 125,
2764
+
"id": "ed4c511e-77d3-463f-bfeb-fb3f1f1e89bc",
2765
+
"metadata": {},
2766
+
"outputs": [
2767
+
{
2768
+
"name": "stdout",
2769
+
"output_type": "stream",
2770
+
"text": [
2771
+
"(Integer[0, 0, 0, 1, 4], [3, 4, 2, 1, 5])\n",
2772
+
"(Integer[0, 0, 0, 2, 0], [5, 3, 2, 4, 1])\n",
2773
+
"(Integer[0, 0, 0, 2, 3], [3, 2, 4, 5, 1])\n",
2774
+
"(Integer[0, 0, 0, 3, 1], [3, 5, 2, 1, 4])\n",
2775
+
"(Integer[0, 0, 1, 0, 3], [4, 2, 3, 5, 1])\n",
2776
+
"(Integer[0, 0, 1, 1, 0], [5, 2, 4, 3, 1])\n",
2777
+
"(Integer[0, 0, 1, 1, 4], [2, 4, 3, 1, 5])\n",
2778
+
"(Integer[0, 0, 1, 2, 1], [2, 5, 3, 4, 1])\n",
2779
+
"(Integer[0, 0, 1, 2, 2], [2, 3, 5, 4, 1])\n",
2780
+
"(Integer[0, 0, 1, 3, 0], [5, 2, 3, 1, 4])\n",
2781
+
"(Integer[0, 0, 1, 3, 2], [2, 3, 5, 1, 4])\n",
2782
+
"(Integer[0, 0, 1, 3, 3], [2, 3, 1, 5, 4])\n",
2783
+
"(Integer[0, 0, 2, 0, 1], [4, 5, 2, 1, 3])\n",
2784
+
"(Integer[0, 0, 2, 0, 2], [4, 2, 5, 1, 3])\n",
2785
+
"(Integer[0, 0, 2, 1, 1], [2, 5, 4, 1, 3])\n",
2786
+
"(Integer[0, 0, 2, 1, 3], [2, 4, 1, 5, 3])\n",
2787
+
"(Integer[0, 0, 2, 2, 3], [2, 1, 4, 5, 3])\n",
2788
+
"(Integer[0, 0, 2, 3, 0], [5, 2, 1, 3, 4])\n",
2789
+
"(Integer[0, 0, 2, 3, 1], [2, 5, 1, 3, 4])\n",
2790
+
"(Integer[0, 0, 2, 3, 2], [2, 1, 5, 3, 4])\n",
2791
+
"(Integer[0, 1, 0, 0, 2], [4, 3, 5, 1, 2])\n",
2792
+
"(Integer[0, 1, 0, 0, 3], [4, 3, 1, 5, 2])\n",
2793
+
"(Integer[0, 1, 0, 0, 4], [4, 3, 1, 2, 5])\n",
2794
+
"(Integer[0, 1, 0, 1, 1], [3, 5, 4, 1, 2])\n",
2795
+
"(Integer[0, 1, 0, 2, 1], [3, 5, 1, 4, 2])\n",
2796
+
"(Integer[0, 1, 0, 2, 3], [3, 1, 4, 5, 2])\n",
2797
+
"(Integer[0, 1, 0, 3, 2], [3, 1, 5, 2, 4])\n",
2798
+
"(Integer[0, 1, 0, 3, 3], [3, 1, 2, 5, 4])\n",
2799
+
"(Integer[0, 1, 1, 0, 1], [4, 5, 1, 3, 2])\n",
2800
+
"(Integer[0, 1, 1, 0, 2], [4, 1, 5, 3, 2])\n",
2801
+
"(Integer[0, 1, 1, 0, 4], [4, 1, 3, 2, 5])\n",
2802
+
"(Integer[0, 1, 1, 1, 2], [1, 4, 5, 3, 2])\n",
2803
+
"(Integer[0, 1, 1, 1, 3], [1, 4, 3, 5, 2])\n",
2804
+
"(Integer[0, 1, 1, 2, 0], [5, 1, 3, 4, 2])\n",
2805
+
"(Integer[0, 1, 1, 2, 4], [1, 3, 4, 2, 5])\n",
2806
+
"(Integer[0, 1, 1, 3, 1], [1, 5, 3, 2, 4])\n",
2807
+
"(Integer[0, 1, 2, 0, 3], [4, 1, 2, 5, 3])\n",
2808
+
"(Integer[0, 1, 2, 1, 1], [1, 5, 4, 2, 3])\n",
2809
+
"(Integer[0, 1, 2, 1, 4], [1, 4, 2, 3, 5])\n",
2810
+
"(Integer[0, 1, 2, 2, 0], [5, 1, 2, 4, 3])\n"
2811
+
]
2812
+
}
2813
+
],
2814
+
"source": [
2815
+
"for lst ∈ costas_5x5 .|> (lst -> (seq(lst), lst)) |> sort\n",
2816
+
" println(lst)\n",
2817
+
"end"
2818
+
]
2819
+
},
2820
+
{
2821
+
"cell_type": "code",
2822
+
"execution_count": 216,
2823
+
"id": "4f0108c1-c4b3-401c-be08-6b6fd23138df",
2824
+
"metadata": {},
2825
+
"outputs": [
2826
+
{
2827
+
"ename": "LoadError",
2828
+
"evalue": "MethodError: no method matching zeros(::Vector{Any}, ::Int64)\n\n\u001b[0mClosest candidates are:\n\u001b[0m zeros(\u001b[91m::Union{Integer, AbstractUnitRange}...\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4marray.jl:631\u001b[24m\u001b[39m\n\u001b[0m zeros(\u001b[91m::Type{T}\u001b[39m, ::Union{Integer, AbstractUnitRange}...) where T\n\u001b[0m\u001b[90m @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4marray.jl:632\u001b[24m\u001b[39m\n",
2829
+
"output_type": "error",
2830
+
"traceback": [
2831
+
"MethodError: no method matching zeros(::Vector{Any}, ::Int64)\n\n\u001b[0mClosest candidates are:\n\u001b[0m zeros(\u001b[91m::Union{Integer, AbstractUnitRange}...\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4marray.jl:631\u001b[24m\u001b[39m\n\u001b[0m zeros(\u001b[91m::Type{T}\u001b[39m, ::Union{Integer, AbstractUnitRange}...) where T\n\u001b[0m\u001b[90m @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4marray.jl:632\u001b[24m\u001b[39m\n",
2832
+
"",
2833
+
"Stacktrace:",
2834
+
" [1] top-level scope",
2835
+
" @ In[216]:1"
2836
+
]
2837
+
}
2838
+
],
2839
+
"source": [
2840
+
"zeros([], factorial(4))"
2841
+
]
2842
+
},
2843
+
{
2844
+
"cell_type": "code",
2845
+
"execution_count": 15,
2846
+
"id": "ba7df634-88e6-46a2-9167-e0d197c7203e",
2847
+
"metadata": {},
2848
+
"outputs": [
2849
+
{
2850
+
"data": {
2851
+
"text/plain": [
2852
+
"searchone (generic function with 1 method)"
2853
+
]
2854
+
},
2855
+
"execution_count": 15,
2856
+
"metadata": {},
2857
+
"output_type": "execute_result"
2858
+
}
2859
+
],
2860
+
"source": [
2861
+
"using Base.Threads\n",
2862
+
"function searchone(n::Integer)::Union{Nothing, Vector{Integer}}\n",
2863
+
" p1 = 0\n",
2864
+
" p2 = 0\n",
2865
+
" p3 = 0\n",
2866
+
" p4 = 0\n",
2867
+
" i1 = 0\n",
2868
+
" i2 = 0\n",
2869
+
" i3 = 0\n",
2870
+
" i4 = 0\n",
2871
+
" \n",
2872
+
" for i in 1:factorial(n)\n",
2873
+
" lst = nthperm(1:n, i)\n",
2874
+
" if (i1 != 0 && p1 == lst[i1]) && (i2 != 0 && p2 == lst[i2]) && (i3 != 0 && p3 == lst[i3]) && (i4 != 0 && p4 == lst[i4])\n",
2875
+
" continue\n",
2876
+
" end\n",
2877
+
" result = iscostasdbg(lst)\n",
2878
+
" if result isa Unit\n",
2879
+
" return lst\n",
2880
+
" else\n",
2881
+
" (i1, i2), (i3, i4) = result\n",
2882
+
" p1, p2, p3, p4 = lst[i1], lst[i2], lst[i3], lst[i4]\n",
2883
+
" end\n",
2884
+
" end\n",
2885
+
" return nothing\n",
2886
+
"end"
2887
+
]
2888
+
},
2889
+
{
2890
+
"cell_type": "code",
2891
+
"execution_count": 13,
2892
+
"id": "f663071d-bc6d-43d7-a5d4-935c18bd4160",
2893
+
"metadata": {},
2894
+
"outputs": [
2895
+
{
2896
+
"name": "stdout",
2897
+
"output_type": "stream",
2898
+
"text": [
2899
+
" 1.959 ms (8464 allocations: 1.27 MiB)\n"
2900
+
]
2901
+
}
2902
+
],
2903
+
"source": [
2904
+
"@btime searchone(10)"
2905
+
]
2906
+
},
2907
+
{
2908
+
"cell_type": "code",
2909
+
"execution_count": 26,
2910
+
"id": "fb4205aa-f425-4e16-a885-07eb10c0d984",
2911
+
"metadata": {},
2912
+
"outputs": [
2913
+
{
2914
+
"data": {
2915
+
"text/plain": [
2916
+
"14-element Vector{Integer}:\n",
2917
+
" 1\n",
2918
+
" 2\n",
2919
+
" 5\n",
2920
+
" 7\n",
2921
+
" 14\n",
2922
+
" 8\n",
2923
+
" 12\n",
2924
+
" 11\n",
2925
+
" 6\n",
2926
+
" 4\n",
2927
+
" 13\n",
2928
+
" 10\n",
2929
+
" 3\n",
2930
+
" 9"
2931
+
]
2932
+
},
2933
+
"execution_count": 26,
2934
+
"metadata": {},
2935
+
"output_type": "execute_result"
2936
+
}
2937
+
],
2938
+
"source": [
2939
+
"v14 = searchone(14)"
2940
+
]
2941
+
},
2942
+
{
2943
+
"cell_type": "code",
2944
+
"execution_count": 27,
2945
+
"id": "c3c135d2-9507-42cf-86e0-c273d2655a60",
2946
+
"metadata": {},
2947
+
"outputs": [
2948
+
{
2949
+
"data": {
2950
+
"text/plain": [
2951
+
"Vector{Integer}[]"
2952
+
]
2953
+
},
2954
+
"execution_count": 27,
2955
+
"metadata": {},
2956
+
"output_type": "execute_result"
2957
+
}
2958
