-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathyangs.html
More file actions
759 lines (682 loc) · 56.9 KB
/
yangs.html
File metadata and controls
759 lines (682 loc) · 56.9 KB
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
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="yangs---Yet-Another-NonoGram-Solver">yangs - Yet Another NonoGram Solver<a class="anchor-link" href="#yangs---Yet-Another-NonoGram-Solver">¶</a></h1>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Aim">Aim<a class="anchor-link" href="#Aim">¶</a></h2><p>Solve the first part of the GCHQ Christmas puzzle using a concise, easy-to-understand Python program.</p>
<h2 id="Method">Method<a class="anchor-link" href="#Method">¶</a></h2><p>The <a href="http://www.gchq.gov.uk/press_and_media/news_and_features/Pages/Directors-Christmas-puzzle-2015.aspx">puzzle</a> is a 25x25 <a href="https://en.wikipedia.org/wiki/Nonogram">nonogram</a>. I decided to write a program that uses the same method that I would use if solving the puzzle by hand:</p>
<ol>
<li>For each row and column, <strong>generate the set of patterns</strong> that match the given clues</li>
<li>For each row, <strong>eliminate the patterns</strong> that don't match the cells we already know</li>
<li>For each row, <strong>deduce the known cells</strong> based on the reduced pattern set</li>
<li>For each column, <strong>eliminate the patterns</strong> that don't match the cells we already know</li>
<li>For each column, <strong>deduce the known cells</strong> based on the reduced pattern set</li>
<li>Go back to 2. and repeat, unless we've solved it</li>
</ol>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Imports-and-settings">Imports and settings<a class="anchor-link" href="#Imports-and-settings">¶</a></h2>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [1]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">combinations_with_replacement</span>
<span class="n">SHOW_TESTS</span> <span class="o">=</span> <span class="bp">True</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Input-data">Input data<a class="anchor-link" href="#Input-data">¶</a></h2><p>Put all the clues into a list of lists:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [2]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">ROW_CLUES</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,],</span>
<span class="p">]</span>
<span class="n">COL_CLUES</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,],</span>
<span class="p">]</span>
<span class="n">ROW_LEN</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">COL_CLUES</span><span class="p">)</span>
<span class="n">COL_LEN</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ROW_CLUES</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Set up a grid to contain the result, and fill in the cells we already know.</p>
<p>Notes:</p>
<ul>
<li>I'm using 1 to represent a known filled cell, 0 for a known blank cell, and None for an unknown cell.</li>
<li>The rows must be repeated using list comprehension. Using list repetition <strong>(i.e. result = [[None] * ROW_LEN] * COL_LEN)</strong> would result in a list of references to the same row list.</li>
</ul>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [3]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="c"># Create blank results grid</span>
<span class="n">result</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">ROW_LEN</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">COL_LEN</span><span class="p">)]</span>
<span class="c"># Fill in the cells we already know</span>
<span class="n">known_coords</span> <span class="o">=</span> <span class="p">{</span><span class="mi">3</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">21</span><span class="p">),</span>
<span class="mi">8</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">14</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">18</span><span class="p">),</span>
<span class="mi">16</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">20</span><span class="p">),</span>
<span class="mi">21</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">21</span><span class="p">)</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">row</span><span class="p">,</span> <span class="n">cols</span> <span class="ow">in</span> <span class="n">known_coords</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">cols</span><span class="p">:</span>
<span class="n">result</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Helper-functions">Helper functions<a class="anchor-link" href="#Helper-functions">¶</a></h2><p>Define some functions to display the results:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [4]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">SYMBOLS</span> <span class="o">=</span> <span class="p">{</span><span class="bp">None</span><span class="p">:</span> <span class="s">'?'</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span><span class="s">'#'</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="s">'.'</span><span class="p">}</span>
