-
Notifications
You must be signed in to change notification settings - Fork 0
/
sudokuAnnealing.go
491 lines (391 loc) · 16.5 KB
/
sudokuAnnealing.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
/* ****************************************************************************
A simulated annealing algorithm to solve sudoku puzzles.
Copyright (c) 2016 Everett Robinson
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
Software without restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the
Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
* ****************************************************************************/
package main
import (
"bufio"
"flag"
"fmt"
"io"
"math"
"math/rand"
"os"
"strconv"
"strings"
"time"
)
// Modified from https://stackoverflow.com/questions/9862443/golang-is-there-a-better-way-read-a-file-of-integers-into-an-array
// Read in the start state of the sudoku puzzle (of arbitrary dimension) in a single line presentation.
func readInOneLine(r io.Reader, line int, delimiter string, emptyValue string, blockXDim int, blockYDim int) (puzzle [][]int, e error) {
scanner := bufio.NewScanner(r)
scanner.Split(bufio.ScanLines)
// Start puzzle at line 1 (more user friendly)
lineCounter := 1
// For each line
for scanner.Scan() {
// Check if it's the line we selected
if line == lineCounter {
// Read the puzzle text in and split it into it's components
puzzleText := scanner.Text()
puzzleElements := strings.Split(puzzleText, delimiter)
puzzleDim := blockXDim * blockYDim
puzzle = make([][]int, puzzleDim)
for i := 0; i < puzzleDim; i++ {
puzzle[i] = make([]int, puzzleDim)
for j := 0; j < puzzleDim; j++ {
element := puzzleElements[(i*puzzleDim)+j]
value, err := strconv.Atoi(element)
if err == nil {
puzzle[i][j] = value
} else if element == emptyValue {
puzzle[i][j] = 0
}
}
}
}
lineCounter++
}
return puzzle, scanner.Err()
}
// return the number of digits in an int up to 4. Sudoku puzzles of greater than
// 9999*9999 are probably not practical.
func numDigits(n int) int {
if n < 0 {
n = -1 * n
}
if n < 10 {
return 1
}
if n < 100 {
return 2
}
if n < 1000 {
return 3
}
return 4
}
func printPuzzle(puzzle [][]int, blockXDim int, blockYDim int) {
width := numDigits(blockXDim * blockYDim)
for r := range puzzle {
if r > 0 && r % blockYDim == 0 {
for i := 0; i < (blockXDim - 1) + (width + 2) * blockXDim * blockYDim; i++ {
fmt.Printf("%s", "-")
}
fmt.Println()
}
for c := range puzzle[r] {
if c > 0 && c % blockXDim == 0 {
fmt.Printf("|")
}
if puzzle[r][c] > 0 {
fmt.Printf("%-*s%d ", width - numDigits(puzzle[r][c]) + 1, " ", puzzle[r][c])
} else {
fmt.Printf("%-*s ", width + 1, " ")
}
}
fmt.Printf("\n")
}
}
// Starts n annealing goroutines at exponentially increasing temperatures 2^n where n is defined by the
// concurrentAnnealerCount value passed to the function. Once each annealing goroutine is returned any
// hotter goroutines with lower costs than their cooler neighbours will trade their candidate solutions
// with that neighbour.
func anneal(originalPuzzle [][]int, blockXDim int, blockYDim int, baseTemperature float64, coolingRate float64, internalIterations int, swapCount int, concurrentAnnealerCount int) (solvedPuzzle [][]int, solutionFound bool) {
initialSolution := randomInitialization(originalPuzzle)
baseTemperature = baseTemperature
finalTemperature := 0.00001
coolingRate = coolingRate
// Create a channel for the concurrent annealers of differing temperatures
annealerSolution := make(chan [][]int)
annealerCost := make(chan float64)
annealerSolutions := make([][][]int, concurrentAnnealerCount)
annealerCosts := make([]float64, concurrentAnnealerCount)
for i := 0; i < concurrentAnnealerCount; i++ {
annealerSolutions[i] = copyPuzzle(initialSolution)
annealerCosts[i] = costFunction(initialSolution, blockXDim, blockYDim)
}
// While the cost is not zero and we haven't hit our final temperature
for baseTemperature > finalTemperature {
for i := 0; i < concurrentAnnealerCount; i++ {
go annealerInternalIterator(originalPuzzle, annealerSolutions[i], blockXDim, blockYDim, baseTemperature*math.Pow(2, float64(i)), internalIterations, swapCount, annealerSolution, annealerCost)
annealerSolutions[i] = <- annealerSolution
annealerCosts[i] = <- annealerCost
}
// If a hotter goroutine has a better solution than a colder one then we swap the solutions
for i := concurrentAnnealerCount - 1; i > 0; i-- {
if annealerCosts[i] < annealerCosts[i-1] {
annealerSolutions[i], annealerSolutions[i-1] = annealerSolutions[i-1], annealerSolutions[i]
annealerCosts[i], annealerCosts[i-1] = annealerCosts[i-1], annealerCosts[i]
}
}
// If the coldest goroutine has cost zero then we have solved the puzzle
if annealerCosts[0] == 0 {
return annealerSolutions[0], true
}
// Cool all of the goroutines
baseTemperature = baseTemperature * coolingRate
}
return annealerSolutions[0], false
}
// Gets a neighbouring candidate solution and runs the probibalistic steps of the annealing process as many times as
// specified by the internalIterations count.