+
],
2959
+
"source": [
2960
+
"buildallnaive(v14, 15)"
2961
+
]
2962
+
},
2963
+
{
2964
+
"cell_type": "code",
2965
+
"execution_count": 32,
2966
+
"id": "7dc7f53a-e84b-433a-9ef8-0c984429e2da",
2967
+
"metadata": {},
2968
+
"outputs": [
2969
+
{
2970
+
"data": {
2971
+
"text/plain": [
2972
+
"true"
2973
+
]
2974
+
},
2975
+
"execution_count": 32,
2976
+
"metadata": {},
2977
+
"output_type": "execute_result"
2978
+
}
2979
+
],
2980
+
"source": [
2981
+
"iscostas([5,3,2,4,1,6])"
2982
+
]
2983
+
},
2984
+
{
2985
+
"cell_type": "code",
2986
+
"execution_count": 33,
2987
+
"id": "fa3a6a7d-9043-46aa-adfd-fe36e27045b6",
2988
+
"metadata": {},
2989
+
"outputs": [
2990
+
{
2991
+
"data": {
2992
+
"text/plain": [
2993
+
"12-element Vector{Int64}:\n",
2994
+
" 2\n",
2995
+
" 3\n",
2996
+
" 5\n",
2997
+
" 7\n",
2998
+
" 11\n",
2999
+
" 13\n",
3000
+
" 17\n",
3001
+
" 19\n",
3002
+
" 23\n",
3003
+
" 29\n",
3004
+
" 31\n",
3005
+
" 37"
3006
+
]
3007
+
},
3008
+
"execution_count": 33,
3009
+
"metadata": {},
3010
+
"output_type": "execute_result"
3011
+
}
3012
+
],
3013
+
"source": [
3014
+
"primes(39)"
3015
+
]
3016
+
},
3017
+
{
3018
+
"cell_type": "code",
3019
+
"execution_count": 38,
3020
+
"id": "b3ede472-67c8-4e16-a604-b652d9d0a820",
3021
+
"metadata": {},
3022
+
"outputs": [
3023
+
{
3024
+
"data": {
3025
+
"text/plain": [
3026
+
"lempelc (generic function with 2 methods)"
3027
+
]
3028
+
},
3029
+
"execution_count": 38,
3030
+
"metadata": {},
3031
+
"output_type": "execute_result"
3032
+
}
3033
+
],
3034
+
"source": [
3035
+
"function lempelc(prime::Integer, c::Integer = 1)::Vector{Vector{Integer}}\n",
3036
+
" welch(prime) .|> lst -> init(lst) .|> n -> findindex(lst, prime + c - n)\n",
3037
+
"end"
3038
+
]
3039
+
},
3040
+
{
3041
+
"cell_type": "markdown",
3042
+
"id": "f6b5d41c-8ac6-4802-b0e4-dfe270d0d9b3",
3043
+
"metadata": {},
3044
+
"source": [
3045
+
"lempelc(37)"
3046
+
]
3047
+
},
3048
+
{
3049
+
"cell_type": "code",
3050
+
"execution_count": 52,
3051
+
"id": "857ac8df-a466-4fd6-b371-fcfce09dbaa7",
3052
+
"metadata": {},
3053
+
"outputs": [
3054
+
{
3055
+
"name": "stdout",
3056
+
"output_type": "stream",
3057
+
"text": [
3058
+
"2: true\n",
3059
+
"3: true\n",
3060
+
"5: true\n",
3061
+
"7: true\n",
3062
+
"11: false\n",
3063
+
"13: false\n",
3064
+
"17: true\n",
3065
+
"19: true\n",
3066
+
"23: false\n",
3067
+
"29: false\n",
3068
+
"31: false\n",
3069
+
"37: false\n"
3070
+
]
3071
+
}
3072
+
],
3073
+
"source": [
3074
+
"for p in primes(40)\n",
3075
+
" flag = false\n",
3076
+
" for l in lempel(p)\n",
3077
+
" if l |> f2(vcat, p) |> iscostas\n",
3078
+
" flag = true\n",
3079
+
" end\n",
3080
+
" if flag\n",
3081
+
" break\n",
3082
+
" end\n",
3083
+
" end\n",
3084
+
" println(\"$(p): $(flag)\")\n",
3085
+
"end"
3086
+
]
3087
+
},
3088
+
{
3089
+
"cell_type": "code",
3090
+
"execution_count": 2,
3091
+
"id": "c703313d-a2c2-4dc8-a61c-45fb425a4369",
3092
+
"metadata": {},
3093
+
"outputs": [
3094
+
{
3095
+
"data": {
3096
+
"text/plain": [
3097
+
"3"
3098
+
]
3099
+
},
3100
+
"execution_count": 2,
3101
+
"metadata": {},
3102
+
"output_type": "execute_result"
3103
+
}
3104
+
],
3105
+
"source": [
3106
+
"n = 20\n",
3107
+
"α₁ = 7\n",
3108
+
"α = 3"
3109
+
]
3110
+
},
3111
+
{
3112
+
"cell_type": "code",
3113
+
"execution_count": 64,
3114
+
"id": "3d185147-705f-4c5b-9ec5-f6ae382acdc9",
3115
+
"metadata": {},
3116
+
"outputs": [
3117
+
{
3118
+
"data": {
3119
+
"text/plain": [
3120
+
"5-element Vector{Integer}:\n",
3121
+
" 1\n",
3122
+
" 3\n",
3123
+
" 4\n",
3124
+
" 2\n",
3125
+
" 5"
3126
+
]
3127
+
},
3128
+
"execution_count": 64,
3129
+
"metadata": {},
3130
+
"output_type": "execute_result"
3131
+
}
3132
+
],
3133
+
"source": [
3134
+
"unseq([0,1,1,2,4])"
3135
+
]
3136
+
},
3137
+
{
3138
+
"cell_type": "code",
3139
+
"execution_count": 3,
3140
+
"id": "06dc523f-8eff-40b3-be3c-05b582bf1a5a",
3141
+
"metadata": {},
3142
+
"outputs": [
3143
+
{
3144
+
"data": {
3145
+
"text/plain": [
3146
+
"seq (generic function with 1 method)"
3147
+
]
3148
+
},
3149
+
"execution_count": 3,
3150
+
"metadata": {},
3151
+
"output_type": "execute_result"
3152
+
}
3153
+
],
3154
+
"source": [
3155
+
"function seq(lst::Vector{<:Integer})::Vector{Integer}\n",
3156
+
" acc = []\n",
3157
+
" for i ∈ 1:length(lst)\n",
3158
+
" counter = 0\n",
3159
+
" for el ∈ lst\n",
3160
+
" if el < i\n",
3161
+
" counter += 1\n",
3162
+
" elseif el == i\n",
3163
+
" break\n",
3164
+
" end\n",
3165
+
" end\n",
3166
+
" push!(acc, counter)\n",
3167
+
" end\n",
3168
+
" acc\n",
3169
+
"end"
3170
+
]
3171
+
},
3172
+
{
3173
+
"cell_type": "code",
3174
+
"execution_count": 6,
3175
+
"id": "f890870c-4307-4215-b987-c1a560db4964",
3176
+
"metadata": {},
3177
+
"outputs": [
3178
+
{
3179
+
"ename": "LoadError",
3180
+
"evalue": "UndefVarError: `costas_7x7` not defined",
3181
+
"output_type": "error",
3182
+
"traceback": [
3183
+
"UndefVarError: `costas_7x7` not defined",
3184
+
"",
3185
+
"Stacktrace:",
3186
+
" [1] top-level scope",
3187
+
" @ ./In[6]:1"
3188
+
]
3189
+
}
3190
+
],
3191
+
"source": [
3192
+
"for l ∈ costas_7x7\n",
3193
+
" if l |> seq |> iscostas\n",
3194
+
" println(l)\n",
3195
+
" end\n",
3196
+
"end"
3197
+
]
3198
+
},
3199
+
{
3200
+
"cell_type": "code",
3201
+
"execution_count": 8,
3202
+
"id": "79b7d083-e78f-4f70-b489-bc80479b769e",
3203
+
"metadata": {},
3204
+
"outputs": [
3205
+
{
3206
+
"data": {
3207
+
"text/plain": [
3208
+
"2-element Vector{Vector{Integer}}:\n",
3209
+
" [0, 0, 0, 2, 3, 2]\n",
3210
+
" [0, 0, 1, 0, 0, 2]"
3211
+
]
3212
+
},
3213
+
"execution_count": 8,
3214
+
"metadata": {},
3215
+
"output_type": "execute_result"
3216
+
}
3217
+
],
3218
+
"source": [
3219
+
"welch(7) .|> seq"
3220
+
]
3221
+
},
3222
+
{
3223
+
"cell_type": "code",
3224
+
"execution_count": 29,
3225
+
"id": "25fd1202-b3fe-4cf4-88d9-fb1937f5d03d",
3226
+
"metadata": {},
3227
+
"outputs": [
3228
+
{
3229
+
"name": "stdout",
3230
+
"output_type": "stream",
3231
+
"text": [
3232
+
"Integer[5, 3, 2, 4, 1] ↦ Integer[0, 0, 0, 2, 0]\n",
3233
+
"Integer[5, 2, 4, 3, 1] ↦ Integer[0, 0, 1, 1, 0]\n"
3234
+
]
3235
+
}
3236
+
],
3237
+
"source": [
3238
+
"for l ∈ lempel(7)\n",
3239
+
" println(l, \" ↦ \", seq(l))\n",
3240
+
"end"
3241
+
]
3242
+
},
3243
+
{
3244
+
"cell_type": "code",
3245
+
"execution_count": 39,
3246
+
"id": "e6923891-0ddb-4943-8888-dfe733cf0650",
3247
+
"metadata": {},
3248
+
"outputs": [
3249
+
{
3250
+
"name": "stdout",
3251
+
"output_type": "stream",
3252
+
"text": [
3253
+
"Integer[3, 2, 6, 4, 5, 1]Integer[3, 2, 6, 4, 5, 1][1] ↦ Integer[0, 0, 0, 2, 3, 2]\n",
3254
+