<span class="k">def</span> <span class="nf">print_row</span><span class="p">(</span><span class="n">row</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="k">print</span> <span class="s">'</span><span class="si">%s</span><span class="s"> [</span><span class="si">%s</span><span class="s">]'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span> <span class="s">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">SYMBOLS</span><span class="p">[</span><span class="n">cell</span><span class="p">]</span> <span class="k">for</span> <span class="n">cell</span> <span class="ow">in</span> <span class="n">row</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">print_grid</span><span class="p">(</span><span class="n">rows</span><span class="p">):</span>
<span class="n">col_labels</span> <span class="o">=</span> <span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rows</span><span class="p">[</span><span class="mi">0</span><span class="p">]))]</span>
<span class="k">print</span> <span class="s">' '</span><span class="p">,</span> <span class="s">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">cl</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">cl</span> <span class="ow">in</span> <span class="n">col_labels</span><span class="p">)</span>
<span class="k">print</span> <span class="s">' '</span><span class="p">,</span> <span class="s">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">cl</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">cl</span> <span class="ow">in</span> <span class="n">col_labels</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">row</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">rows</span><span class="p">):</span>
<span class="n">print_row</span><span class="p">(</span><span class="n">row</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="c"># Test</span>
<span class="k">if</span> <span class="n">SHOW_TESTS</span><span class="p">:</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre> 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
1 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
2 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
3 [? ? ? # # ? ? ? ? ? ? ? # # ? ? ? ? ? ? ? # ? ? ?]
4 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
5 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
6 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
7 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
8 [? ? ? ? ? ? # # ? ? # ? ? ? # # ? ? # ? ? ? ? ? ?]
9 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
10 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
11 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
12 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
13 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
14 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
15 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
16 [? ? ? ? ? ? # ? ? ? ? # ? ? ? ? # ? ? ? # ? ? ? ?]
17 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
18 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
19 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
20 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
21 [? ? ? # # ? ? ? ? # # ? ? ? ? # ? ? ? ? # # ? ? ?]
22 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
23 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
24 [? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?]
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>And a function to count the number of unknown cells in the results. We'll use this to check if we've solved the puzzle, or if we're not making progress.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [5]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">count_unknowns</span><span class="p">(</span><span class="n">rows</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">row</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="bp">None</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">rows</span><span class="p">)</span>
<span class="c"># Test</span>
<span class="k">if</span> <span class="n">SHOW_TESTS</span><span class="p">:</span>
<span class="k">print</span> <span class="s">'Unknowns = </span><span class="si">%s</span><span class="s">'</span> <span class="o">%</span> <span class="n">count_unknowns</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>Unknowns = 603
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Generate-sets-of-patterns">Generate sets of patterns<a class="anchor-link" href="#Generate-sets-of-patterns">¶</a></h2><p>Terminology:</p>
<ul>
<li>Block = one or more consecutive filled cells</li>
<li>Space = an unfilled cell</li>
<li>Clue = the lengths of each block</li>
<li>Pattern = a series of cells that match the clue</li>
