-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathindex.html
More file actions
2389 lines (1030 loc) · 176 KB
/
index.html
File metadata and controls
2389 lines (1030 loc) · 176 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
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html class="theme-next muse use-motion" lang="zh-cn">
<head>
<meta charset="UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"/>
<meta name="theme-color" content="#222">
<meta http-equiv="Cache-Control" content="no-transform" />
<meta http-equiv="Cache-Control" content="no-siteapp" />
<link href="/lib/fancybox/source/jquery.fancybox.css?v=2.1.5" rel="stylesheet" type="text/css" />
<link href="/lib/font-awesome/css/font-awesome.min.css?v=4.6.2" rel="stylesheet" type="text/css" />
<link href="/css/main.css?v=5.1.4" rel="stylesheet" type="text/css" />
<link rel="apple-touch-icon" sizes="180x180" href="/images/poker.png?v=5.1.4">
<link rel="icon" type="image/png" sizes="32x32" href="/images/poker.png?v=5.1.4">
<link rel="icon" type="image/png" sizes="16x16" href="/images/poker.png?v=5.1.4">
<link rel="mask-icon" href="/images/logo.svg?v=5.1.4" color="#222">
<meta name="keywords" content="Hexo, NexT" />
<meta property="og:type" content="website">
<meta property="og:title" content="RedJACK">
<meta property="og:url" content="https://jacksalad.github.io/index.html">
<meta property="og:site_name" content="RedJACK">
<meta property="og:locale" content="zh_CN">
<meta property="article:author" content="Jack">
<meta name="twitter:card" content="summary">
<script type="text/javascript" id="hexo.configurations">
var NexT = window.NexT || {};
var CONFIG = {
root: '',
scheme: 'Muse',
version: '5.1.4',
sidebar: {"position":"left","display":"post","offset":12,"b2t":false,"scrollpercent":false,"onmobile":false},
fancybox: true,
tabs: true,
motion: {"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideUpIn"}},
duoshuo: {
userId: '0',
author: 'Author'
},
algolia: {
applicationID: '',
apiKey: '',
indexName: '',
hits: {"per_page":10},
labels: {"input_placeholder":"Search for Posts","hits_empty":"We didn't find any results for the search: ${query}","hits_stats":"${hits} results found in ${time} ms"}
}
};
</script>
<link rel="canonical" href="https://jacksalad.github.io/"/>
<title>RedJACK</title>
<meta name="generator" content="Hexo 6.2.0"></head>
<body itemscope itemtype="http://schema.org/WebPage" lang="zh-cn">
<div class="container sidebar-position-left
page-home">
<div class="headband"></div>
<header id="header" class="header" itemscope itemtype="http://schema.org/WPHeader">
<div class="header-inner"><div class="site-brand-wrapper">
<div class="site-meta ">
<div class="custom-logo-site-title">
<a href="/" class="brand" rel="start">
<span class="logo-line-before"><i></i></span>
<span class="site-title">RedJACK</span>
<span class="logo-line-after"><i></i></span>
</a>
</div>
<p class="site-subtitle">一个乐于使用技术手段探索世界本质的计算机爱好者</p>
</div>
<div class="site-nav-toggle">
<button>
<span class="btn-bar"></span>
<span class="btn-bar"></span>
<span class="btn-bar"></span>
</button>
</div>
</div>
<nav class="site-nav">
<ul id="menu" class="menu">
<li class="menu-item menu-item-home">
<a href="/" rel="section">
<i class="menu-item-icon fa fa-fw fa-home"></i> <br />
Home
</a>
</li>
<li class="menu-item menu-item-about">
<a href="/about/" rel="section">
<i class="menu-item-icon fa fa-fw fa-user"></i> <br />
About
</a>
</li>
<li class="menu-item menu-item-archives">
<a href="/archives/" rel="section">
<i class="menu-item-icon fa fa-fw fa-archive"></i> <br />
Archives
</a>
</li>
<li class="menu-item menu-item-categories">
<a href="/categories/" rel="section">
<i class="menu-item-icon fa fa-fw fa-th"></i> <br />
Categories
</a>
</li>
<li class="menu-item menu-item-tags">
<a href="/tags/" rel="section">
<i class="menu-item-icon fa fa-fw fa-tags"></i> <br />
Tags
</a>
</li>
<li class="menu-item menu-item-schedule">
<a href="/schedule/" rel="section">
<i class="menu-item-icon fa fa-fw fa-calendar"></i> <br />
Schedule
</a>
</li>
</ul>
</nav>
</div>
</header>
<main id="main" class="main">
<div class="main-inner">
<div class="content-wrap">
<div id="content" class="content">
<section id="posts" class="posts-expand">
<article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
<div class="post-block">
<link itemprop="mainEntityOfPage" href="https://jacksalad.github.io/2022/11/02/%E6%8E%A8%E4%BC%98%E7%AB%9E%E9%80%89%E5%8F%91%E8%A8%80%E7%A8%BF/">
<span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
<meta itemprop="name" content="">
<meta itemprop="description" content="">
<meta itemprop="image" content="https://s1.ax1x.com/2022/07/12/jc4sDx.png">
</span>
<span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
<meta itemprop="name" content="RedJACK">
</span>
<header class="post-header">
<h1 class="post-title" itemprop="name headline">
<a class="post-title-link" href="/2022/11/02/%E6%8E%A8%E4%BC%98%E7%AB%9E%E9%80%89%E5%8F%91%E8%A8%80%E7%A8%BF/" itemprop="url">院级优秀学生推优竞选发言稿</a></h1>
<div class="post-meta">
<span class="post-time">
<span class="post-meta-item-icon">
<i class="fa fa-calendar-o"></i>
</span>
<span class="post-meta-item-text">Posted on</span>
<time title="Post created" itemprop="dateCreated datePublished" datetime="2022-11-02T16:53:14+08:00">
2022-11-02
</time>
</span>
<span class="post-category" >
<span class="post-meta-divider">|</span>
<span class="post-meta-item-icon">
<i class="fa fa-folder-o"></i>
</span>
<span class="post-meta-item-text">In</span>
<span itemprop="about" itemscope itemtype="http://schema.org/Thing">
<a href="/categories/%E7%94%9F%E6%B4%BB/" itemprop="url" rel="index">
<span itemprop="name">生活</span>
</a>
</span>
</span>
</div>
</header>
<div class="post-body" itemprop="articleBody">
这是一篇加密博文
<!--noindex-->
<div class="post-button text-center">
<a class="btn" href="/2022/11/02/%E6%8E%A8%E4%BC%98%E7%AB%9E%E9%80%89%E5%8F%91%E8%A8%80%E7%A8%BF/#more" rel="contents">
Read more »
</a>
</div>
<!--/noindex-->
</div>
<footer class="post-footer">
<div class="post-eof"></div>
</footer>
</div>
</article>
<article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
<div class="post-block">