"Integer[5, 4, 6, 2, 3, 1]Integer[5, 4, 6, 2, 3, 1][1] ↦ Integer[0, 0, 1, 0, 0, 2]\n"
3255
+
]
3256
+
}
3257
+
],
3258
+
"source": [
3259
+
"for l ∈ welch(7)\n",
3260
+
" println(l, \"$l[1] ↦ \", seq(l))\n",
3261
+
"end"
3262
+
]
3263
+
},
3264
+
{
3265
+
"cell_type": "code",
3266
+
"execution_count": 134,
3267
+
"id": "a1ee9bac-aaf4-406f-9c0d-b8da541dd68e",
3268
+
"metadata": {},
3269
+
"outputs": [],
3270
+
"source": [
3271
+
"for p ∈ primes(50)\n",
3272
+
" for l ∈ welch(p)\n",
3273
+
" if !issorted(l)\n",
3274
+
" #println(\"$l ↦ $(seq(l))\")\n",
3275
+
" end\n",
3276
+
" end\n",
3277
+
"end"
3278
+
]
3279
+
},
3280
+
{
3281
+
"cell_type": "code",
3282
+
"execution_count": 4,
3283
+
"id": "1850d8a1-9af0-4162-b43c-d8e3bdd613a2",
3284
+
"metadata": {},
3285
+
"outputs": [
3286
+
{
3287
+
"data": {
3288
+
"text/plain": [
3289
+
"unseq (generic function with 1 method)"
3290
+
]
3291
+
},
3292
+
"execution_count": 4,
3293
+
"metadata": {},
3294
+
"output_type": "execute_result"
3295
+
}
3296
+
],
3297
+
"source": [
3298
+
"function unseq(lst::Vector{<:Integer})::Vector{Integer}\n",
3299
+
" acc = []\n",
3300
+
" for (idx, elem) ∈ enumerate(lst)\n",
3301
+
" l, r = splitat(acc, elem)\n",
3302
+
" acc = [l;[idx];r]\n",
3303
+
" end\n",
3304
+
" acc\n",
3305
+
"end"
3306
+
]
3307
+
},
3308
+
{
3309
+
"cell_type": "code",
3310
+
"execution_count": 5,
3311
+
"id": "07e7a13b-f593-47f1-99e7-158c4f39dfc3",
3312
+
"metadata": {},
3313
+
"outputs": [
3314
+
{
3315
+
"data": {
3316
+
"text/plain": [
3317
+
"splitat (generic function with 1 method)"
3318
+
]
3319
+
},
3320
+
"execution_count": 5,
3321
+
"metadata": {},
3322
+
"output_type": "execute_result"
3323
+
}
3324
+
],
3325
+
"source": [
3326
+
"function splitat(v::Vector{T}, i::Integer)::Tuple{Vector{T}, Vector{T}} where T\n",
3327
+
" (v |> Take(i), v |> Drop(i)) .|> collect\n",
3328
+
"end"
3329
+
]
3330
+
},
3331
+
{
3332
+
"cell_type": "code",
3333
+
"execution_count": 82,
3334
+
"id": "b60c2be3-4c88-4178-9909-59a3e7e7228c",
3335
+
"metadata": {},
3336
+
"outputs": [
3337
+
{
3338
+
"data": {
3339
+
"text/plain": [
3340
+
"dfs (generic function with 1 method)"
3341
+
]
3342
+
},
3343
+
"execution_count": 82,
3344
+
"metadata": {},
3345
+
"output_type": "execute_result"
3346
+
}
3347
+
],
3348
+
"source": [
3349
+
"function dfs(current::Vector{<:Integer})::Vector{Integer}\n",
3350
+
" longest = copy(current)\n",
3351
+
" while length(current) != 0\n",
3352
+
" if iscostas(unseq(current))\n",
3353
+
" if length(current) > length(longest)\n",
3354
+
" longest = copy(current)\n",
3355
+
" end\n",
3356
+
" push!(current, 0)\n",
3357
+
" else\n",
3358
+
" while length(current) > 0 && last(current) + 1 >= length(current)\n",
3359
+
" pop!(current)\n",
3360
+
" end\n",
3361
+
" if length(current) == 0\n",
3362
+
" break\n",
3363
+
" end\n",
3364
+
" current[length(current)] = last(current) + 1\n",
3365
+
" end\n",
3366
+
" end\n",
3367
+
" longest\n",
3368
+
"end"
3369
+
]
3370
+
},
3371
+
{
3372
+
"cell_type": "code",
3373
+
"execution_count": 68,
3374
+
"id": "7b2aa6c4-2a54-4eff-92ac-103a791282c3",
3375
+
"metadata": {},
3376
+
"outputs": [
3377
+
{
3378
+
"data": {
3379
+
"text/plain": [
3380
+
"([1, 2], [3, 4, 5, 6, 7, 8, 9, 10])"
3381
+
]
3382
+
},
3383
+
"execution_count": 68,
3384
+
"metadata": {},
3385
+
"output_type": "execute_result"
3386
+
}
3387
+
],
3388
+
"source": [
3389
+
"1:10 |> collect |> x -> splitat(x, 2)"
3390
+
]
3391
+
},
3392
+
{
3393
+
"cell_type": "code",
3394
+
"execution_count": 85,
3395
+
"id": "9597cace-4837-449a-a679-cc65bfb8b75a",
3396
+
"metadata": {},
3397
+
"outputs": [
3398
+
{
3399
+
"name": "stdout",
3400
+
"output_type": "stream",
3401
+
"text": [
3402
+
"1 3 4 2 5 \n",
3403
+
"1 4 2 3 5 \n",
3404
+
"1 4 3 5 2 \n",
3405
+
"1 4 5 3 2 \n",
3406
+
"1 5 3 2 4 \n",
3407
+
"1 5 4 2 3 \n",
3408
+
"2 1 4 5 3 \n",
3409
+
"2 1 5 3 4 \n",
3410
+
"2 3 1 5 4 \n",
3411
+
"2 3 5 1 4 \n",
3412
+
"2 3 5 4 1 \n",
3413
+
"2 4 1 5 3 \n",
3414
+
"2 4 3 1 5 \n",
3415
+
"2 5 1 3 4 \n",
3416
+
"2 5 3 4 1 \n",
3417
+
"2 5 4 1 3 \n",
3418
+
"3 1 2 5 4 \n",
3419
+
"3 1 4 5 2 \n",
3420
+
"3 1 5 2 4 \n",
3421
+
"3 2 4 5 1 \n",
3422
+
"3 4 2 1 5 \n",
3423
+
"3 5 1 4 2 \n",
3424
+
"3 5 2 1 4 \n",
3425
+
"3 5 4 1 2 \n",
3426
+
"4 1 2 5 3 \n",
3427
+
"4 1 3 2 5 \n",
3428
+
"4 1 5 3 2 \n",
3429
+
"4 2 3 5 1 \n",
3430
+
"4 2 5 1 3 \n",
3431
+
"4 3 1 2 5 \n",
3432
+
"4 3 1 5 2 \n",
3433
+
"4 3 5 1 2 \n",
3434
+
"4 5 1 3 2 \n",
3435
+
"4 5 2 1 3 \n",
3436
+
"5 1 2 4 3 \n",
3437
+
"5 1 3 4 2 \n",
3438
+
"5 2 1 3 4 \n",
3439
+
"5 2 3 1 4 \n",
3440
+
"5 2 4 3 1 \n",
3441
+
"5 3 2 4 1 \n"
3442
+
]
3443
+
}
3444
+
],
3445
+
"source": [
3446
+
"for l in costas_5x5\n",
3447
+
" for e in l\n",
3448
+
" print(\"$e \")\n",
3449
+
" end\n",
3450
+
" println()\n",
3451
+
"end"
3452
+
]
3453
+
},
3454
+
{
3455
+
"cell_type": "code",
3456
+
"execution_count": 135,
3457
+
"id": "55ba2a3c-0930-42c8-b319-f0864dcc3972",
3458
+
"metadata": {},
3459
+
"outputs": [
3460
+
{
3461
+
"name": "stdout",
3462
+
"output_type": "stream",
3463
+
"text": [
3464
+
"Any[(4, 11), (6, 11), (10, 11), (10, 12), (12, 12), (12, 14), (16, 16), (16, 18), (18, 18), (22, 22), (28, 28), (30, 30), (36, 36), (40, 40), (42, 42), (46, 46)]\n"
3465
+
]
3466
+
}
3467
+
],
3468
+
"source": [
3469
+
"counter = 0\n",
3470
+
"longest = []\n",
3471
+
"s = []\n",
3472
+
"for p ∈ primes(50)\n",
3473
+
" if counter < 2\n",
3474
+
" counter += 1\n",
3475
+
" continue\n",
3476
+
" end\n",
3477
+
" for w ∈ welch(p)\n",
3478
+
" c = dfs(seq(w))\n",
3479
+
" push!(s, (length(w), length(c)))\n",
3480
+
" end\n",
3481
+
"end\n",
3482
+
"println(s |> sort |> unique)"
3483
+
]
3484
+
},
3485
+
{
3486
+
"cell_type": "code",
3487
+
"execution_count": 136,
3488
+
"id": "1ee862d6-97d2-4b0d-bb14-efdbaa969ea8",
3489
+
"metadata": {},
3490
+
"outputs": [
3491
+
{
3492
+
"name": "stdout",
3493
+
"output_type": "stream",
3494
+
"text": [
3495
+
"Any[(3, 9), (3, 11), (5, 11), (9, 10), (9, 11), (11, 11), (11, 12), (15, 15), (15, 16), (15, 17), (17, 17), (21, 21), (21, 22), (27, 27), (27, 28), (29, 29), (29, 30), (35, 35), (35, 36), (39, 39), (39, 40), (41, 41), (41, 42), (45, 45), (45, 46)]\n"
3496
+
]
3497
+
}
3498
+
],
3499
+
"source": [
3500
+
"counter = 0\n",
3501
+
"longest = []\n",
3502
+
"s = []\n",
3503
+
"for p ∈ primes(50)\n",
3504
+
" if counter < 2\n",
3505
+
" counter += 1\n",
3506
+
" continue\n",
3507
+
" end\n",
3508
+
" for w ∈ lempel(p)\n",
3509
+
" c = dfs(seq(w))\n",
3510
+
" push!(s, (length(w), length(c)))\n",
3511
+
" end\n",
3512
+
"end\n",
3513
+
"println(s |> sort |> unique)"