</ul>
<p>The <strong>generate_patterns</strong> function does step 1 of the general approach: give it the clue and the pattern length, and it generates all the possible patterns.</p>
<p>For the clue [7, 3, 1, 1, 7] and length = 25:</p>
<ul>
<li>There are 5 blocks, comprising 7 + 3 + 1 + 1 + 7 = 19 filled cells.</li>
<li>There are 6 <strong>positions</strong> where spaces can be inserted (numbered 0 through 5)</li>
<li>The middle 4 positions all must have at least one space - so there are 4 <strong>fixed spaces</strong></li>
<li>That means there are 25 - 19 - 4 = 2 <strong>movable spaces</strong>, which can go in any permutation of the 6 positions</li>
<li>Therefore, there are 6CR2 = 21 different patterns that match this clue</li>
</ul>
<table>
<thead><tr>
<th>position</th>
<th>0</th>
<th>1</th>
<th>1</th>
<th>2</th>
<th>2</th>
<th>3</th>
<th>3</th>
<th>4</th>
<th>4</th>
<th>5</th>
<th>5</th>
</tr>
</thead>
<tbody>
<tr>
<td>blocks and fixed spaces</td>
<td></td>
<td>1111111</td>
<td>0</td>
<td>111</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>1111111</td>
<td></td>
</tr>
<tr>
<td>movable spaces (any 2 of 6 positions)</td>
<td>?</td>
<td></td>
<td>?</td>
<td></td>
<td>?</td>
<td></td>
<td>?</td>
<td></td>
<td>?</td>
<td></td>
<td>?</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [6]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">generate_patterns</span><span class="p">(</span><span class="n">clue</span><span class="p">,</span> <span class="n">length</span><span class="p">):</span>
<span class="n">blocks</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">clue</span>
<span class="n">fixed_spaces</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">clue</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">positions</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">blocks</span><span class="p">))</span>
<span class="n">n_movable_spaces</span> <span class="o">=</span> <span class="n">length</span> <span class="o">-</span> <span class="nb">sum</span><span class="p">(</span><span class="n">clue</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">clue</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">space_positions</span> <span class="ow">in</span> <span class="n">combinations_with_replacement</span><span class="p">(</span><span class="n">positions</span><span class="p">,</span> <span class="n">n_movable_spaces</span><span class="p">):</span>
<span class="n">movable_spaces</span> <span class="o">=</span> <span class="p">[</span><span class="n">space_positions</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">positions</span><span class="p">]</span>
<span class="k">yield</span> <span class="nb">sum</span><span class="p">(([</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">fs</span> <span class="o">+</span> <span class="n">ms</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span><span class="p">,</span> <span class="n">fs</span><span class="p">,</span> <span class="n">ms</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="n">fixed_spaces</span><span class="p">,</span> <span class="n">movable_spaces</span><span class="p">)),</span> <span class="p">[])</span>
<span class="c"># Test</span>
<span class="k">if</span> <span class="n">SHOW_TESTS</span><span class="p">:</span>
<span class="n">test_pats</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">generate_patterns</span><span class="p">([</span><span class="mi">7</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span> <span class="mi">25</span><span class="p">))</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">test_pats</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre> 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [. . # # # # # # # . # # # . # . # . # # # # # # #]
1 [. # # # # # # # . . # # # . # . # . # # # # # # #]
2 [. # # # # # # # . # # # . . # . # . # # # # # # #]
3 [. # # # # # # # . # # # . # . . # . # # # # # # #]
4 [. # # # # # # # . # # # . # . # . . # # # # # # #]
5 [. # # # # # # # . # # # . # . # . # # # # # # # .]
6 [# # # # # # # . . . # # # . # . # . # # # # # # #]
7 [# # # # # # # . . # # # . . # . # . # # # # # # #]
8 [# # # # # # # . . # # # . # . . # . # # # # # # #]
9 [# # # # # # # . . # # # . # . # . . # # # # # # #]
10 [# # # # # # # . . # # # . # . # . # # # # # # # .]
11 [# # # # # # # . # # # . . . # . # . # # # # # # #]
12 [# # # # # # # . # # # . . # . . # . # # # # # # #]
13 [# # # # # # # . # # # . . # . # . . # # # # # # #]
14 [# # # # # # # . # # # . . # . # . # # # # # # # .]
15 [# # # # # # # . # # # . # . . . # . # # # # # # #]
16 [# # # # # # # . # # # . # . . # . . # # # # # # #]
17 [# # # # # # # . # # # . # . . # . # # # # # # # .]
18 [# # # # # # # . # # # . # . # . . . # # # # # # #]
19 [# # # # # # # . # # # . # . # . . # # # # # # # .]
20 [# # # # # # # . # # # . # . # . # # # # # # # . .]