<link itemprop="mainEntityOfPage" href="https://jacksalad.github.io/2022/08/11/LeetCode%20%E5%88%B7%E9%A2%98%E7%AC%94%E8%AE%B0%20-%20749.%20%E9%9A%94%E7%A6%BB%E7%97%85%E6%AF%92%20-%20%E6%A8%A1%E6%8B%9F%20+%20%E6%90%9C%E7%B4%A2/">
<span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
<meta itemprop="name" content="">
<meta itemprop="description" content="">
<meta itemprop="image" content="https://s1.ax1x.com/2022/07/12/jc4sDx.png">
</span>
<span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
<meta itemprop="name" content="RedJACK">
</span>
<header class="post-header">
<h1 class="post-title" itemprop="name headline">
<a class="post-title-link" href="/2022/08/11/LeetCode%20%E5%88%B7%E9%A2%98%E7%AC%94%E8%AE%B0%20-%20749.%20%E9%9A%94%E7%A6%BB%E7%97%85%E6%AF%92%20-%20%E6%A8%A1%E6%8B%9F%20+%20%E6%90%9C%E7%B4%A2/" itemprop="url">LeetCode刷题笔记-749. 隔离病毒-模拟+搜索</a></h1>
<div class="post-meta">
<span class="post-time">
<span class="post-meta-item-icon">
<i class="fa fa-calendar-o"></i>
</span>
<span class="post-meta-item-text">Posted on</span>
<time title="Post created" itemprop="dateCreated datePublished" datetime="2022-08-11T21:10:44+08:00">
2022-08-11
</time>
</span>
<span class="post-category" >
<span class="post-meta-divider">|</span>
<span class="post-meta-item-icon">
<i class="fa fa-folder-o"></i>
</span>
<span class="post-meta-item-text">In</span>
<span itemprop="about" itemscope itemtype="http://schema.org/Thing">
<a href="/categories/%E7%AE%97%E6%B3%95/" itemprop="url" rel="index">
<span itemprop="name">算法</span>
</a>
</span>
</span>
</div>
</header>
<div class="post-body" itemprop="articleBody">
<blockquote>
<p>原文地址 <a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/549633877">zhuanlan.zhihu.com</a></p>
</blockquote>
<h2 id="题目描述"><a href="#题目描述" class="headerlink" title="题目描述"></a>题目描述</h2><h3 id="749-隔离病毒-困难"><a href="#749-隔离病毒-困难" class="headerlink" title="749. 隔离病毒 困难"></a><a href="https://link.zhihu.com/?target=https://leetcode.cn/problems/contain-virus/">749. 隔离病毒</a> 困难</h3><p>病毒扩散得很快，现在你的任务是尽可能地通过安装防火墙来隔离病毒。</p>
<p>假设世界由 <code>m x n</code> 的二维矩阵 <code>isInfected</code> 组成， <code>isInfected[i][j] == 0</code> 表示该区域未感染病毒，而 <code>isInfected[i][j] == 1</code> 表示该区域已感染病毒。可以在任意 2 个相邻单元之间的共享边界上安装一个防火墙（并且只有一个防火墙）。</p>
<p>每天晚上，病毒会从被感染区域向相邻未感染区域扩散，除非被防火墙隔离。现由于资源有限，每天你只能安装一系列防火墙来隔离其中一个被病毒感染的区域（一个区域或连续的一片区域），且该感染区域对未感染区域的威胁最大且 保证唯一 。</p>
<p>你需要努力使得最后有部分区域不被病毒感染，如果可以成功，那么返回需要使用的防火墙个数; 如果无法实现，则返回在世界被病毒全部感染时已安装的防火墙个数。</p>
<p><strong>示例 1：</strong></p>
<p><img src="https://pic1.zhimg.com/v2-d1f3cf1c7135222996087a5b23d5b8e4_r.jpg"></p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line">输入: isInfected = [[0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0]]</span><br><span class="line">输出: 10</span><br><span class="line">解释:一共有两块被病毒感染的区域。</span><br><span class="line">在第一天，添加 5 墙隔离病毒区域的左侧。</span><br><span class="line">第二天，在右侧添加 5 个墙来隔离病毒区域。此时病毒已经被完全控制住了。</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<p><img src="https://pic2.zhimg.com/v2-08a40d7ae84a0f37ac9ee2774ed5e11d_r.jpg"></p>
<p><strong>示例 2：</strong></p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">输入: isInfected = [[1,1,1],[1,0,1],[1,1,1]]</span><br><span class="line">输出: 4</span><br><span class="line">解释: 虽然只保存了一个小区域，但却有四面墙。</span><br><span class="line">注意，防火墙只建立在两个不同区域的共享边界上。</span><br></pre></td></tr></table></figure>
<p><img src="https://pic1.zhimg.com/v2-10fd45217c0e1190fc290ae63c951c2c_r.jpg"></p>
<p><strong>示例 3:</strong></p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">输入: isInfected = [[1,1,1,0,0,0,0,0,0],[1,0,1,0,1,1,1,1,1],[1,1,1,0,0,0,0,0,0]]</span><br><span class="line">输出: 13</span><br><span class="line">解释: 在隔离右边感染区域后，隔离左边病毒区域只需要 2 个防火墙。</span><br></pre></td></tr></table></figure>
<h2 id="解题思路"><a href="#解题思路" class="headerlink" title="解题思路"></a>解题思路</h2><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">NoYes获取当天最大的感染面积区域和所需的防火墙数目对最大感染面积区域的病毒进行阻断消杀存活的病毒进行扩散处理所需防火墙数目是否为零?输出结果</span><br><span class="line"></span><br><span class="line"></span><br></pre></td></tr></table></figure>
<ul>
<li>获取最大的感染面积区域和所需的防火墙数目</li>
<li>对最大感染面积区域的病毒进行阻断消杀</li>
<li>存活的病毒进行扩散处理</li>
<li>重复上述步骤，直到所需防火墙为 0 为止</li>
</ul>
<h3 id="如何获取最大感染面积"><a href="#如何获取最大感染面积" class="headerlink" title="如何获取最大感染面积"></a>如何获取最大感染面积</h3><ul>
<li><p>先遍历到病毒区域</p>
</li>
<li><p>对对每个病毒区域进行搜索 </p>
</li>
<li><p>统计该区域可以感染的面积</p>
</li>
<li><p>统计该区域所需的防火墙</p>
</li>
<li><p>对当天最大病毒感染面积区域的病毒进行阻断消杀</p>
</li>
<li><p>对剩余病毒区域进行扩散处理</p>
</li>
</ul>
<p>其中状态数<code>s</code>需要特别注意，因为每一天一个位置可以有四个方向来感染，同时也可以有多个病毒区域来感染。因此要进行区分，这里就是通过状态数<code>s</code>来完成的。</p>
<p><img src="https://pic3.zhimg.com/v2-32d3dc217276f101a6afa4f4bfc44ae2_r.jpg"><img src="https://pic4.zhimg.com/v2-37ab420aa65de3584c54eff18f27c7ef_r.jpg"><img src="https://pic3.zhimg.com/v2-556c1ac12d16e6a00ac2a690471f33ee_r.jpg"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br></pre></td><td class="code"><pre><span class="line">func getMaxAreaNeedWalls() <span class="built_in">int</span> {</span><br><span class="line"> /*</span><br><span class="line"> m: 最大的感染面积</span><br><span class="line"> cnt: 当前最大感染面积的区域所需的防火墙数目</span><br><span class="line"> x,y: 病毒区域</span><br><span class="line"> s: 表示当前区域要修建墙的状态,并且每个区域的s都是不一样的，互相不能影响 DFS完给s-<span class="number">1</span></span><br><span class="line"> */</span><br><span class="line"> m, cnt, x, y, s := <span class="number">0</span>, <span class="number">0</span>, -<span class="number">1</span>, -<span class="number">1</span>, -<span class="number">3</span></span><br><span class="line"> vis := make([][]<span class="built_in">int</span>, r) // 访问标记数组</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> vis[i] = make([]<span class="built_in">int</span>, c)</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> <span class="keyword">for</span> j := <span class="number">0</span>; j < c; j++ {</span><br><span class="line"> // 找到没有访问的病毒区域</span><br><span class="line"> <span class="keyword">if</span> grid[i][j] == <span class="number">1</span> && vis[i][j] != <span class="number">1</span> {</span><br><span class="line"> //当前区域需要的防火墙数量</span><br><span class="line"> cur = <span class="number">0</span></span><br><span class="line"> //当前区域能感染的面积</span><br><span class="line"> temp := DFS(i, j, s, vis)</span><br><span class="line"> <span class="keyword">if</span> temp > m {</span><br><span class="line"> m = temp</span><br><span class="line"> cnt = cur</span><br><span class="line"> x, y = i, j</span><br><span class="line"> }</span><br><span class="line"> s-- // 区域状态数递减</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> // 没有病毒区域了只需<span class="number">0</span>个防火墙</span><br><span class="line"> <span class="keyword">if</span> x == -<span class="number">1</span> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span></span><br><span class="line"> }</span><br><span class="line"> // 对当天最大病毒感染面积区域的病毒进行阻断消杀</span><br><span class="line"> toDead(x, y)</span><br><span class="line"> // 重置访问数组</span><br><span class="line"> vis = make([][]<span class="built_in">int</span>, r)</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> vis[i] = make([]<span class="built_in">int</span>, c)</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> <span class="keyword">for</span> j := <span class="number">0</span>; j < c; j++ {</span><br><span class="line"> // 对剩余病毒区域进行扩散处理</span><br><span class="line"> <span class="keyword">if</span> grid[i][j] == <span class="number">1</span> && vis[i][j] != <span class="number">1</span> {</span><br><span class="line"> spread(i, j, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> // 返回最大感染面积区域所需的防火墙数目</span><br><span class="line"> <span class="keyword">return</span> cnt</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h3 id="如何进行阻断消杀"><a href="#如何进行阻断消杀" class="headerlink" title="如何进行阻断消杀"></a>如何进行阻断消杀</h3><ul>
<li>对该病毒区域的病毒进行死亡标记<code>grid[x][y] = -2</code></li>
<li>对病毒位置进行四个方向的 DFS 搜索，同时需要做访问标记。</li>
</ul>
<p><img src="https://pic3.zhimg.com/v2-9b234e9d10619d0bfb76deba9284439a_r.jpg"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line">func toDead(x, y <span class="built_in">int</span>) {</span><br><span class="line"> // 病毒消杀标记</span><br><span class="line"> grid[x][y] = -<span class="number">2</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> // 未越界且未访问且为病毒(状态转移)</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && grid[x_][y_] == <span class="number">1</span> {</span><br><span class="line"> toDead(x_, y_)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h3 id="如何进行扩散处理"><a href="#如何进行扩散处理" class="headerlink" title="如何进行扩散处理"></a>如何进行扩散处理</h3><ul>
<li>对当前病毒地点的四处进行 DFS 搜索。</li>
<li>如果为空，进行感染（边界条件）。</li>
<li>如果为病毒，继续搜索（状态转移）。</li>
</ul>
<p><img src="https://pic2.zhimg.com/v2-31b456fd0e8a22193607ac29dd49820d_r.jpg"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line">func spread(x, y <span class="built_in">int</span>, vis [][]<span class="built_in">int</span>) {</span><br><span class="line"> // 访问标记</span><br><span class="line"> vis[x][y] = <span class="number">1</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> // 未越界且未访问</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && vis[x_][y_] != <span class="number">1</span> {</span><br><span class="line"> <span class="keyword">if</span> grid[x_][y_] == <span class="number">0</span> { // 边界条件</span><br><span class="line"> grid[x_][y_] = <span class="number">1</span></span><br><span class="line"> vis[x_][y_] = <span class="number">1</span></span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> grid[x_][y_] == <span class="number">1</span> { // 状态转移</span><br><span class="line"> spread(x_, y_, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h3 id="如何对病毒区域搜索"><a href="#如何对病毒区域搜索" class="headerlink" title="如何对病毒区域搜索"></a>如何对病毒区域搜索</h3><ul>
<li>对当前病毒地点的四处进行 DFS 搜索。</li>
<li>如果为空，防火墙数<code>cur</code>（函数内的全局变量）自增，且未访问过的话感染面积自增（边界条件）。</li>
<li>如果为病毒，继续搜索（状态转移）。</li>
</ul>
<p><img src="https://pic2.zhimg.com/v2-d794731d4175cfe8b9931844a33e9935_r.jpg"></p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line">func DFS(x, y, s <span class="built_in">int</span>, vis [][]<span class="built_in">int</span>) <span class="built_in">int</span> {</span><br><span class="line"> // 当前病毒区域所感染面积</span><br><span class="line"> res := <span class="number">0</span></span><br><span class="line"> // 访问标记</span><br><span class="line"> vis[x][y] = <span class="number">1</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && vis[x_][y_] != <span class="number">1</span> {</span><br><span class="line"> // 未感染区域</span><br><span class="line"> <span class="keyword">if</span> grid[x_][y_] == <span class="number">0</span> {</span><br><span class="line"> cur++ // 防火墙数目递增</span><br><span class="line"> // 判断是否为该病毒区域访问过</span><br><span class="line"> <span class="keyword">if</span> vis[x_][y_] != s {</span><br><span class="line"> res++</span><br><span class="line"> vis[x_][y_] = s</span><br><span class="line"> }</span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> grid[x_][y_] == <span class="number">1</span> { // 感染区域(状态转移)</span><br><span class="line"> res += DFS(x_, y_, s, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h2 id="AC-代码（Go-语言）"><a href="#AC-代码（Go-语言）" class="headerlink" title="AC 代码（Go 语言）"></a>AC 代码（Go 语言）</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br></pre></td><td class="code"><pre><span class="line">// 方向数组</span><br><span class="line">var <span class="built_in">dir</span> [<span class="number">4</span>][<span class="number">2</span>]<span class="built_in">int</span> = [<span class="number">4</span>][<span class="number">2</span>]<span class="built_in">int</span>{{<span class="number">1</span>, <span class="number">0</span>}, {-<span class="number">1</span>, <span class="number">0</span>}, {<span class="number">0</span>, <span class="number">1</span>}, {<span class="number">0</span>, -<span class="number">1</span>}}</span><br><span class="line"></span><br><span class="line">func containVirus(grid [][]<span class="built_in">int</span>) <span class="built_in">int</span> {</span><br><span class="line"> /*</span><br><span class="line"> <span class="number">1.</span> 获取最大的感染面积区域和所需的防火墙数目</span><br><span class="line"> <span class="number">2.</span> 对最大感染面积区域的病毒进行阻断消杀</span><br><span class="line"> <span class="number">3.</span> 存活的病毒进行扩散处理</span><br><span class="line"> <span class="number">4.