3514
+
]
3515
+
},
3516
+
{
3517
+
"cell_type": "code",
3518
+
"execution_count": 112,
3519
+
"id": "de864d75-3be6-4ee3-9b02-fa34d74479ac",
3520
+
"metadata": {},
3521
+
"outputs": [
3522
+
{
3523
+
"data": {
3524
+
"text/plain": [
3525
+
"false"
3526
+
]
3527
+
},
3528
+
"execution_count": 112,
3529
+
"metadata": {},
3530
+
"output_type": "execute_result"
3531
+
}
3532
+
],
3533
+
"source": [
3534
+
"[0, 0, 1, 3, 3, 4, 3, 0, 8, 2, 2, 8, 5, 1, 5, 9, 11, 0, 13, 12, 9, 3, 12, 23, 11, 13, 3, 8, 27, 4, 3, 8] |> unseq |> iscostas"
3535
+
]
3536
+
},
3537
+
{
3538
+
"cell_type": "code",
3539
+
"execution_count": 27,
3540
+
"id": "17e599a4-a91c-49b0-bb55-a169a6c37333",
3541
+
"metadata": {},
3542
+
"outputs": [
3543
+
{
3544
+
"data": {
3545
+
"text/plain": [
3546
+
"40-element Vector{Vector{Int64}}:\n",
3547
+
" []\n",
3548
+
" []\n",
3549
+
" []\n",
3550
+
" []\n",
3551
+
" []\n",
3552
+
" []\n",
3553
+
" []\n",
3554
+
" []\n",
3555
+
" []\n",
3556
+
" []\n",
3557
+
" []\n",
3558
+
" []\n",
3559
+
" []\n",
3560
+
" ⋮\n",
3561
+
" []\n",
3562
+
" []\n",
3563
+
" []\n",
3564
+
" []\n",
3565
+
" []\n",
3566
+
" []\n",
3567
+
" []\n",
3568
+
" []\n",
3569
+
" []\n",
3570
+
" []\n",
3571
+
" []\n",
3572
+
" []"
3573
+
]
3574
+
},
3575
+
"execution_count": 27,
3576
+
"metadata": {},
3577
+
"output_type": "execute_result"
3578
+
}
3579
+
],
3580
+
"source": [
3581
+
"costas_5x5"
3582
+
]
3583
+
},
3584
+
{
3585
+
"cell_type": "code",
3586
+
"execution_count": 29,
3587
+
"id": "3b83149d-1693-4086-ac44-0c3f49732223",
3588
+
"metadata": {},
3589
+
"outputs": [
3590
+
{
3591
+
"name": "stdout",
3592
+
"output_type": "stream",
3593
+
"text": [
3594
+
"Integer[7, 6, 1, 3, 4, 2, 5]\n",
3595
+
"Integer[7, 6, 1, 4, 2, 3, 8, 5]\n",
3596
+
"Integer[5, 1, 7, 6, 8, 3, 4, 2]\n",
3597
+
"Integer[5, 1, 7, 6, 8, 3, 4, 2]\n",
3598
+
"Integer[9, 6, 1, 5, 3, 2, 4, 7, 8]\n",
3599
+
"Integer[7, 1, 5, 4, 2, 3, 6, 8]\n",
3600
+
"Integer[9, 6, 4, 5, 1, 8, 3, 2, 7]\n",
3601
+
"Integer[7, 3, 1, 6, 5, 2, 4, 8, 9]\n",
3602
+
"Integer[7, 3, 1, 6, 5, 2, 4, 8, 9]\n",
3603
+
"Integer[8, 3, 5, 9, 10, 1, 4, 2, 7, 6]\n",
3604
+
"Integer[7, 3, 1, 6, 5, 2, 4, 8, 9]\n",
3605
+
"Integer[9, 8, 4, 6, 1, 2, 5, 3, 7]\n",
3606
+
"Integer[5, 1, 7, 6, 8, 3, 4, 2]\n",
3607
+
"Integer[5, 1, 7, 6, 8, 3, 4, 2]\n",
3608
+
"Integer[7, 3, 1, 6, 5, 2, 4, 8, 9]\n",
3609
+
"Integer[9, 6, 4, 5, 1, 8, 3, 2, 7]\n",
3610
+
"Integer[7, 5, 1, 2, 4, 8, 3, 6]\n",
3611
+
"Integer[5, 1, 7, 6, 8, 3, 4, 2]\n"
3612
+
]
3613
+
}
3614
+
],
3615
+
"source": [
3616
+
"for c in costas_5x5\n",
3617
+
" l = c |> seq |> dfs |> unseq\n",
3618
+
" if length(l) <= 10\n",
3619
+
" println(l)\n",
3620
+
" end\n",
3621
+
"end"
3622
+
]
3623
+
},
3624
+
{
3625
+
"cell_type": "code",
3626
+
"execution_count": 30,
3627
+
"id": "b4f239f6-0a9b-4a35-af34-7a30e4f77d4c",
3628
+
"metadata": {},
3629
+
"outputs": [
3630
+
{
3631
+
"data": {
3632
+
"text/plain": [
3633
+
"2160-element Vector{Vector{Int64}}:\n",
3634
+
" [1, 2, 4, 8, 5, 10, 9, 7, 3, 6]\n",
3635
+
" [1, 2, 5, 7, 3, 10, 9, 6, 4, 8]\n",
3636
+
" [1, 2, 5, 9, 3, 8, 4, 10, 7, 6]\n",
3637
+
" [1, 2, 5, 9, 3, 10, 8, 7, 4, 6]\n",
3638
+
" [1, 2, 6, 9, 8, 5, 7, 3, 10, 4]\n",
3639
+
" [1, 2, 8, 5, 10, 4, 6, 9, 7, 3]\n",
3640
+
" [1, 2, 8, 10, 6, 3, 7, 5, 4, 9]\n",
3641
+
" [1, 2, 9, 3, 5, 10, 8, 4, 7, 6]\n",
3642
+
" [1, 2, 9, 6, 5, 7, 10, 4, 8, 3]\n",
3643
+
" [1, 2, 10, 6, 4, 7, 9, 3, 8, 5]\n",
3644
+
" [1, 2, 10, 8, 5, 4, 6, 9, 3, 7]\n",
3645
+
" [1, 3, 4, 9, 8, 6, 10, 7, 2, 5]\n",
3646
+
" [1, 3, 7, 10, 9, 4, 2, 8, 5, 6]\n",
3647
+
" ⋮\n",
3648
+
" [10, 8, 7, 2, 3, 5, 1, 4, 9, 6]\n",
3649
+
" [10, 9, 1, 3, 6, 7, 5, 2, 8, 4]\n",
3650
+
" [10, 9, 1, 5, 7, 4, 2, 8, 3, 6]\n",
3651
+
" [10, 9, 2, 5, 6, 4, 1, 7, 3, 8]\n",
3652
+
" [10, 9, 2, 8, 6, 1, 3, 7, 4, 5]\n",
3653
+
" [10, 9, 3, 1, 5, 8, 4, 6, 7, 2]\n",
3654
+
" [10, 9, 3, 6, 1, 7, 5, 2, 4, 8]\n",
3655
+
" [10, 9, 5, 2, 3, 6, 4, 8, 1, 7]\n",
3656
+
" [10, 9, 6, 2, 8, 1, 3, 4, 7, 5]\n",
3657
+
" [10, 9, 6, 2, 8, 3, 7, 1, 4, 5]\n",
3658
+
" [10, 9, 6, 4, 8, 1, 2, 5, 7, 3]\n",
3659
+
" [10, 9, 7, 3, 6, 1, 2, 4, 8, 5]"
3660
+
]
3661
+
},
3662
+
"execution_count": 30,
3663
+
"metadata": {},
3664
+
"output_type": "execute_result"
3665
+
}
3666
+
],
3667
+
"source": [
3668
+
"costas_10x10"
3669
+
]
3670
+
},
3671
+
{
3672
+
"cell_type": "code",
3673
+
"execution_count": 39,
3674
+
"id": "6cc018cf-347a-4c9f-af3c-d3fcd31b2984",
3675
+
"metadata": {},
3676
+
"outputs": [
3677
+
{
3678
+
"name": "stdout",
3679
+
"output_type": "stream",
3680
+
"text": [
3681
+
"1 2 4 8 5 10 9 7 3 6 "
3682
+
]
3683
+
}
3684
+
],
3685
+
"source": [
3686
+
"l = costas_10x10[1]\n",
3687
+
"for e in l\n",
3688
+
" print(\"$e \")\n",
3689
+
"end"
3690
+
]
3691
+
},
3692
+
{
3693
+
"cell_type": "code",
3694
+
"execution_count": 35,
3695
+
"id": "eb7e4533-7c4a-4442-82e5-8f2b0e3d485b",
3696
+
"metadata": {},
3697
+
"outputs": [
3698
+
{
3699
+
"name": "stdout",
3700
+
"output_type": "stream",
3701
+
"text": [
3702
+
"29, 23, 22, 19, 27, 17, 21, 16, 18, 24, 25, 28, 20, 30, 26, 31, "
3703
+
]
3704
+
}
3705
+
],
3706
+
"source": [
3707
+
"for e in [3, 9, 10, 13, 5, 15, 11, 16, 14, 8, 7, 4, 12, 2, 6, 1]\n",
3708
+
" print(\"$(-e % 32 + 32), \")\n",
3709
+
"end"
3710
+
]
3711
+
},
3712
+
{
3713
+
"cell_type": "code",
3714
+
"execution_count": 38,
3715
+
"id": "0ada109c-c642-4fb7-a0eb-15a58e836140",
3716
+
"metadata": {},
3717
+
"outputs": [
3718
+
{
3719
+
"data": {
3720
+
"text/plain": [
3721
+
"false"
3722
+
]
3723
+
},
3724
+
"execution_count": 38,
3725
+
"metadata": {},
3726
+
"output_type": "execute_result"
3727
+
}
3728
+
],
3729
+
"source": [
3730
+
"[3, 9, 10, 13, 5, 15, 11, 16, 14, 8, 7, 4, 12, 2, 6, 1, 29, 23, 22, 19, 27, 17, 21, 16, 18, 24, 25, 28, 20, 30, 26, 31] |> iscostas"
3731
+
]
3732
+
},
3733
+
{
3734
+
"cell_type": "code",
3735
+
"execution_count": 72,
3736
+
"id": "8074cb68-e0b0-4a50-a97c-59165de15d99",
3737
+
"metadata": {},
3738
+
"outputs": [
3739
+
{
3740
+
"name": "stdout",
3741
+
"output_type": "stream",
3742
+
"text": [
3743
+
"Integer[0, 1, 1, 2, 4, 0, 0]: 7\n",
3744
+
"Integer[0, 1, 2, 1, 4, 0, 0, 6]: 8\n",
3745
+
"Integer[0, 1, 1, 2, 0, 2, 2, 4]: 8\n",
3746
+
"Integer[0, 1, 1, 2, 0, 2, 2, 4]: 8\n",
3747
+
"Integer[0, 1, 1, 3, 1, 0, 6, 7, 0]: 9\n",
3748
+
"Integer[0, 1, 2, 1, 1, 5, 0, 7]: 8\n",
3749
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3750
+
"Integer[0, 1, 0, 0, 3, 2, 3, 7, 0, 9, 0]: 11\n",
3751
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3752
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3753
