-
Notifications
You must be signed in to change notification settings - Fork 3
Expand file tree
/
Copy path20_Graph_ShortestPath_Dijkstra.html
More file actions
877 lines (781 loc) · 46.4 KB
/
20_Graph_ShortestPath_Dijkstra.html
File metadata and controls
877 lines (781 loc) · 46.4 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
<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>20 图的应用：Dijkstra 最短路径</title>
<script src="https://unpkg.com/@tailwindcss/browser@4"></script>
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css" rel="stylesheet"/>
<style type="text/tailwindcss">
@theme {
--color-bg-dark: #030712;
--color-text-main: #f1f5f9;
--color-dijkstra: #f59e0b; /* Amber */
--color-floyd: #ec4899; /* Pink */
--color-success: #22c55e;
--color-info: #06b6d4;
--color-code-bg: #1e293b;
}
@layer base {
body { @apply bg-black text-text-main font-sans overflow-hidden flex justify-center items-center h-screen; }
}
@layer utilities {
@keyframes fadeIn {
from { opacity: 0; transform: translateY(10px); }
to { opacity: 1; transform: translateY(0); }
}
@keyframes highlight-cell {
0% { background-color: rgba(245, 158, 11, 0.5); transform: scale(1); }
50% { background-color: rgba(245, 158, 11, 0.8); transform: scale(1.1); }
100% { background-color: rgba(245, 158, 11, 0.2); transform: scale(1); }
}
.slide-container { @apply relative w-[1920px] h-[1080px] bg-bg-dark overflow-hidden shadow-2xl; }
.slide { @apply absolute inset-0 hidden flex-col p-14 opacity-0 transition-opacity duration-400 ease-in-out; }
.slide.active { @apply flex opacity-100; }
.bg-decoration { @apply absolute inset-0 z-0 pointer-events-none; background-image: radial-gradient(circle at 10% 10%, rgba(245,158,11,0.08) 0%, transparent 30%), radial-gradient(circle at 90% 90%, rgba(236,72,153,0.08) 0%, transparent 30%); }
.grid-overlay { @apply absolute inset-0 z-0; background-size: 60px 60px; background-image: linear-gradient(to right, rgba(255,255,255,0.02) 1px, transparent 1px), linear-gradient(to bottom, rgba(255,255,255,0.02) 1px, transparent 1px); }
h1 { @apply text-[100px] font-extrabold leading-tight mb-8; background: linear-gradient(135deg, #fff 0%, var(--color-dijkstra) 100%); -webkit-background-clip: text; background-clip: text; -webkit-text-fill-color: transparent; }
h2 { @apply text-[64px] mb-8 text-white inline-block pb-4 border-b-4 border-white/20; }
h3 { @apply text-[42px] mb-6 text-dijkstra; }
p { @apply text-[32px] mb-4 text-slate-200 leading-relaxed; }
.slide-content li { @apply text-[32px] mb-4 text-slate-200; }
strong { @apply text-white font-bold; }
.card { @apply bg-white/5 border border-white/10 rounded-3xl p-8 mb-6 backdrop-blur-sm shadow-lg; }
.code-block { @apply font-mono bg-code-bg p-6 rounded-2xl border border-slate-700 text-[22px] leading-relaxed text-slate-200 overflow-auto whitespace-pre; }
/* Syntax Highlighting */
.code-kw { @apply text-[#c678dd]; }
.code-type { @apply text-[#e5c07b]; }
.code-cm { @apply text-[#94a3b8] italic; }
.code-num { @apply text-[#d19a66]; }
.code-str { @apply text-[#98c379]; }
.code-fn { @apply text-[#61afef]; }
.btn-primary { @apply px-6 py-3 bg-dijkstra/20 border border-dijkstra/50 rounded-xl text-dijkstra font-bold text-[24px] cursor-pointer transition-all hover:bg-dijkstra/30 hover:scale-105 active:scale-95; }
.btn-secondary { @apply px-6 py-3 bg-slate-700/50 border border-slate-600 rounded-xl text-slate-200 font-bold text-[24px] cursor-pointer transition-all hover:bg-slate-600/50; }
/* Custom Scrollbar */
.custom-scrollbar::-webkit-scrollbar { width: 10px; height: 10px; }
.custom-scrollbar::-webkit-scrollbar-track { background: #1e293b; border-radius: 5px; }
.custom-scrollbar::-webkit-scrollbar-thumb { background: #475569; border-radius: 5px; }
}
</style>
</head>
<body>
<div id="app" class="slide-container">
<div class="bg-decoration"></div>
<div class="grid-overlay"></div>