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Eliminate-patterns">Eliminate patterns<a class="anchor-link" href="#Eliminate-patterns">¶</a></h2><p>The <strong>eliminate_patterns</strong> function does steps 2 and 4 of the general approach: give it a list of patterns, and it will eliminate the patterns that don't match the already-known cells.</p>
<p>Notes:</p>
<ul>
<li>The set of patterns is iterated in reverse order so that deleting an item won't change the indices of the items yet to be iterated.</li>
<li>The <strong>any</strong> function will short circuit as soon as it finds a cell in the pattern that conflicts with the known cells</li>
<li>I've used <strong>del patterns[i]</strong> instead of <strong>patterns.pop(i)</strong> because we don't need to do anything with the item after it's removed from the list</li>
</ul>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [7]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">eliminate_patterns</span><span class="p">(</span><span class="n">patterns</span><span class="p">,</span> <span class="n">knowns</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">patterns</span><span class="p">))):</span>
<span class="k">if</span> <span class="nb">any</span><span class="p">(</span><span class="n">k</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="bp">None</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span><span class="p">,</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">patterns</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">knowns</span><span class="p">)):</span>
<span class="k">del</span> <span class="n">patterns</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="c"># Test</span>
<span class="k">if</span> <span class="n">SHOW_TESTS</span><span class="p">:</span>
<span class="k">print</span> <span class="s">'Before:'</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">test_pats</span><span class="p">)</span>
<span class="k">print</span>
<span class="k">print</span> <span class="s">'Apply Knowns:'</span>
<span class="n">test_knowns</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">[</span><span class="bp">None</span><span class="p">]</span><span class="o">*</span><span class="mi">23</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">print_row</span><span class="p">(</span><span class="n">test_knowns</span><span class="p">)</span>
<span class="k">print</span>
<span class="k">print</span> <span class="s">'After:'</span>
<span class="n">eliminate_patterns</span><span class="p">(</span><span class="n">test_pats</span><span class="p">,</span> <span class="n">test_knowns</span><span class="p">)</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">test_pats</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>Before:
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [. . # # # # # # # . # # # . # . # . # # # # # # #]
1 [. # # # # # # # . . # # # . # . # . # # # # # # #]
2 [. # # # # # # # . # # # . . # . # . # # # # # # #]
3 [. # # # # # # # . # # # . # . . # . # # # # # # #]
4 [. # # # # # # # . # # # . # . # . . # # # # # # #]
5 [. # # # # # # # . # # # . # . # . # # # # # # # .]
6 [# # # # # # # . . . # # # . # . # . # # # # # # #]
7 [# # # # # # # . . # # # . . # . # . # # # # # # #]
8 [# # # # # # # . . # # # . # . . # . # # # # # # #]
9 [# # # # # # # . . # # # . # . # . . # # # # # # #]
10 [# # # # # # # . . # # # . # . # . # # # # # # # .]
11 [# # # # # # # . # # # . . . # . # . # # # # # # #]
12 [# # # # # # # . # # # . . # . . # . # # # # # # #]
13 [# # # # # # # . # # # . . # . # . . # # # # # # #]
14 [# # # # # # # . # # # . . # . # . # # # # # # # .]
15 [# # # # # # # . # # # . # . . . # . # # # # # # #]
16 [# # # # # # # . # # # . # . . # . . # # # # # # #]
17 [# # # # # # # . # # # . # . . # . # # # # # # # .]
18 [# # # # # # # . # # # . # . # . . . # # # # # # #]
19 [# # # # # # # . # # # . # . # . . # # # # # # # .]
20 [# # # # # # # . # # # . # . # . # # # # # # # . .]