</span> 重复上述步骤，直到所需防火墙为<span class="number">0</span>为止</span><br><span class="line"> */</span><br><span class="line"> res := <span class="number">0</span> // 最终需要的防火墙数目</span><br><span class="line"> r, c := <span class="built_in">len</span>(grid), <span class="built_in">len</span>(grid[<span class="number">0</span>])</span><br><span class="line"> // 当前区域的防火墙临时数目</span><br><span class="line"> cur := <span class="number">0</span></span><br><span class="line"> // 对当前区域的防火墙内的病毒进行阻断消杀</span><br><span class="line"> var toDead func(<span class="built_in">int</span>, <span class="built_in">int</span>)</span><br><span class="line"> // 对未隔离的病毒进行扩散</span><br><span class="line"> var spread func(<span class="built_in">int</span>, <span class="built_in">int</span>, [][]<span class="built_in">int</span>)</span><br><span class="line"> // 对当前区域的扩散范围进行搜索并统计所需防火墙</span><br><span class="line"> var DFS func(<span class="built_in">int</span>, <span class="built_in">int</span>, <span class="built_in">int</span>, [][]<span class="built_in">int</span>) <span class="built_in">int</span></span><br><span class="line"> // 搜索一天内感染最大的区域所需要的防火墙数目</span><br><span class="line"> var getMaxAreaNeedWalls func() <span class="built_in">int</span></span><br><span class="line"></span><br><span class="line"> getMaxAreaNeedWalls = func() <span class="built_in">int</span> {</span><br><span class="line"> /*</span><br><span class="line"> m: 最大的感染面积</span><br><span class="line"> cnt: 当前最大感染面积的区域所需的防火墙数目</span><br><span class="line"> x,y: 病毒区域</span><br><span class="line"> s: 表示当前区域要修建墙的状态,并且每个区域的s都是不一样的，互相不能影响 DFS完给s-<span class="number">1</span></span><br><span class="line"> */</span><br><span class="line"> m, cnt, x, y, s := <span class="number">0</span>, <span class="number">0</span>, -<span class="number">1</span>, -<span class="number">1</span>, -<span class="number">3</span></span><br><span class="line"> vis := make([][]<span class="built_in">int</span>, r) // 访问标记数组</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> vis[i] = make([]<span class="built_in">int</span>, c)</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> <span class="keyword">for</span> j := <span class="number">0</span>; j < c; j++ {</span><br><span class="line"> // 找到没有访问的病毒区域</span><br><span class="line"> <span class="keyword">if</span> grid[i][j] == <span class="number">1</span> && vis[i][j] != <span class="number">1</span> {</span><br><span class="line"> //当前区域需要的防火墙数量</span><br><span class="line"> cur = <span class="number">0</span></span><br><span class="line"> //当前区域能感染的面积</span><br><span class="line"> temp := DFS(i, j, s, vis)</span><br><span class="line"> <span class="keyword">if</span> temp > m {</span><br><span class="line"> m = temp</span><br><span class="line"> cnt = cur</span><br><span class="line"> x, y = i, j</span><br><span class="line"> }</span><br><span class="line"> s-- // 区域状态数递减</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> // 没有病毒区域了只需<span class="number">0</span>个防火墙</span><br><span class="line"> <span class="keyword">if</span> x == -<span class="number">1</span> {</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span></span><br><span class="line"> }</span><br><span class="line"> // 对当天最大病毒感染面积区域的病毒进行阻断消杀</span><br><span class="line"> toDead(x, y)</span><br><span class="line"> // 重置访问数组</span><br><span class="line"> vis = make([][]<span class="built_in">int</span>, r)</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> vis[i] = make([]<span class="built_in">int</span>, c)</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < r; i++ {</span><br><span class="line"> <span class="keyword">for</span> j := <span class="number">0</span>; j < c; j++ {</span><br><span class="line"> // 对剩余病毒区域进行扩散处理</span><br><span class="line"> <span class="keyword">if</span> grid[i][j] == <span class="number">1</span> && vis[i][j] != <span class="number">1</span> {</span><br><span class="line"> spread(i, j, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> // 返回最大感染面积区域所需的防火墙数目</span><br><span class="line"> <span class="keyword">return</span> cnt</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> toDead = func(x, y <span class="built_in">int</span>) {</span><br><span class="line"> // 病毒消杀标记</span><br><span class="line"> grid[x][y] = -<span class="number">2</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> // 未越界且未访问且为病毒(状态转移)</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && grid[x_][y_] == <span class="number">1</span> {</span><br><span class="line"> toDead(x_, y_)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> spread = func(x, y <span class="built_in">int</span>, vis [][]<span class="built_in">int</span>) {</span><br><span class="line"> // 访问标记</span><br><span class="line"> vis[x][y] = <span class="number">1</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> // 未越界且未访问</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && vis[x_][y_] != <span class="number">1</span> {</span><br><span class="line"> <span class="keyword">if</span> grid[x_][y_] == <span class="number">0</span> { // 边界条件</span><br><span class="line"> grid[x_][y_] = <span class="number">1</span></span><br><span class="line"> vis[x_][y_] = <span class="number">1</span></span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> grid[x_][y_] == <span class="number">1</span> { // 状态转移</span><br><span class="line"> spread(x_, y_, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> DFS = func(x, y, s <span class="built_in">int</span>, vis [][]<span class="built_in">int</span>) <span class="built_in">int</span> {</span><br><span class="line"> // 当前病毒区域所感染面积</span><br><span class="line"> res := <span class="number">0</span></span><br><span class="line"> // 访问标记</span><br><span class="line"> vis[x][y] = <span class="number">1</span></span><br><span class="line"> // 四处搜索</span><br><span class="line"> <span class="keyword">for</span> i := <span class="number">0</span>; i < <span class="number">4</span>; i++ {</span><br><span class="line"> x_, y_ := x+<span class="built_in">dir</span>[i][<span class="number">0</span>], y+<span class="built_in">dir</span>[i][<span class="number">1</span>]</span><br><span class="line"> <span class="keyword">if</span> x_ >= <span class="number">0</span> && x_ < r && y_ >= <span class="number">0</span> && y_ < c && vis[x_][y_] != <span class="number">1</span> {</span><br><span class="line"> // 未感染区域</span><br><span class="line"> <span class="keyword">if</span> grid[x_][y_] == <span class="number">0</span> {</span><br><span class="line"> cur++ // 防火墙数目递增</span><br><span class="line"> // 判断是否为该病毒区域访问过</span><br><span class="line"> <span class="keyword">if</span> vis[x_][y_] != s {</span><br><span class="line"> res++</span><br><span class="line"> vis[x_][y_] = s</span><br><span class="line"> }</span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> grid[x_][y_] == <span class="number">1</span> { // 感染区域(状态转移)</span><br><span class="line"> res += DFS(x_, y_, s, vis)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span> { // 每次大循环模拟一整天</span><br><span class="line"> walls := getMaxAreaNeedWalls()</span><br><span class="line"> <span class="keyword">if</span> walls == <span class="number">0</span> {</span><br><span class="line"> <span class="keyword">break</span></span><br><span class="line"> }</span><br><span class="line"> res += walls // 统计当天最大感染区域所需防火墙数目</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res</span><br><span class="line">}</span><br></pre></td></tr></table></figure><script type="text/javascript" src="https://unpkg.com/kity@2.0.4/dist/kity.min.js"></script><script type="text/javascript" src="https://unpkg.com/kityminder-core@1.4.50/dist/kityminder.core.min.js"></script><script defer="true" type="text/javascript" src="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.js"></script><link rel="stylesheet" type="text/css" href="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.css">
</div>
<footer class="post-footer">
<div class="post-eof"></div>
</footer>
</div>
</article>
<article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
<div class="post-block">
<link itemprop="mainEntityOfPage" href="https://jacksalad.github.io/2022/07/25/%E7%94%A8%E6%A0%88%E8%A7%A3%E5%86%B3%E8%BF%B7%E5%AE%AB%E9%97%AE%E9%A2%98-Go%E8%AF%AD%E8%A8%80/">
<span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
<meta itemprop="name" content="">
<meta itemprop="description" content="">
<meta itemprop="image" content="https://s1.ax1x.com/2022/07/12/jc4sDx.png">
</span>
<span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
<meta itemprop="name" content="RedJACK">
</span>
<header class="post-header">
<h1 class="post-title" itemprop="name headline">
<a class="post-title-link" href="/2022/07/25/%E7%94%A8%E6%A0%88%E8%A7%A3%E5%86%B3%E8%BF%B7%E5%AE%AB%E9%97%AE%E9%A2%98-Go%E8%AF%AD%E8%A8%80/" itemprop="url">用栈解决迷宫问题-Go语言</a></h1>
<div class="post-meta">
<span class="post-time">
<span class="post-meta-item-icon">
<i class="fa fa-calendar-o"></i>
</span>
<span class="post-meta-item-text">Posted on</span>
<time title="Post created" itemprop="dateCreated datePublished" datetime="2022-07-25T17:02:46+08:00">
2022-07-25
</time>
</span>
<span class="post-category" >
<span class="post-meta-divider">|</span>
<span class="post-meta-item-icon">
<i class="fa fa-folder-o"></i>
</span>
<span class="post-meta-item-text">In</span>
<span itemprop="about" itemscope itemtype="http://schema.org/Thing">
<a href="/categories/Go/" itemprop="url" rel="index">
<span itemprop="name">Go</span>
</a>
</span>
</span>
</div>
</header>
<div class="post-body" itemprop="articleBody">
<blockquote>
<p>原文地址 <a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/499440732">zhuanlan.zhihu.com</a></p>
</blockquote>
<h1 id="用栈解决迷宫问题-Go语言"><a href="#用栈解决迷宫问题-Go语言" class="headerlink" title="用栈解决迷宫问题-Go语言"></a>用栈解决迷宫问题-Go语言</h1><h2 id="问题描述"><a href="#问题描述" class="headerlink" title="问题描述"></a>问题描述</h2><p><img src="https://s2.loli.net/2022/04/16/HmoLr1i3KMebsT5.png" alt="image-20220416010800925"></p>
<p>以上是一个迷宫，我们要从右上角的入口走到左下角的出口。现在要设计一个程序输出可走的路线，如果无法到达出口则输出不能。</p>
<h2 id="问题分析"><a href="#问题分析" class="headerlink" title="问题分析"></a>问题分析</h2><p>对于以上的迷宫图我们要用一个二维数组进行模拟：</p>
<p><img src="https://s2.loli.net/2022/04/16/aU9jHPdOS48i6Vn.png" alt="code"></p>
<figure class="highlight go"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">const</span> N, M = <span class="number">8</span>, <span class="number">8</span> <span class="comment">// 迷宫大小</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// 迷宫图</span></span><br><span class="line"><span class="keyword">var</span> mg [N + <span class="number">2</span>][M + <span class="number">2</span>]<span class="type">int</span> = [N + <span class="number">2</span>][M + <span class="number">2</span>]<span class="type">int</span>{</span><br><span class="line"> {<span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>},</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<p>首先要声明一个位置向量结构体：</p>
<figure class="highlight go"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">type</span> pos <span class="keyword">struct</span> {</span><br><span class="line"> x, y, dir <span class="type">int</span> <span class="comment">// dir表示方向:0,1,2,3-右,下,左,上</span></span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<p>这里如果不存放指向<code>dir</code>的话我们很难知道当前位置点的哪些方向都遍历过了。</p>
<p>然后我们要针对这种位置向量设计一个栈：</p>
<figure class="highlight go"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 位置向量栈</span></span><br><span class="line"><span class="keyword">type</span> stack []pos</span><br><span class="line"></span><br><span class="line"><span class="comment">// 入栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this *stack)</span></span> Push(x pos) { *this = <span class="built_in">append</span>(*this, x) }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 出栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this *stack)</span></span> Pop() pos {</span><br><span class="line"> res := (*this)[<span class="built_in">len</span>(*this)<span class="number">-1</span>]</span><br><span class="line"> *this = (*this)[<span class="number">0</span> : <span class="built_in">len</span>(*this)<span class="number">-1</span>]</span><br><span class="line"> <span class="keyword">return</span> res</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 获取栈顶元素</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> getTop() pos { <span class="keyword">return</span> this[<span class="built_in">len</span>(this)<span