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3754
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3755
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3756
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3757
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3758
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3759
+
"Integer[0, 1, 1, 0, 1, 0, 6, 4, 0]: 9\n",
3760
+
"Integer[0, 1, 0, 3, 2, 2, 0, 7, 8]: 9\n",
3761
+
"Integer[0, 1, 0, 3, 2, 2, 0, 7, 8]: 9\n",
3762
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3763
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3764
+
"Integer[0, 1, 0, 2, 1, 5, 5, 0, 3, 4]: 10\n",
3765
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3766
+
"Integer[0, 1, 0, 3, 2, 2, 0, 7, 8]: 9\n",
3767
+
"Integer[0, 1, 2, 0, 3, 1, 6, 0, 0]: 9\n",
3768
+
"Integer[0, 1, 1, 2, 0, 2, 2, 4]: 8\n",
3769
+
"Integer[0, 1, 1, 2, 0, 2, 2, 4]: 8\n",
3770
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3771
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3772
+
"Integer[0, 1, 0, 3, 2, 2, 0, 7, 8]: 9\n",
3773
+
"Integer[0, 1, 0, 0, 3, 2, 3, 7, 0, 9, 0]: 11\n",
3774
+
"Integer[0, 1, 0, 0, 3, 2, 3, 7, 0, 9, 0]: 11\n",
3775
+
"Integer[0, 1, 1, 0, 1, 0, 6, 4, 0]: 9\n",
3776
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3777
+
"Integer[0, 1, 2, 2, 0, 5, 0, 5]: 8\n",
3778
+
"Integer[0, 1, 1, 2, 0, 2, 2, 4]: 8\n",
3779
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3780
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3781
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n",
3782
+
"Integer[0, 0, 2, 3, 1, 3, 3, 0, 8, 0, 10]: 11\n"
3783
+
]
3784
+
}
3785
+
],
3786
+
"source": [
3787
+
"for lst in costas_5x5\n",
3788
+
" dfs(seq(lst)) |> l -> println(\"$l: $(length(l))\")\n",
3789
+
"end"
3790
+
]
3791
+
},
3792
+
{
3793
+
"cell_type": "code",
3794
+
"execution_count": 17,
3795
+
"id": "70c019a2-b9f2-4b1c-83de-54ef7424bad0",
3796
+
"metadata": {},
3797
+
"outputs": [
3798
+
{
3799
+
"data": {
3800
+
"text/plain": [
3801
+
"590105"
3802
+
]
3803
+
},
3804
+
"execution_count": 17,
3805
+
"metadata": {},
3806
+
"output_type": "execute_result"
3807
+
}
3808
+
],
3809
+
"source": [
3810
+
"a = \"#!/usr/bin/env sh\"\n",
3811
+
"fname = \"foobar.jmd\"\n",
3812
+
"dirpath = \"/tmp\"\n",
3813
+
"fpath = joinpath(dirpath, fname)\n",
3814
+
"\n",
3815
+
"for lst in costas_13x13\n",
3816
+
" a *= \"echo \\\"\"\n",
3817
+
" for e in lst[1:12]\n",
3818
+
" a *= \"$e \"\n",
3819
+
" end\n",
3820
+
" a *= \"$(last(lst))\\\" | ./main\\n\"\n",
3821
+
"end\n",
3822
+
"\n",
3823
+
"\n",
3824
+
"open(fpath, \"w\") do file\n",
3825
+
" write(file, a)\n",
3826
+
"end\n"
3827
+
]
3828
+
},
3829
+
{
3830
+
"cell_type": "code",
3831
+
"execution_count": 12,
3832
+
"id": "84fca448-b604-4c5a-9690-f2f1db5cb2e1",
3833
+
"metadata": {},
3834
+
"outputs": [
3835
+
{
3836
+
"data": {
3837
+
"text/plain": [
3838
+
"3-element Vector{Int64}:\n",
3839
+
" 2\n",
3840
+
" 3\n",
3841
+
" 4"
3842
+
]
3843
+
},
3844
+
"execution_count": 12,
3845
+
"metadata": {},
3846
+
"output_type": "execute_result"
3847
+
}
3848
+
],
3849
+
"source": [
3850
+
"lst = [1,2,3,4,5]\n",
3851
+
"lst[2:4]"
3852
+
]
3853
+
},
3854
+
{
3855
+
"cell_type": "code",
3856
+
"execution_count": 1,
3857
+
"id": "5f460720-57f0-4673-909e-fdcc4840c6bc",
3858
+
"metadata": {},
3859
+
"outputs": [
3860
+
{
3861
+
"name": "stderr",
3862
+
"output_type": "stream",
3863
+
"text": [
3864
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
3865
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
3866
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
3867
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
3868
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
3869
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
3870
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
3871
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
3872
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
3873
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
3874
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
3875
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
3876
+
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
3877
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
3878
+
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n"
3879
+
]
3880
+
},
3881
+
{
3882
+
"name": "stdout",
3883
+
"output_type": "stream",
3884
+
"text": [
3885
+
"inputs has 17 many elements\n",
3886
+
"Any[Any[(4, 2, 5)], Any[(2, 3, 5), (3, 5, 2), (5, 3, 2)], Any[(3, 2, 4), (4, 2, 3)], Any[(4, 5, 3), (5, 3, 4)], Any[(1, 5, 4), (5, 1, 4), (5, 4, 1)], Any[(1, 5, 3), (3, 1, 5)], Any[(1, 3, 4), (3, 4, 1), (4, 1, 3)], Any[(2, 5, 4), (4, 5, 2), (5, 2, 4)], Any[(4, 5, 1)], Any[(2, 1, 5)], Any[(1, 4, 2), (2, 1, 4), (4, 1, 2)], Any[(2, 5, 3), (3, 2, 5), (5, 3, 2)], Any[(3, 5, 1), (5, 1, 3)], Any[(1, 2, 5), (1, 5, 2), (5, 1, 2)], Any[(1, 3, 2), (2, 1, 3)], Any[(2, 4, 3), (3, 4, 2)], Any[(1, 3, 4), (3, 1, 4), (4, 3, 1)]]\n"
3887
+
]
3888
+
},
3889
+
{
3890
+
"data": {
3891
+
"image/svg+xml": [
3892
+
"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
3893
+
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
3894
+
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
3895
+
"<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
3896
+
" width=\"180mm\" height=\"25mm\"\n",
3897
+
" viewBox=\"0 0 19 1\" preserveAspectRatio=\"none\"\n",
3898
+
" shape-rendering=\"crispEdges\" stroke=\"none\">\n",
3899
+
"<rect width=\".89\" height=\".96\" x=\"0\" y=\"0\" fill=\"#FFA500\" />\n",
3900
+
"<rect width=\".89\" height=\".96\" x=\"1\" y=\"0\" fill=\"#F19C0E\" />\n",
3901
+
"<rect width=\".89\" height=\".96\" x=\"2\" y=\"0\" fill=\"#E3931C\" />\n",
3902
+
"<rect width=\".89\" height=\".96\" x=\"3\" y=\"0\" fill=\"#D48A2B\" />\n",
3903
+
"<rect width=\".89\" height=\".96\" x=\"4\" y=\"0\" fill=\"#C68039\" />\n",
3904
+
"<rect width=\".89\" height=\".96\" x=\"5\" y=\"0\" fill=\"#B87747\" />\n",
3905
+
"<rect width=\".89\" height=\".96\" x=\"6\" y=\"0\" fill=\"#AA6E55\" />\n",
3906
+
"<rect width=\".89\" height=\".96\" x=\"7\" y=\"0\" fill=\"#9C6563\" />\n",
3907
+
"<rect width=\".89\" height=\".96\" x=\"8\" y=\"0\" fill=\"#8E5C71\" />\n",
3908
+
"<rect width=\".89\" height=\".96\" x=\"9\" y=\"0\" fill=\"#805280\" />\n",
3909
+
"<rect width=\".89\" height=\".96\" x=\"10\" y=\"0\" fill=\"#71498E\" />\n",
3910
+
"<rect width=\".89\" height=\".96\" x=\"11\" y=\"0\" fill=\"#63409C\" />\n",
3911
+
"<rect width=\".89\" height=\".96\" x=\"12\" y=\"0\" fill=\"#5537AA\" />\n",
3912
+