func annealerInternalIterator(originalPuzzle [][]int, candidateSolution [][]int, blockXDim int, blockYDim int, temperature float64, internalIterations int, swapCount int, as chan [][]int, ac chan float64) {
// Set updatedSolution and updatedCost to the current values associated with candidateSolution
updatedSolution := copyPuzzle(candidateSolution)
updatedCost := costFunction(updatedSolution, blockXDim, blockYDim)
for i := 0; i < internalIterations; i++ {
newCandidateSolution := getNeighbour(updatedSolution, swapCount, originalPuzzle)
newCandidateCost := costFunction(newCandidateSolution, blockXDim, blockYDim)
// If the cost is zero, then we found a viable solution. exit!
if newCandidateCost == 0 {
as <- newCandidateSolution
ac <- 0
return
}
// Otherwise, if the cost is less then switch to that solution
if newCandidateCost < updatedCost {
updatedSolution = newCandidateSolution
updatedCost = newCandidateCost
// And finally switch to a more costly solution randomly based on the acceptance probablity
} else {
ap := acceptanceProbability(updatedCost, newCandidateCost, temperature)
if ap > rand.Float64() {
updatedSolution = newCandidateSolution
updatedCost = newCandidateCost
}
}
}
as <- updatedSolution
ac <- updatedCost
return
}
// Gets a neighbouring candidate solution to the current one by randomly swapping two numbers in the puzzle.
// It also ensures that the neighbouring solution created does not modify or swap one of the clues in the
// original puzzle.
func getNeighbour(currentPuzzle [][]int, swapCount int, originalPuzzle [][]int) (neighbourPuzzle [][]int) {
puzzleDim := len(originalPuzzle)
// Copy the current puzzle into neighbourPuzzle
neighbourPuzzle = copyPuzzle(currentPuzzle)
for i := 0; i < swapCount; i++ {
randomXIndex1 := rand.Intn(puzzleDim)
randomYIndex1 := rand.Intn(puzzleDim)
randomXIndex2 := rand.Intn(puzzleDim)
randomYIndex2 := rand.Intn(puzzleDim)
// Keep randomly reassigning the index until we get one that wasn't defined in the
// original puzzle.
for originalPuzzle[randomXIndex1][randomYIndex1] > 0 {
randomXIndex1 = rand.Intn(puzzleDim)
randomYIndex1 = rand.Intn(puzzleDim)
}
for originalPuzzle[randomXIndex2][randomYIndex2] > 0 {
randomXIndex2 = rand.Intn(puzzleDim)
randomYIndex2 = rand.Intn(puzzleDim)
}
// Swap the two randomly selected elements
neighbourPuzzle[randomXIndex1][randomYIndex1], neighbourPuzzle[randomXIndex2][randomYIndex2] = neighbourPuzzle[randomXIndex2][randomYIndex2], neighbourPuzzle[randomXIndex1][randomYIndex1]
}
return neighbourPuzzle
}
// A cost function for the provided sudoku puzzle. The cost is defined as the sum over all rows, columns
// and blocks of the absolute difference between the occurances of a number in that row block or column
// and it's expected occurance of 1. A cost of zero for the whole puzzle indicates that it has been solved.
func costFunction(puzzle [][]int, blockXDim int, blockYDim int) (cost float64) {
// Figure out the full dimension of the puzzle from the passed block dimensions
puzzleDim := blockXDim * blockYDim
// Initialize the cost to zero
cost = 0.0
// For each row and column: (takes advantage of the square nature of the puzzle by swapping the
// two iterators)
for dim1 := 0; dim1 < puzzleDim; dim1++ {
// Create two slices to track the occurances of each number by row and by column.