class="number">-1</span>] }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 获取当前栈元素个数</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> Size() <span class="type">int</span> { <span class="keyword">return</span> <span class="built_in">len</span>(this) }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 判断是否为空栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> Empty() <span class="type">bool</span> { <span class="keyword">return</span> <span class="built_in">len</span>(this) == <span class="number">0</span> }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 打印输出</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> show() {</span><br><span class="line"> <span class="keyword">for</span> i, v := <span class="keyword">range</span> this {</span><br><span class="line"> <span class="keyword">if</span> i != this.Size()<span class="number">-1</span> {</span><br><span class="line"> fmt.Printf(<span class="string">"(%d,%d)->"</span>, v.x, v.y)</span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> fmt.Printf(<span class="string">"(%d,%d)\n"</span>, v.x, v.y)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<p>迷宫的路径搜索</p>
<pre class="mermaid">graph TD
A(创建路径栈和相关临时变量) --> B[初始位置向量入栈,并标记标记地图] -->C
C{判断是否为空栈} -->|No|I{是否到达终点}
I -->|Yes| K(输出路线)
I -->|No| D[朝四个方向依次进行遍历]
D --> E{是否找到可走路线} -->|Yes| F[记录可走方向,该可走的位置向量入栈]
E -->|No|G[无路可走,所以当前栈顶位置向量出栈并撤回标记]
F --> C
G --> C
C ----->|Yes| H(该迷宫行不通)</pre>
<figure class="highlight go"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 迷宫路径搜索</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="title">mgpath</span><span class="params">(xe, ye <span class="type">int</span>)</span></span> <span class="type">bool</span> {</span><br><span class="line"> <span class="keyword">var</span> e pos</span><br><span class="line"> <span class="keyword">var</span> i, j <span class="type">int</span></span><br><span class="line"> <span class="keyword">var</span> find <span class="type">bool</span></span><br><span class="line"> <span class="keyword">var</span> st stack</span><br><span class="line"> e.x, e.y, e.dir = <span class="number">1</span>, <span class="number">1</span>, <span class="number">-1</span> <span class="comment">// dir=-1表示还没向四个方向搜索过</span></span><br><span class="line"> st.Push(e)</span><br><span class="line"> mg[e.x][e.y] = <span class="number">-1</span> <span class="comment">// 标记已走过</span></span><br><span class="line"> <span class="keyword">for</span> !st.Empty() { <span class="comment">// 有路可走</span></span><br><span class="line"> e = st.getTop()</span><br><span class="line"> <span class="keyword">if</span> e.x == xe && e.y == ye { <span class="comment">// 找到出口</span></span><br><span class="line"> st.show()</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span></span><br><span class="line"> }</span><br><span class="line"> find = <span class="literal">false</span></span><br><span class="line"> <span class="keyword">for</span> e.dir < <span class="number">4</span> && !find {</span><br><span class="line"> e.dir++</span><br><span class="line"> <span class="keyword">switch</span> e.dir {</span><br><span class="line"> <span class="keyword">case</span> <span class="number">0</span>: <span class="comment">// 右</span></span><br><span class="line"> i = e.x</span><br><span class="line"> j = e.y + <span class="number">1</span></span><br><span class="line"> <span class="keyword">case</span> <span class="number">1</span>: <span class="comment">// 下</span></span><br><span class="line"> i = e.x + <span class="number">1</span></span><br><span class="line"> j = e.y</span><br><span class="line"> <span class="keyword">case</span> <span class="number">2</span>: <span class="comment">// 左</span></span><br><span class="line"> i = e.x</span><br><span class="line"> j = e.y - <span class="number">1</span></span><br><span class="line"> <span class="keyword">case</span> <span class="number">3</span>: <span class="comment">// 上</span></span><br><span class="line"> i = e.x - <span class="number">1</span></span><br><span class="line"> j = e.y</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> mg[i][j] == <span class="number">0</span> { <span class="comment">// 如果未走过且为空</span></span><br><span class="line"> find = <span class="literal">true</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> find { <span class="comment">// 有路可走</span></span><br><span class="line"> st[st.Size()<span class="number">-1</span>].dir = e.dir <span class="comment">// 记录方向，这里如果不记录方向返回的时候还会重新遍历方向导致死循环</span></span><br><span class="line"> e.x, e.y, e.dir = i, j, <span class="number">-1</span></span><br><span class="line"> st.Push(e)</span><br><span class="line"> mg[e.x][e.y] = <span class="number">-1</span></span><br><span class="line"> } <span class="keyword">else</span> { <span class="comment">// 当前位置无路可走</span></span><br><span class="line"> st.Pop() <span class="comment">// 退回去</span></span><br><span class="line"> mg[e.x][e.y] = <span class="number">0</span> <span class="comment">// 撤回</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span></span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h2 id="完整代码"><a href="#完整代码" class="headerlink" title="完整代码"></a>完整代码</h2><figure class="highlight go"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">package</span> main</span><br><span class="line"></span><br><span class="line"><span class="keyword">import</span> <span class="string">"fmt"</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">type</span> pos <span class="keyword">struct</span> {</span><br><span class="line"> x, y, dir <span class="type">int</span> <span class="comment">// dir表示方向:0,1,2,3-右,下,左,上</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 位置向量栈</span></span><br><span class="line"><span class="keyword">type</span> stack []pos</span><br><span class="line"></span><br><span class="line"><span class="comment">// 入栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this *stack)</span></span> Push(x pos) { *this = <span class="built_in">append</span>(*this, x) }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 出栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this *stack)</span></span> Pop() pos {</span><br><span