"<rect width=\".89\" height=\".96\" x=\"13\" y=\"0\" fill=\"#472EB8\" />\n",
3913
+
"<rect width=\".89\" height=\".96\" x=\"14\" y=\"0\" fill=\"#3925C6\" />\n",
3914
+
"<rect width=\".89\" height=\".96\" x=\"15\" y=\"0\" fill=\"#2A1BD5\" />\n",
3915
+
"<rect width=\".89\" height=\".96\" x=\"16\" y=\"0\" fill=\"#1C12E3\" />\n",
3916
+
"<rect width=\".89\" height=\".96\" x=\"17\" y=\"0\" fill=\"#0E09F1\" />\n",
3917
+
"<rect width=\".89\" height=\".96\" x=\"18\" y=\"0\" fill=\"#0000FF\" />\n",
3918
+
"</svg>"
3919
+
],
3920
+
"text/plain": [
3921
+
"ColorPalette(ColorSchemes.ColorScheme{Vector{RGB{Float64}}, String, String}(RGB{Float64}[RGB(1.0, 0.6470588235294118, 0.0), RGB(0.9444444444444444, 0.6111111111111112, 0.05555555555555558), RGB(0.8888888888888888, 0.5751633986928104, 0.11111111111111116), RGB(0.8333333333333333, 0.5392156862745098, 0.16666666666666674), RGB(0.7777777777777777, 0.5032679738562091, 0.22222222222222232), RGB(0.7222222222222223, 0.46732026143790856, 0.2777777777777777), RGB(0.6666666666666667, 0.4313725490196079, 0.33333333333333326), RGB(0.6111111111111112, 0.39542483660130723, 0.38888888888888884), RGB(0.5555555555555556, 0.3594771241830066, 0.4444444444444444), RGB(0.5, 0.3235294117647059, 0.5), RGB(0.4444444444444444, 0.2875816993464052, 0.5555555555555556), RGB(0.38888888888888884, 0.25163398692810457, 0.6111111111111112), RGB(0.3333333333333335, 0.21568627450980402, 0.6666666666666665), RGB(0.2777777777777777, 0.1797385620915032, 0.7222222222222223), RGB(0.22222222222222232, 0.1437908496732027, 0.7777777777777777), RGB(0.16666666666666652, 0.10784313725490187, 0.8333333333333335), RGB(0.11111111111111116, 0.07189542483660134, 0.8888888888888888), RGB(0.05555555555555558, 0.03594771241830067, 0.9444444444444444), RGB(0.0, 0.0, 1.0)], \"\", \"\"))"
3922
+
]
3923
+
},
3924
+
"execution_count": 1,
3925
+
"metadata": {},
3926
+
"output_type": "execute_result"
3927
+
}
3928
+
],
3929
+
"source": [
3930
+
"import Pkg\n",
3931
+
"import Serialization\n",
3932
+
"Pkg.add(\"Combinatorics\")\n",
3933
+
"Pkg.add(\"Primes\")\n",
3934
+
"Pkg.add(\"BenchmarkTools\")\n",
3935
+
"Pkg.add(\"Transducers\")\n",
3936
+
"Pkg.add(\"Plots\")\n",
3937
+
"using Combinatorics\n",
3938
+
"using Primes\n",
3939
+
"using BenchmarkTools\n",
3940
+
"using Transducers\n",
3941
+
"using Plots\n",
3942
+
"\n",
3943
+
"include(\"header.jl\")\n",
3944
+
"\n",
3945
+
"import Base.Iterators\n",
3946
+
"\n",
3947
+
"loadvar(file_path::String) = Serialization.deserialize(file_path)\n",
3948
+
"\n",
3949
+
"costas_10x10 = loadvar(\"costas_10x10.dat\")\n",
3950
+
"costas_5x5 = loadvar(\"costas_5x5.dat\")\n",
3951
+
"\n",
3952
+
"kw = (proj_type = :ortho, legend = false, aspect_ratio = :equal, xlimits = (0,10), ylimits = (0,10), zlimits = (0,10))\n"
3953
+
]
3954
+
},
3955
+
{
3956
+
"cell_type": "code",
3957
+
"execution_count": 19,
3958
+
"id": "2c6ce2ce-e746-4629-a5d8-d0c78cd6b7b5",
3959
+
"metadata": {},
3960
+
"outputs": [
3961
+
{
3962
+
"data": {
3963
+
"text/plain": [
3964
+
"116-element Vector{Vector{Int64}}:\n",
3965
+
" [1, 2, 5, 4, 6, 3]\n",
3966
+
" [1, 2, 6, 4, 3, 5]\n",
3967
+
" [1, 3, 2, 5, 6, 4]\n",
3968
+
" [1, 3, 2, 6, 4, 5]\n",
3969
+
" [1, 3, 6, 4, 5, 2]\n",
3970
+
" [1, 4, 3, 5, 6, 2]\n",
3971
+
" [1, 4, 5, 3, 2, 6]\n",
3972
+
" [1, 4, 6, 5, 2, 3]\n",
3973
+
" [1, 5, 3, 4, 6, 2]\n",
3974
+
" [1, 5, 3, 6, 2, 4]\n",
3975
+
" [1, 5, 4, 2, 3, 6]\n",
3976
+
" [1, 5, 4, 6, 2, 3]\n",
3977
+
" [1, 5, 6, 2, 4, 3]\n",
3978
+
" ⋮\n",
3979
+
" [6, 2, 3, 1, 5, 4]\n",
3980
+
" [6, 2, 3, 5, 4, 1]\n",
3981
+
" [6, 2, 4, 1, 5, 3]\n",
3982
+
" [6, 2, 4, 3, 1, 5]\n",
3983
+
" [6, 3, 1, 2, 5, 4]\n",
3984
+
" [6, 3, 2, 4, 5, 1]\n",
3985
+
" [6, 3, 4, 2, 1, 5]\n",
3986
+
" [6, 4, 1, 3, 2, 5]\n",
3987
+
" [6, 4, 5, 1, 3, 2]\n",
3988
+
" [6, 4, 5, 2, 1, 3]\n",
3989
+
" [6, 5, 1, 3, 4, 2]\n",
3990
+
" [6, 5, 2, 3, 1, 4]"
3991
+
]
3992
+
},
3993
+
"execution_count": 19,
3994
+
"metadata": {},
3995
+
"output_type": "execute_result"
3996
+
}
3997
+
],
3998
+
"source": [
3999
+
"costas_6x6 |> sort"
4000
+
]
4001
+
},
4002
+
{
4003
+
"cell_type": "code",
4004
+
"execution_count": 34,
4005
+
"id": "c2b846d7-b93a-4e34-82bc-c42511a7536e",
4006
+
"metadata": {},
4007
+
"outputs": [
4008
+
{
4009
+
"name": "stdout",
4010
+
"output_type": "stream",
4011
+
"text": [
4012
+
"inputs has 0 many elements\n",
4013
+
"Any[]\n"
4014
+
]
4015
+
},
4016
+
{
4017
+
"data": {
4018
+
"image/svg+xml": [
4019
+
"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
4020
+
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
4021
+
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
4022
+
"<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\"\n",
4023
+
" width=\"25mm\" height=\"25mm\"\n",
4024
+
" viewBox=\"0 0 1 1\" preserveAspectRatio=\"none\"\n",
4025
+
" shape-rendering=\"crispEdges\" stroke=\"none\">\n",
4026
+
"<rect width=\".96\" height=\".96\" x=\"0\" y=\"0\" fill=\"#FF0000\" />\n",
4027
+
"</svg>"
4028
+
],
4029
+
"text/plain": [
4030
+
"ColorPalette(ColorSchemes.ColorScheme{Vector{RGB{Float64}}, String, String}(RGB{Float64}[RGB(1.0, 0.0, 0.0)], \"\", \"\"))"
4031
+
]
4032
+
},
4033
+
"execution_count": 34,
4034
+
"metadata": {},
4035
+
"output_type": "execute_result"
4036
+
}
4037
+
],
4038
+
"source": [
4039
+
"\n",
4040
+
"size = 4\n",
4041
+
"lists = costas_4x4\n",
4042
+
"last = lists[1][1:size - 3]\n",
4043
+
"inputs = []\n",
4044
+
"arr = []\n",
4045
+
"for l in lists\n",
4046
+
" if last != l[1:size - 3]\n",
4047
+
" push!(inputs, arr)\n",
4048
+
" global last = l[1:size - 3]\n",
4049
+
" global arr = []\n",
4050
+
" end\n",
4051
+
" push!(arr, (l[size - 2], l[size - 1], l[size]))\n",
4052
+
"end\n",
4053
+
"\n",
4054
+
"println(\"inputs has $(length(inputs)) many elements\")\n",
4055
+
"println(inputs)\n",
4056
+
"\n",
4057
+
"limit = length(inputs)\n",
4058
+
"colors = palette([:red, :orange, :yellow, :green, :blue, :indigo, :violet], limit)"
4059
+
]
4060
+
},
4061
+
{
4062
+
"cell_type": "code",
4063
+
"execution_count": 30,
4064
+
"id": "a4b94713-6485-4bfb-800d-a42368b608a7",
4065
+
"metadata": {},
4066
+
"outputs": [
4067
+
{
4068
+
"data": {
4069
+
"text/plain": [
4070
+
"Tuple{Any, Any}[]"
4071
+
]
4072
+
},
4073
+
"execution_count": 30,
4074
+
"metadata": {},
4075
+
"output_type": "execute_result"
4076
+
}
4077
+
],
4078
+
"source": [
4079
+
"idx = 0\n",
4080
+
"inputs = inputs .|> l -> begin\n",
4081
+
" global idx += 1\n",
4082
+
" (l, idx)\n",
4083
+
"end"
4084
+
]
4085
+
},
4086
+
{
4087
+
"cell_type": "code",
4088
+
"execution_count": null,
4089
+
"id": "ed8f9984-89a0-4368-851a-f4749b2a657b",