// Numbers are shifted down by one, so 1 is stored in index 0, 2 in index 1, and so forth.
rowCounts := make([]int, puzzleDim, puzzleDim)
columnCounts := make([]int, puzzleDim, puzzleDim)
// For each entry in this row or column
for dim2 := 0; dim2 < puzzleDim; dim2++ {
// rows
if puzzle[dim1][dim2] > 0 {
number := puzzle[dim1][dim2]
rowCounts[number-1]++
}
// columns
if puzzle[dim2][dim1] > 0 {
number := puzzle[dim2][dim1]
columnCounts[number-1]++
}
}
// Figure out the cost for this row
for _, count := range rowCounts {
cost += math.Abs(float64(count - 1))
}
// And the cost for this column
for _, count := range columnCounts {
cost += math.Abs(float64(count - 1))
}
}
// Also figure out the cost for each block in the puzzle (puzzleDim = number of blocks)
horizontalBlockCount := blockYDim
verticalBlockCount := blockXDim
// For each block in the horizontal
for i := 0; i < horizontalBlockCount; i++ {
// For each block in the vertical
for j := 0; j < verticalBlockCount; j++ {
// Keep track of the occurances of each number for the given block
blockCounts := make([]int, puzzleDim, puzzleDim)
for k := 0; k < puzzleDim; k++ {
horizontalIndex := i * blockXDim + k % blockXDim
verticalIndex := j * blockYDim + k / blockXDim
if puzzle[horizontalIndex][verticalIndex] > 0 {
number := puzzle[horizontalIndex][verticalIndex]
blockCounts[number-1]++
}
}
// The cost for this block
for _, count := range blockCounts {
cost += math.Abs(float64(count - 1))
}
}
}
return cost
}
func acceptanceProbability(oldCost float64, newCost float64, temperature float64) (probability float64) {
return math.Exp((oldCost - newCost) / temperature)
}
// Randomly sets all blank values in the original puzzle to number within the
// dimension of the puzzle so the anneaing function has a complete (but incorrect)
// base to start from. It ensures that the occurances of each number is correct
// for the puzzle. Eg. for a standard sudoku, there will be 9 of each number.
func randomInitialization(originalPuzzle [][]int) (initializedPuzzle [][]int) {
puzzleDim := len(originalPuzzle)
remainingNumbers := make(map[int]int)
var emptySpots [][]int
emptySpots = make([][]int,0)
initializedPuzzle = make([][]int, puzzleDim)
// Set all of the remainingNumbers to the maximum possible (puzzleDim)
for i := 1; i <= puzzleDim; i++ {
remainingNumbers[i] = puzzleDim
}
// For each occurance of a number in the originalPuzzle, subtract one from
// remainingNumbers and duplicate it in the initializedPuzzle
for i := 0; i < puzzleDim; i++ {
initializedPuzzle[i] = make([]int, puzzleDim)
for j := 0; j < puzzleDim; j++ {
if originalPuzzle[i][j] > 0 {
remainingNumbers[originalPuzzle[i][j]]--
initializedPuzzle[i][j] = originalPuzzle[i][j]
} else {
emptySpots = append(emptySpots, []int{i, j})
}
}
}
// For every remaining number, randomly assign it to one of the remaining empty spots
// then delete that empty spot from the slice
for remainingNumber, count := range remainingNumbers {
for i := 0; i < count; i++ {
spotIndex := rand.Intn(len(emptySpots))
spot := emptySpots[spotIndex]
initializedPuzzle[spot[0]][spot[1]] = remainingNumber
emptySpots[spotIndex] = emptySpots[len(emptySpots)-1]
emptySpots = emptySpots[0 : len(emptySpots)-1]
}
}
return initializedPuzzle
}
func copyPuzzle(originalPuzzle [][]int) (copiedPuzzle [][]int) {
puzzleDim := len(originalPuzzle)
copiedPuzzle = make([][]int, puzzleDim, puzzleDim)
for i := 0; i < puzzleDim; i++ {
copiedPuzzle[i] = make([]int, puzzleDim, puzzleDim)
copy(copiedPuzzle[i], originalPuzzle[i])
}
return copiedPuzzle
}
func main() {
// Seed the random number generator for use throughout the program.