class="line"> res := (*this)[<span class="built_in">len</span>(*this)<span class="number">-1</span>]</span><br><span class="line"> *this = (*this)[<span class="number">0</span> : <span class="built_in">len</span>(*this)<span class="number">-1</span>]</span><br><span class="line"> <span class="keyword">return</span> res</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 获取栈顶元素</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> getTop() pos { <span class="keyword">return</span> this[<span class="built_in">len</span>(this)<span class="number">-1</span>] }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 获取当前栈元素个数</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> Size() <span class="type">int</span> { <span class="keyword">return</span> <span class="built_in">len</span>(this) }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 判断是否为空栈</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> Empty() <span class="type">bool</span> { <span class="keyword">return</span> <span class="built_in">len</span>(this) == <span class="number">0</span> }</span><br><span class="line"></span><br><span class="line"><span class="comment">// 打印输出</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="params">(this stack)</span></span> show() {</span><br><span class="line"> <span class="keyword">for</span> i, v := <span class="keyword">range</span> this {</span><br><span class="line"> <span class="keyword">if</span> i != this.Size()<span class="number">-1</span> {</span><br><span class="line"> fmt.Printf(<span class="string">"(%d,%d)->"</span>, v.x, v.y)</span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> fmt.Printf(<span class="string">"(%d,%d)\n"</span>, v.x, v.y)</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> N, M = <span class="number">8</span>, <span class="number">8</span> <span class="comment">// 迷宫大小</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// 迷宫图</span></span><br><span class="line"><span class="keyword">var</span> mg [N + <span class="number">2</span>][M + <span class="number">2</span>]<span class="type">int</span> = [N + <span class="number">2</span>][M + <span class="number">2</span>]<span class="type">int</span>{</span><br><span class="line"> {<span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>},</span><br><span class="line"> {<span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>}, {<span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>},</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 迷宫路径搜索</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="title">mgpath</span><span class="params">(xe, ye <span class="type">int</span>)</span></span> <span class="type">bool</span> {</span><br><span class="line"> <span class="keyword">var</span> e pos</span><br><span class="line"> <span class="keyword">var</span> i, j <span class="type">int</span></span><br><span class="line"> <span class="keyword">var</span> find <span class="type">bool</span></span><br><span class="line"> <span class="keyword">var</span> st stack</span><br><span class="line"> e.x, e.y, e.dir = <span class="number">1</span>, <span class="number">1</span>, <span class="number">-1</span> <span class="comment">// dir=-1表示还没向四个方向搜索过</span></span><br><span class="line"> st.Push(e)</span><br><span class="line"> mg[e.x][e.y] = <span class="number">-1</span> <span class="comment">// 标记已走过</span></span><br><span class="line"> <span class="keyword">for</span> !st.Empty() { <span class="comment">// 有路可走</span></span><br><span class="line"> e = st.getTop()</span><br><span class="line"> <span class="keyword">if</span> e.x == xe && e.y == ye { <span class="comment">// 找到出口</span></span><br><span class="line"> st.show()</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span></span><br><span class="line"> }</span><br><span class="line"> find = <span class="literal">false</span></span><br><span class="line"> <span class="keyword">for</span> e.dir < <span class="number">4</span> && !find {</span><br><span class="line"> e.dir++</span><br><span class="line"> <span class="keyword">switch</span> e.dir {</span><br><span class="line"> <span class="keyword">case</span> <span class="number">0</span>: <span class="comment">// 右</span></span><br><span class="line"> i = e.x</span><br><span class="line"> j = e.y + <span class="number">1</span></span><br><span class="line"> <span class="keyword">case</span> <span class="number">1</span>: <span class="comment">// 下</span></span><br><span class="line"> i = e.x + <span class="number">1</span></span><br><span class="line"> j = e.y</span><br><span class="line"> <span class="keyword">case</span> <span class="number">2</span>: <span class="comment">// 左</span></span><br><span class="line"> i = e.x</span><br><span class="line"> j = e.y - <span class="number">1</span></span><br><span class="line"> <span class="keyword">case</span> <span class="number">3</span>: <span class="comment">// 上</span></span><br><span class="line"> i = e.x - <span class="number">1</span></span><br><span class="line"> j = e.y</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> mg[i][j] == <span class="number">0</span> { <span class="comment">// 如果未走过且为空</span></span><br><span class="line"> find = <span class="literal">true</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> find { <span class="comment">// 有路可走</span></span><br><span class="line"> st[st.Size()<span class="number">-1</span>].dir = e.dir <span class="comment">// 记录方向，这里如果不记录方向返回的时候还会重新遍历方向导致死循环</span></span><br><span class="line"> e.x, e.y, e.dir = i, j, <span class="number">-1</span></span><br><span class="line"> st.Push(e)</span><br><span class="line"> mg[e.x][e.y] = <span class="number">-1</span></span><br><span class="line"> } <span class="keyword">else</span> { <span class="comment">// 当前位置无路可走</span></span><br><span class="line"> st.Pop() <span class="comment">// 退回去</span></span><br><span class="line"> mg[e.x][e.y] = <span class="number">0</span> <span class="comment">// 撤回</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 主函数</span></span><br><span class="line"><span class="function"><span class="keyword">func</span> <span class="title">main</span><span class="params">()</span></span> {</span><br><span class="line"> <span class="keyword">if</span> mgpath(N, M) {</span><br><span class="line"> fmt.Println(<span class="string">"Succuss!"</span>) <span class="comment">// 迷宫可解</span></span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> fmt.Println(<span class="string">"fail!"</span>) <span class="comment">// 迷宫无解</span></span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment">(1,1)->(1,2)->(2,2)->(3,2)->(3,1)->(4,1)->(5,1)->(5,2)->(5,3)->(6,3)->(6,4)->(6,5)->(7,5)->(8,5)->(8,6)->(8,7)->(8,8)</span></span><br><span class="line"><span class="comment">Succuss!</span></span><br><span class="line"><span class="comment">*/</span></span><br></pre></td></tr></table></figure>