4090
+
"metadata": {},
4091
+
"outputs": [],
4092
+
"source": [
4093
+
"@gif for i in 0:360\n",
4094
+
" for pt in costas_3x3\n",
4095
+
" x = pt[1]\n",
4096
+
" y = pt[2]\n",
4097
+
" z = pt[3]\n",
4098
+
" scatter!(x, y, z; markercolor = colors[1], camera = (i, round(atand(1 / √2); digits = 3)), kw...)\n",
4099
+
" end\n",
4100
+
"end"
4101
+
]
4102
+
},
4103
+
{
4104
+
"cell_type": "code",
4105
+
"execution_count": 32,
4106
+
"id": "8508e758-0f4b-4271-a6de-6b75d06b0f48",
4107
+
"metadata": {},
4108
+
"outputs": [
4109
+
{
4110
+
"data": {
4111
+
"text/plain": [
4112
+
"4-element Vector{Vector{Int64}}:\n",
4113
+
" [1, 3, 2]\n",
4114
+
" [2, 1, 3]\n",
4115
+
" [2, 3, 1]\n",
4116
+
" [3, 1, 2]"
4117
+
]
4118
+
},
4119
+
"execution_count": 32,
4120
+
"metadata": {},
4121
+
"output_type": "execute_result"
4122
+
}
4123
+
],
4124
+
"source": [
4125
+
"costas_3x3"
4126
+
]
4127
+
},
4128
+
{
4129
+
"cell_type": "code",
4130
+
"execution_count": null,
4131
+
"id": "e950515a-a3c4-4108-9ad2-b92ed7714cc0",
4132
+
"metadata": {},
4133
+
"outputs": [],
4134
+
"source": []
4135
+
}
4136
+
],
4137
+
"metadata": {
4138
+
"kernelspec": {
4139
+
"display_name": "Julia 1.10.4",
4140
+
"language": "julia",
4141
+
"name": "julia-1.10"
4142
+
},
4143
+
"language_info": {
4144
+
"file_extension": ".jl",
4145
+
"mimetype": "application/julia",
4146
+
"name": "julia",
4147
+
"version": "1.10.4"
4148
+
}
4149
+
},
4150
+
"nbformat": 4,
4151
+
"nbformat_minor": 5
4152
+
}
+399
src/jupyter/.ipynb_checkpoints/processing-checkpoint.ipynb
+399
src/jupyter/.ipynb_checkpoints/processing-checkpoint.ipynb
···
1
+
{
2
+
"cells": [
3
+
{
4
+
"cell_type": "code",
5
+
"execution_count": 1,
6
+
"id": "078f9d4f-ee7f-46b1-be3b-7f2bb1197d00",
7
+
"metadata": {},
8
+
"outputs": [],
9
+
"source": [
10
+
"from header import *\n",
11
+
"from algs import *"
12
+
]
13
+
},
14
+
{
15
+
"cell_type": "code",
16
+
"execution_count": 5,
17
+
"id": "2ed6be02-3a12-4517-b7e5-176e70fc8fdc",
18
+
"metadata": {},
19
+
"outputs": [],
20
+
"source": [
21
+
"c_2x2 = load_file(\"results/costas_2x2.txt\")\n",
22
+
"c_3x3 = load_file(\"results/costas_3x3.txt\")\n",
23
+
"c_4x4 = load_file(\"results/costas_4x4.txt\")\n",
24
+
"c_5x5 = load_file(\"results/costas_5x5.txt\")\n",
25
+
"c_6x6 = load_file(\"results/costas_6x6.txt\")\n",
26
+
"c_7x7 = load_file(\"results/costas_7x7.txt\")\n",
27
+
"# c_8x8 = load_file(\"results/costas_8x8.txt\")\n",
28
+
"# c_9x9 = load_file(\"results/costas_9x9.txt\")\n",
29
+
"# c_10x10 = load_file(\"results/min/costas_10x10.min.txt\")\n",
30
+
"# c_11x11 = load_file(\"results/min/costas_11x11.min.txt\")\n",
31
+
"# c_12x12 = load_file(\"results/min/costas_12x12.min.txt\")\n",
32
+
"c_nxns = [c_2x2,c_3x3,c_4x4,c_5x5,c_6x6,c_7x7]"
33
+
]
34
+
},
35
+
{
36
+
"cell_type": "code",
37
+
"execution_count": 23,
38
+
"id": "0584959d-1b91-4037-a599-48622b9f97ee",
39
+
"metadata": {},
40
+
"outputs": [
41
+
{
42
+
"name": "stdout",
43
+
"output_type": "stream",
44
+
"text": [
45
+
"2\n",
46
+
"4\n",
47
+
"12\n",
48
+
"44\n",
49
+
"176\n",
50
+
"788\n"
51
+
]
52
+
}
53
+
],
54
+
"source": [
55
+
"for c in c_nxns:\n",
56
+
" print(len(c))"
57
+
]
58
+
},
59
+
{
60
+
"cell_type": "code",
61
+
"execution_count": 4,
62
+
"id": "e7b26414-fcb6-48d3-a32b-56038dd54616",
63
+
"metadata": {},
64
+
"outputs": [
65
+
{
66
+
"name": "stdout",
67
+
"output_type": "stream",
68
+
"text": [
69
+
"2 2\n",
70
+
"3 4\n",
71
+
"4 8\n",
72
+
"5 20\n",
73
+
"6 50\n",
74
+
"7 130\n",
75
+
"8 362\n",
76
+
"9 1104\n",
77
+
"10 3614\n"
78
+
]
79
+
}
80
+
],
81
+
"source": [
82
+
"prev = set([(1,2), (2,1)])\n",
83
+
"counts2 = []\n",
84
+
"for i in range(2, 11):\n",
85
+
" print(i, len(prev))\n",
86
+
" counts2.append(prev)\n",
87
+
" nxt = [build_all_naive(lst, i + 1) for lst in prev]\n",
88
+
" prev = set()\n",
89
+
" for lsts in nxt:\n",
90
+
" for lst in lsts:\n",
91
+
" prev.add(tuple(lst))\n"
92
+
]
93
+
},
94
+
{
95
+
"cell_type": "code",
96
+
"execution_count": 11,
97
+
"id": "4aba47ce-3bab-4d7e-bcf0-160ad1fc49d0",
98
+
"metadata": {},
99
+
"outputs": [
100
+
{
101
+
"name": "stdout",
102
+
"output_type": "stream",
103
+
"text": [
104
+
"0 set()\n",
105
+
"0 set()\n",
106
+
"4 {(3, 4, 2, 1), (1, 4, 2, 3), (1, 2, 4, 3), (3, 2, 4, 1)}\n",
107
+
"24 {(1, 5, 4, 2, 3), (3, 1, 4, 5, 2), (3, 4, 2, 1, 5), (5, 1, 2, 4, 3), (1, 4, 3, 5, 2), (2, 5, 3, 4, 1), (5, 3, 2, 4, 1), (1, 5, 3, 2, 4), (2, 3, 5, 4, 1), (3, 5, 2, 1, 4), (3, 2, 4, 5, 1), (3, 5, 1, 4, 2), (4, 1, 2, 5, 3), (2, 5, 4, 1, 3), (4, 2, 3, 5, 1), (5, 1, 4, 2, 3), (1, 4, 5, 3, 2), (3, 5, 4, 1, 2), (2, 4, 1, 5, 3), (3, 4, 2, 5, 1), (3, 2, 4, 1, 5), (1, 4, 2, 3, 5), (1, 5, 2, 4, 3), (2, 1, 4, 5, 3)}\n"
108
+
]
109
+
}
110
+
],
111
+
"source": [
112
+
"for calc, built in list(zip(c_nxns, counts2))[:4]:\n",
113
+
" diffs = calc - built\n",
114
+
" print(len(diffs), diffs)"
115
+
]
116
+
},
117
+
{
118
+
"cell_type": "code",
119
+
"execution_count": 15,
120
+
"id": "b7fe429a-d95b-457f-9f74-f2bf547e00a5",
121
+
"metadata": {},
122
+
"outputs": [
123
+
{
124
+
"data": {
125
+
"text/plain": [
126
+
"[[1, 4, 2, 3], [1, 2, 4, 3]]"
127
+
]
128
+
},
129
+
"execution_count": 15,
130
+
"metadata": {},
131
+
"output_type": "execute_result"
132
+
}
133
+
],
134
+
"source": [
135
+
"build_all_naive([1,2,3], 4)"
136
+
]
137
+
},
138
+
{
139
+
"cell_type": "code",
140
+
"execution_count": 14,
141
+
"id": "7be18ac1-4eda-4e8a-b719-d92ac551c2bb",
142
+
"metadata": {},
143
+
"outputs": [],
144
+
"source": [
145
+
"fours = counts2[2]"
146
+
]
147
+
},
148
+
{
149
+
"cell_type": "code",
150
+
"execution_count": 16,
151
+
"id": "8fc81260-b4be-417b-ad6d-2f3ff452f41d",
152
+
"metadata": {},
153
+
"outputs": [],
154
+
"source": [
155
+
"fours |= {(3,4,2,1),(3,2,4,1),(1,4,2,3),(1,2,4,3)}"
156
+
]
157
+
},
158
+
{
159
+
"cell_type": "code",
160
+
"execution_count": 17,
161
+
"id": "6ec26162-7d61-4adb-9468-c68285469943",
162
+
"metadata": {},
163
+
"outputs": [
164
+
{
165
+
"data": {
166
+
"text/plain": [
167
+
"{(1, 2, 4, 3),\n",
168
+
" (1, 3, 4, 2),\n",
169
+
" (1, 4, 2, 3),\n",
170
+
" (2, 1, 3, 4),\n",
171
+
" (2, 3, 1, 4),\n",
172
+
" (2, 4, 3, 1),\n",
173
+
" (3, 1, 2, 4),\n",
174
+
" (3, 2, 4, 1),\n",
175
+
" (3, 4, 2, 1),\n",
176
+
" (4, 1, 3, 2),\n",
177
+
" (4, 2, 1, 3),\n",
178
+
" (4, 3, 1, 2)}"
179
+
]
180
+
},
181
+
"execution_count": 17,
182
+
"metadata": {},
183
+
"output_type": "execute_result"
184
+
}
185
+
],
186
+
"source": [
187
+
"fours"
188
+
]
189
+
},
190
+
{
191
+
"cell_type": "code",
192
+
"execution_count": 18,
193
+
"id": "379d075a-e20b-47ca-9302-ebe09e465927",