rand.Seed(time.Now().Unix())
start := time.Now()
inputModePtr := flag.String("m", "one-line", "An input mode used to interpret the input file")
delimiterPtr := flag.String("del", "", "The delimeter used to separate the puzzle squares in the input")
emptyValuePtr := flag.String("e", ".", "The character used to indicate an empty square in the puzzle")
dimPtr := flag.String("d", "3x3", "The dimensions of one of the puzzle blocks (eg. standard sudoku is 3x3)")
filePtr := flag.String("f", "puzzles.txt", "The filename to be checked")
linePtr := flag.String("l", "1", "The line of the puzzle to be solved")
temperaturePtr := flag.String("t", "1.0", "The lowest base temperature for the concurrent annealers (temperature increases by 2^i for each goroutine i)")
coolingRatePtr := flag.String("c", "0.9", "The rate of cooling for each step in the annealing process (a number greater than 0 and less than 1)")
iterationPtr := flag.String("i", "1000", "The number of iterations at each step of the annealing process")
swapPtr := flag.String("s", "1", "The number of swaps in each iteration of the anneling process")
concurrentAnnealerPtr := flag.String("a", "6", "The number of concurrent annealing goroutines")
trainingModePtr := flag.Bool("training-mode", false, "Enables a minimal output indicating only if a solution was found and how long that result took in seconds."+
" Intended for collecting data to determine the optimal combination of the other flags.")
flag.Parse()
puzzleLine, _ := strconv.Atoi(*linePtr)
puzzleDim := strings.Split(*dimPtr, "x")
baseTemperature, _ := strconv.ParseFloat(*temperaturePtr, 64)
coolingRate,_ := strconv.ParseFloat(*coolingRatePtr, 64)
internalIterations, _ := strconv.Atoi(*iterationPtr)
swapCount,_ := strconv.Atoi(*swapPtr)
annealerCount, _ := strconv.Atoi(*concurrentAnnealerPtr)
blockXDim, _ := strconv.Atoi(puzzleDim[0])
blockYDim, _ := strconv.Atoi(puzzleDim[1])
inFile, err := os.Open(*filePtr)
if err != nil {
fmt.Println(err)
os.Exit(1)
}
var originalPuzzle [][]int
if *inputModePtr == "one-line" {
// Read the file into an array
originalPuzzle, err = readInOneLine(inFile, puzzleLine, *delimiterPtr, *emptyValuePtr, blockXDim, blockYDim)
if err != nil {
fmt.Println(err)
os.Exit(1)
}
} else {
fmt.Println("No appropriate input mode for the puzzle was entered.")
os.Exit(1)
}
if !*trainingModePtr {
fmt.Println()
fmt.Println("Original Puzzle:")
printPuzzle(originalPuzzle, blockXDim, blockYDim)
fmt.Printf("\nPuzzle cost: %v\n", costFunction(originalPuzzle, blockXDim, blockYDim))
}
solvedPuzzle, successfullySolved := anneal(originalPuzzle, blockXDim, blockYDim, baseTemperature, coolingRate, internalIterations, swapCount, annealerCount)
if !*trainingModePtr {
if successfullySolved {
fmt.Println()
fmt.Println("Solved Puzzle:")
printPuzzle(solvedPuzzle, blockXDim, blockYDim)
} else {
fmt.Println()
fmt.Println("No viable solution to the puzzle was found.\n")
fmt.Printf("Final puzzle candidate:\n")
printPuzzle(solvedPuzzle, blockXDim, blockYDim)
fmt.Println()
fmt.Printf("Cost at end: %v\n\n", costFunction(solvedPuzzle, blockXDim, blockYDim))
}
}
elapsed := time.Since(start)
if !*trainingModePtr {
fmt.Printf("Execution completed in %s \n", elapsed)
} else {
// Return a csv line of the form
// puzzleLine, baseTemperature, coolingRate, internalIterations, swapCount, annealerCount, solved, time
fmt.Printf("%v,%v,%v,%v,%v,%v,%v,%v\n", puzzleLine, baseTemperature, coolingRate, internalIterations, swapCount, annealerCount, successfullySolved, elapsed.Seconds())
}
}