<p><img src="https://s2.loli.net/2022/04/16/NcV7T5phedRg1In.png" alt="image-20220416015831474"></p>
<script type="text/javascript" src="https://unpkg.com/kity@2.0.4/dist/kity.min.js"></script><script type="text/javascript" src="https://unpkg.com/kityminder-core@1.4.50/dist/kityminder.core.min.js"></script><script defer="true" type="text/javascript" src="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.js"></script><link rel="stylesheet" type="text/css" href="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.css">
</div>
<footer class="post-footer">
<div class="post-eof"></div>
</footer>
</div>
</article>
<article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
<div class="post-block">
<link itemprop="mainEntityOfPage" href="https://jacksalad.github.io/2022/07/25/%E4%B8%80%E9%81%93%E9%AB%98%E6%95%B0%E6%9E%81%E9%99%90%E8%AE%A1%E7%AE%97%E9%A2%98-%E6%B3%B0%E5%8B%92%E5%B1%95%E5%BC%80%E6%B3%95%E6%9A%B4%E5%8A%9B%E6%B1%82%E8%A7%A3/">
<span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
<meta itemprop="name" content="">
<meta itemprop="description" content="">
<meta itemprop="image" content="https://s1.ax1x.com/2022/07/12/jc4sDx.png">
</span>
<span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
<meta itemprop="name" content="RedJACK">
</span>
<header class="post-header">
<h1 class="post-title" itemprop="name headline">
<a class="post-title-link" href="/2022/07/25/%E4%B8%80%E9%81%93%E9%AB%98%E6%95%B0%E6%9E%81%E9%99%90%E8%AE%A1%E7%AE%97%E9%A2%98-%E6%B3%B0%E5%8B%92%E5%B1%95%E5%BC%80%E6%B3%95%E6%9A%B4%E5%8A%9B%E6%B1%82%E8%A7%A3/" itemprop="url">一道高数极限计算题-泰勒展开法暴力求解</a></h1>
<div class="post-meta">
<span class="post-time">
<span class="post-meta-item-icon">
<i class="fa fa-calendar-o"></i>
</span>
<span class="post-meta-item-text">Posted on</span>
<time title="Post created" itemprop="dateCreated datePublished" datetime="2022-07-25T16:52:08+08:00">
2022-07-25
</time>
</span>
<span class="post-category" >
<span class="post-meta-divider">|</span>
<span class="post-meta-item-icon">
<i class="fa fa-folder-o"></i>
</span>
<span class="post-meta-item-text">In</span>
<span itemprop="about" itemscope itemtype="http://schema.org/Thing">
<a href="/categories/%E6%95%B0%E5%AD%A6/" itemprop="url" rel="index">
<span itemprop="name">数学</span>
</a>
</span>
</span>
</div>
</header>
<div class="post-body" itemprop="articleBody">
<blockquote>
<p>原文地址 <a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/456585739">zhuanlan.zhihu.com</a></p>
</blockquote>
<p>$$<br>\lim_{x \to + \infty} x^2[(1 + \frac{1}{x + 1})^{x + 1} - (1 + \frac{1}{x})^x]<br>$$</p>
<p><em>解：</em><br>$$<br>= \lim_{x \to +\infty} x^2 [e^{(x + 1)\ln{(1 + \frac{1}{x + 1})}} - e^{x\ln{(1 + \frac{1}{x})}}]<br>$$</p>
<p>$$<br>泰勒公式 ： ln(1 + x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots<br>$$</p>
<p>$$<br>其中 \lim_{x \to +\infty} [e^{(x + 1)\ln{(1 + \frac{1}{x + 1})}} - e^{x\ln{(1 + \frac{1}{x})}}]<br>$$</p>
<p>$$<br>= \lim_{x \to \infty} {e^{(x + 1)[\frac{1}{x + 1} - \frac{1}{2(x + 1)^2} + \frac{1}{3(x + 1)^3}]} - e^{x[\frac{1}{x} - \frac{1}{2x^2} + \frac{1}{3x^3}]} }<br>$$</p>
<p>$$<br>= \lim_{x \to +\infty} {e^{[1 - \frac{1}{2(x + 1)} + \frac{1}{3(x + 1)^2}]} - e^{[1 - \frac{1}{2x} + \frac{1}{3x^2}]} }<br>$$</p>
<p>$$<br>无穷小量代换：e^{\alpha} - e^{\beta} = e^{\beta}(e^{\alpha - \beta} - 1) \sim e^{\beta}(\alpha - \beta) ,当 (\alpha - \beta) \to 0 时<br>$$</p>
<p>$$<br>=\lim_{x \to +\infty} e^{1 - \frac{1}{2x} + \frac{1}{3x^2}} [e^{\frac{1}{2x} - \frac{1}{2(x + 1)} - \frac{1}{3x^2} + \frac{1}{3(x + 1)^2}} - 1]<br>$$</p>
<p>$$<br>= \lim_{x \to +\infty} e [\frac{1}{2x(x + 1)} - \frac{2x + 1}{3x^2(x + 1)^2}]<br>$$</p>
<p>$$<br>原式 = \lim_{x \to +\infty}x^2 e [\frac{1}{2x(x + 1)} - \frac{2x + 1}{3x^2(x + 1)^2}]<br>$$</p>
<p>$$<br>= \lim_{x \to +\infty} e [\frac{x}{2(x + 1)} - \frac{2x + 1}{3(x + 1)^2}]<br>$$</p>
<p>$$<br>= \frac{e}{2}<br>$$</p>
<script type="text/javascript" src="https://unpkg.com/kity@2.0.4/dist/kity.min.js"></script><script type="text/javascript" src="https://unpkg.com/kityminder-core@1.4.50/dist/kityminder.core.min.js"></script><script defer="true" type="text/javascript" src="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.js"></script><link rel="stylesheet" type="text/css" href="https://unpkg.com/hexo-simple-mindmap@0.8.0/dist/mindmap.min.css">
</div>
<footer class="post-footer">
<div class="post-eof"></div>
</footer>
</div>
</article>
<article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
<div class="post-block">
<link itemprop="mainEntityOfPage" href="https://jacksalad.github.io/2022/07/25/%E6%AC%A7%E6%8B%89%E5%85%AC%E5%BC%8F%E7%9A%84%E8%AF%81%E6%98%8E/">
<span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
<meta itemprop="name" content="">
<meta itemprop="description" content="">
<meta itemprop="image" content="https://s1.ax1x.com/2022/07/12/jc4sDx.png">
</span>
<span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
<meta itemprop="name" content="RedJACK">
</span>
<header class="post-header">
<h1 class="post-title" itemprop="name headline">
<a class="post-title-link" href="/2022/07/25/%E6%AC%A7%E6%8B%89%E5%85%AC%E5%BC%8F%E7%9A%84%E8%AF%81%E6%98%8E/" itemprop="url">欧拉公式的证明</a></h1>
<div class="post-meta">
<span class="post-time">
<span class="post-meta-item-icon">
<i class="fa fa-calendar-o"></i>
</span>
<span class="post-meta-item-text">Posted on</span>
<time title="Post created" itemprop="dateCreated datePublished" datetime="2022-07-25T16:51:15+08:00">
2022-07-25
</time>
</span>
<span class="post-category" >