194
+
"metadata": {},
195
+
"outputs": [],
196
+
"source": [
197
+
"nxt = [build_all_naive(lst, 5) for lst in fours]"
198
+
]
199
+
},
200
+
{
201
+
"cell_type": "code",
202
+
"execution_count": 21,
203
+
"id": "b60186ac-3842-49c9-bb21-dfb668a57781",
204
+
"metadata": {},
205
+
"outputs": [],
206
+
"source": [
207
+
"fives = set()\n",
208
+
"for lsts in nxt:\n",
209
+
" for lst in lsts:\n",
210
+
" fives.add(tuple(lst))"
211
+
]
212
+
},
213
+
{
214
+
"cell_type": "code",
215
+
"execution_count": 22,
216
+
"id": "797a0c23-2df7-44b1-aa74-8fbd2b9ccb3c",
217
+
"metadata": {},
218
+
"outputs": [
219
+
{
220
+
"data": {
221
+
"text/plain": [
222
+
"30"
223
+
]
224
+
},
225
+
"execution_count": 22,
226
+
"metadata": {},
227
+
"output_type": "execute_result"
228
+
}
229
+
],
230
+
"source": [
231
+
"len(fives)"
232
+
]
233
+
},
234
+
{
235
+
"cell_type": "code",
236
+
"execution_count": 27,
237
+
"id": "378e0d4a-1000-4e56-b2f4-856e05690917",
238
+
"metadata": {},
239
+
"outputs": [],
240
+
"source": [
241
+
"leftovers = c_nxns[3] - fives"
242
+
]
243
+
},
244
+
{
245
+
"cell_type": "code",
246
+
"execution_count": 37,
247
+
"id": "0ea7a681-5d44-4cb5-a91b-e4d20ffd6095",
248
+
"metadata": {},
249
+
"outputs": [
250
+
{
251
+
"name": "stdout",
252
+
"output_type": "stream",
253
+
"text": [
254
+
"14\n"
255
+
]
256
+
},
257
+
{
258
+
"data": {
259
+
"text/plain": [
260
+
"{(1, 4, 3, 5, 2),\n",
261
+
" (1, 4, 5, 3, 2),\n",
262
+
" (1, 5, 3, 2, 4),\n",
263
+
" (2, 1, 4, 5, 3),\n",
264
+
" (2, 3, 5, 4, 1),\n",
265
+
" (2, 4, 1, 5, 3),\n",
266
+
" (2, 5, 3, 4, 1),\n",
267
+
" (2, 5, 4, 1, 3),\n",
268
+
" (3, 1, 4, 5, 2),\n",
269
+
" (3, 5, 1, 4, 2),\n",
270
+
" (3, 5, 2, 1, 4),\n",
271
+
" (3, 5, 4, 1, 2),\n",
272
+
" (4, 1, 2, 5, 3),\n",
273
+
" (4, 2, 3, 5, 1)}"
274
+
]
275
+
},
276
+
"execution_count": 37,
277
+
"metadata": {},
278
+
"output_type": "execute_result"
279
+
}
280
+
],
281
+
"source": [
282
+
"print(len(leftovers))\n",
283
+
"leftovers"
284
+
]
285
+
},
286
+
{
287
+
"cell_type": "code",
288
+
"execution_count": 35,
289
+
"id": "6b618d96-7e6c-4ba1-ab59-c008b0266683",
290
+
"metadata": {},
291
+
"outputs": [],
292
+
"source": [
293
+
"leftovers_four = set()\n",
294
+
"for lst in leftovers:\n",
295
+
" lst = list(filter(lambda x: x != 5, list(lst)))\n",
296
+
" leftovers_four.add(tuple(lst))"
297
+
]
298
+
},
299
+
{
300
+
"cell_type": "code",
301
+
"execution_count": 38,
302
+
"id": "f53549d3-56e1-4ae8-ae17-2c8ea4cea3e8",
303
+
"metadata": {},
304
+
"outputs": [
305
+
{
306
+
"name": "stdout",
307
+
"output_type": "stream",
308
+
"text": [
309
+
"10\n"
310
+
]
311
+
},
312
+
{
313
+
"data": {
314
+
"text/plain": [
315
+
"{(1, 3, 2, 4),\n",
316
+
" (1, 4, 3, 2),\n",
317
+
" (2, 1, 4, 3),\n",
318
+
" (2, 3, 4, 1),\n",
319
+
" (2, 4, 1, 3),\n",
320
+
" (3, 1, 4, 2),\n",
321
+
" (3, 2, 1, 4),\n",
322
+
" (3, 4, 1, 2),\n",
323
+
" (4, 1, 2, 3),\n",
324
+
" (4, 2, 3, 1)}"
325
+
]
326
+
},
327
+
"execution_count": 38,
328
+
"metadata": {},
329
+
"output_type": "execute_result"
330
+
}
331
+
],
332
+
"source": [
333
+
"print(len(leftovers_four))\n",
334
+
"leftovers_four"
335
+
]
336
+
},
337
+
{
338
+
"cell_type": "code",
339
+
"execution_count": 1,
340
+
"id": "e725f79c-10f4-454a-bf19-7fc6128f6991",
341
+
"metadata": {},
342
+
"outputs": [
343
+
{
344
+
"ename": "NameError",
345
+
"evalue": "name 'dataclass' is not defined",
346
+
"output_type": "error",
347
+
"traceback": [
348
+
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
349
+
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
350
+
"Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;129m@dataclass\u001b[39m\n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mclass\u001b[39;00m \u001b[38;5;21;01mMaybe\u001b[39;00m:\n\u001b[1;32m 3\u001b[0m x: \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtyping.Any\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m 4\u001b[0m empty: \u001b[38;5;28mbool\u001b[39m\n",
351
+
"\u001b[0;31mNameError\u001b[0m: name 'dataclass' is not defined"
352
+
]
353
+
}
354
+
],
355
+
"source": [
356
+
"class Maybe:\n",
357
+
" empty = True\n",
358
+
" def __init__(self, x) -> Maybe:\n",
359
+
" \n",
360
+
" def __sub__(self, other: Maybe) -> Maybe:\n",
361
+
" if self.empty:\n",
362
+
" return None\n",
363
+
" elif other.empty:\n",
364
+
" return None\n",
365
+
" else:\n",
366
+
" return self.x - other.x"
367
+
]
368
+
},
369
+
{
370
+
"cell_type": "code",
371
+
"execution_count": null,
372
+
"id": "e4ecb1bc-bf3e-4637-920b-eb5bd16d4dbb",
373
+
"metadata": {},
374
+
"outputs": [],
375
+
"source": []
376
+
}
377
+
],
378
+
"metadata": {
379
+
"kernelspec": {
380
+
"display_name": "Python 3 (ipykernel)",
381
+
"language": "python",
382
+
"name": "python3"
383
+
},
384
+
"language_info": {
385
+
"codemirror_mode": {
386
+
"name": "ipython",
387
+
"version": 3
388
+
},
389
+
"file_extension": ".py",
390
+
"mimetype": "text/x-python",
391
+
"name": "python",
392
+
"nbconvert_exporter": "python",
393
+
"pygments_lexer": "ipython3",
394
+
"version": "3.12.4"
395
+
}
396
+
},
397
+
"nbformat": 4,
398
+
"nbformat_minor": 5
399
+
}
+6
src/jupyter/.ipynb_checkpoints/sat-checkpoint.ipynb
+6
src/jupyter/.ipynb_checkpoints/sat-checkpoint.ipynb
+42
src/jupyter/.ipynb_checkpoints/search-checkpoint.jl
+42
src/jupyter/.ipynb_checkpoints/search-checkpoint.jl
···
1
+
import Pkg;
2
+
using Serialization
3
+
Pkg.add("Transducers")
4
+
using Transducers
5
+
Pkg.add("Primes")
6
+
using Primes
7
+
Pkg.add("Combinatorics")
8
+
using Combinatorics
9
+
10
+
function iscostashelper2(lst::Vector{T}, n::Integer)::Bool where T
11
+
all(begin
12
+
seen::Vector{Bool} = zeros(Bool, 2 * n)
13
+
all(begin
14
+
result = lst[i+k] - lst[i] + n
15
+
prev = seen[result]
16
+
seen[result] = true
17
+
!prev
18
+
end for i ∈ 1:(n - k))
19
+
end for k ∈ 1:n)
20
+
end
21
+
22
+
# Check if a sequence is a Costas sequence
23
+
function iscostas(lst::Vector{T})::Bool where T
24
+
length(unique(lst)) == length(lst) && iscostashelper2(lst, length(lst))
25
+
end
26
+
27
+
const START = 14
28
+
const LIMIT = 16
29
+
30
+
Threads.@threads for n in (START + 1):LIMIT
31
+
out = 1:n |> permutations |> Filter(iscostas) |> tcollect
32
+
file_path = "costas_$(n)x$n.dat"
33
+
serialize(file_path, out)
34
+
println("$file_path has $(length(out)) arrays.")
35
+
end
36
+
37
+
Threads.@threads for n in START:LIMIT
38
+
out = 2:n |> permutations |> Filter(iscostas) |> tcollect
39
+
file_path = "costas_$(n)x$(n + 1).dat"
40
+
serialize(file_path, out)
41
+
println("$file_path has $(length(out)) arrays.")
42
+
end