Apply Knowns:
0 [# ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? #]
After:
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [# # # # # # # . . . # # # . # . # . # # # # # # #]
1 [# # # # # # # . . # # # . . # . # . # # # # # # #]
2 [# # # # # # # . . # # # . # . . # . # # # # # # #]
3 [# # # # # # # . . # # # . # . # . . # # # # # # #]
4 [# # # # # # # . # # # . . . # . # . # # # # # # #]
5 [# # # # # # # . # # # . . # . . # . # # # # # # #]
6 [# # # # # # # . # # # . . # . # . . # # # # # # #]
7 [# # # # # # # . # # # . # . . . # . # # # # # # #]
8 [# # # # # # # . # # # . # . . # . . # # # # # # #]
9 [# # # # # # # . # # # . # . # . . . # # # # # # #]
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Deduce-known-cells">Deduce known cells<a class="anchor-link" href="#Deduce-known-cells">¶</a></h2><p>The <strong>generate_knowns</strong> function does steps 3 and 5 of the general approach: give it a set of patterns, and it will deduce which cells are now known.</p>
<p>For each cell, if all the patterns have the same value for each cell, then that is the only possible value for that cell.</p>
<p>Notes:</p>
<ul>
<li><strong>zip(*patterns)</strong> transposes the pattern set so that we check one column at a time instead of one row a time</li>
<li>the <strong>all</strong> function will short circuit as soon as it finds a cell that doesn't match the cell in first pattern</li>
</ul>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [8]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">generate_knowns</span><span class="p">(</span><span class="n">patterns</span><span class="p">):</span>
<span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">patterns</span><span class="p">):</span>
<span class="k">yield</span> <span class="n">col</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">c</span> <span class="o">==</span> <span class="n">col</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">col</span><span class="p">)</span> <span class="k">else</span> <span class="bp">None</span>
<span class="c"># Test</span>
<span class="k">if</span> <span class="n">SHOW_TESTS</span><span class="p">:</span>
<span class="k">print</span> <span class="s">'Patterns:'</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">test_pats</span><span class="p">)</span>
<span class="k">print</span>
<span class="k">print</span> <span class="s">'Knowns:'</span>
<span class="n">test_knowns</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">generate_knowns</span><span class="p">(</span><span class="n">test_pats</span><span class="p">))</span>
<span class="n">print_row</span><span class="p">(</span><span class="n">test_knowns</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>Patterns:
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [# # # # # # # . . . # # # . # . # . # # # # # # #]
1 [# # # # # # # . . # # # . . # . # . # # # # # # #]
2 [# # # # # # # . . # # # . # . . # . # # # # # # #]
3 [# # # # # # # . . # # # . # . # . . # # # # # # #]
4 [# # # # # # # . # # # . . . # . # . # # # # # # #]
5 [# # # # # # # . # # # . . # . . # . # # # # # # #]
6 [# # # # # # # . # # # . . # . # . . # # # # # # #]
7 [# # # # # # # . # # # . # . . . # . # # # # # # #]
8 [# # # # # # # . # # # . # . . # . . # # # # # # #]
9 [# # # # # # # . # # # . # . # . . . # # # # # # #]
Knowns:
0 [# # # # # # # . ? ? # ? ? ? ? ? ? . # # # # # # #]
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Solve-it">Solve it<a class="anchor-link" href="#Solve-it">¶</a></h2><p>Do step 1: generate sets of patterns that match the clues given for each row and column.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [9]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">rows_valid_patterns</span> <span class="o">=</span> <span class="p">[</span><span class="nb">list</span><span class="p">(</span><span class="n">generate_patterns</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ROW_LEN</span><span class="p">))</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">ROW_CLUES</span><span class="p">]</span>
<span class="n">cols_valid_patterns</span> <span class="o">=</span> <span class="p">[</span><span class="nb">list</span><span class="p">(</span><span class="n">generate_patterns</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">COL_LEN</span><span class="p">))</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">COL_CLUES</span><span class="p">]</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Calculate how many unknowns there are before we start trying to solve:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [10]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">unknowns</span> <span class="o">=</span> <span class="p">[</span><span class="n">count_unknowns</span><span class="p">(</span><span class="n">result</span><span class="p">)]</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Repeat through steps 2-5 until either:</p>
<ul>
<li>There are no more unknowns i.e. we've solved it</li>
<li>The number of unknowns hasn't decreased since the last pass i.e. we've solved as much as possible</li>
</ul>
<p>Notes:</p>
<ul>
<li><strong>map</strong> is used to apply <strong>eliminate_patterns</strong> and <strong>generate_knowns</strong> to multiple rows/columns</li>
<li><strong>zip(*)</strong> is used to transpose the <strong>results</strong> grid when working on columns, and transpose it back again before working on rows</li>
</ul>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [11]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">unknowns</span><span class="p">)</span> <span class="o"><</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">unknowns</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">unknowns</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">]):</span>
<span class="nb">map</span><span class="p">(</span><span class="n">eliminate_patterns</span><span class="p">,</span> <span class="n">rows_valid_patterns</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">generate_knowns</span><span class="p">,</span> <span class="n">rows_valid_patterns</span><span class="p">)</span>
<span class="nb">map</span><span class="p">(</span><span class="n">eliminate_patterns</span><span class="p">,</span> <span class="n">cols_valid_patterns</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">result</span><span class="p">))</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="nb">map</span><span class="p">(</span><span class="n">generate_knowns</span><span class="p">,</span> <span class="n">cols_valid_patterns</span><span class="p">))</span>
<span class="n">unknowns</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">count_unknowns</span><span class="p">(</span><span class="n">result</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Display the results:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [12]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">u</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">unknowns</span><span class="p">):</span>
<span class="k">print</span> <span class="s">'pass </span><span class="si">%s</span><span class="s">: </span><span class="si">%s</span><span class="s"> unknowns'</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
<span class="n">print_grid</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre>pass 0: 603 unknowns
pass 1: 317 unknowns
pass 2: 58 unknowns
pass 3: 10 unknowns
pass 4: 0 unknowns
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
0 [# # # # # # # . # # # . . . # . # . # # # # # # #]
1 [# . . . . . # . # # . # # . . . . . # . . . . . #]
2 [# . # # # . # . . . . . # # # . # . # . # # # . #]
3 [# . # # # . # . # . . # # # # # # . # . # # # . #]
4 [# . # # # . # . . # # # # # . # # . # . # # # . #]
5 [# . . . . . # . . # # . . . . . . . # . . . . . #]
6 [# # # # # # # . # . # . # . # . # . # # # # # # #]
7 [. . . . . . . . # # # . . . # # # . . . . . . . .]
8 [# . # # . # # # . . # . # . # # # . # . . # . # #]
9 [# . # . . . . . . # # # . # # . . . . # . . . # .]
10 [. # # # # . # . # # # # . # # . # . . . . # # . .]
11 [. # . # . . . # . . . # . # . # # # # . # . # # #]
12 [. . # # . . # . # . # . . . . . . # # . # # # # #]
13 [. . . # # # . # # . # # . # # # # # # . # # # . #]
14 [# . # # # # # # # # # . # . # . . # # . . . . # .]
15 [. # # . # . . # # . . . # # . # # # . . . . . # .]
16 [# # # . # . # . # . . # . . . . # # # # # . # . .]
17 [. . . . . . . . # . . . # # . # # . . . # # # # #]
18 [# # # # # # # . # . . # # . . . # . # . # . # # #]
19 [# . . . . . # . # # . . # . . # # . . . # # . # .]
20 [# . # # # . # . . . # # # # . . # # # # # . . # .]
21 [# . # # # . # . # # # . # # # # # # # # # # . # #]
22 [# . # # # . # . # . . # # # # # # . # # # # # # .]
23 [# . . . . . # . . # # . . . . . . # . # . # # . .]
24 [# # # # # # # . # # . . . # . # # . . . # # # # #]
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre>
</pre></div>
</div>
</div>
</div>
</div>