<!-- P01: 封面 -->
<section class="slide active justify-center items-center text-center" data-title="封面">
<div class="flex flex-col items-center z-10 relative -mt-20">
<div class="flex gap-16 mb-12">
<!-- Icon -->
<div class="w-40 h-40 relative flex items-center justify-center">
<i class="fas fa-route text-8xl text-dijkstra drop-shadow-[0_0_25px_rgba(245,158,11,0.5)] animate-pulse"></i>
<div class="absolute -right-12 -bottom-4 bg-slate-800 px-4 py-2 rounded-lg border border-slate-600 text-xl text-white">min(dist)</div>
</div>
</div>
<div class="bg-slate-800/50 px-8 py-3 rounded-full border border-slate-600 mb-8 backdrop-blur-md">
<span class="text-slate-300 text-2xl font-mono tracking-[0.2em]">GRAPH ALGORITHMS</span>
</div>
<h1>数据结构与算法</h1>
<p class="text-[56px] text-slate-300 mt-4">Dijkstra 最短路径算法</p>
</div>
</section>
<!-- P02: 核心问题 -->
<section class="slide" data-title="核心问题">
<h2>最短路径问题</h2>
<div class="grid grid-cols-2 gap-16 flex-1 min-h-0 items-center">
<div class="flex flex-col gap-8">
<div class="card border-l-8 border-dijkstra">
<h3 class="text-dijkstra text-[40px] mb-4">定义</h3>
<p class="text-[32px] text-white leading-relaxed">
在带权图中，寻找从<strong class="text-dijkstra">起点 (Source)</strong> 到<strong class="text-floyd">终点 (Destination)</strong> 的路径，使得路径上所有边的<strong class="text-white">权值之和最小</strong>。
</p>
</div>
<div class="card bg-slate-800/30">
<h3 class="text-slate-200 text-[32px] mb-6">Dijkstra 适用场景</h3>
<ul class="space-y-6 text-[28px] text-slate-300">
<li>
<strong class="text-white block mb-2">单源最短路径 (One-to-All)</strong>
求图中<strong>某一顶点</strong>到其他所有顶点的最短路径
</li>
<li>
<strong class="text-white block mb-2">限制条件</strong>
<span class="text-red-400"><i class="fas fa-times-circle mr-2"></i>不适用于包含负权边的图</span>
</li>
</ul>
</div>
</div>
<div class="flex flex-col items-center justify-center relative h-full gap-8">
<!-- Weighted Graph Visualization -->
<div class="bg-slate-900/50 p-8 rounded-3xl border border-slate-700 w-full flex items-center justify-center relative overflow-hidden">
<svg width="600" height="400" viewBox="0 0 600 400" class="w-full h-full overflow-visible">
<defs>
<marker id="arrow-head" markerWidth="12" markerHeight="12" refX="42" refY="3.5" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 10 3.5, 0 7" fill="#64748b" />
</marker>
<marker id="arrow-head-highlight" markerWidth="12" markerHeight="12" refX="42" refY="3.5" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 10 3.5, 0 7" fill="#f59e0b" />
</marker>
</defs>
<!-- Edges -->
<!-- Path 1 (Top): S -> A -> E (Longer: 5+6=11) -->
<line x1="100" y1="200" x2="300" y2="80" stroke="#64748b" stroke-width="2" marker-end="url(#arrow-head)" />
<text x="190" y="130" fill="#94a3b8" font-size="24">5</text>
<line x1="300" y1="80" x2="500" y2="200" stroke="#64748b" stroke-width="2" marker-end="url(#arrow-head)" />
<text x="410" y="130" fill="#94a3b8" font-size="24">6</text>
<!-- Path 2 (Middle): S -> D -> E (Shortest: 2+2=4) -->
<line x1="100" y1="200" x2="300" y2="200" stroke="#f59e0b" stroke-width="2" marker-end="url(#arrow-head-highlight)" />
<text x="200" y="180" fill="#f59e0b" font-weight="bold" font-size="28">2</text>
<line x1="300" y1="200" x2="500" y2="200" stroke="#f59e0b" stroke-width="2" marker-end="url(#arrow-head-highlight)" />
<text x="400" y="180" fill="#f59e0b" font-weight="bold" font-size="28">2</text>
<!-- Path 3 (Bottom): S -> C -> E (Longer: 4+5=9) -->
<line x1="100" y1="200" x2="300" y2="320" stroke="#64748b" stroke-width="2" marker-end="url(#arrow-head)" />
<text x="190" y="280" fill="#94a3b8" font-size="24">4</text>
<line x1="300" y1="320" x2="500" y2="200" stroke="#64748b" stroke-width="2" marker-end="url(#arrow-head)" />
<text x="410" y="280" fill="#94a3b8" font-size="24">5</text>
<!-- Nodes -->
<!-- S -->
<circle cx="100" cy="200" r="30" fill="#0f172a" stroke="#22c55e" stroke-width="4" />
<text x="100" y="210" text-anchor="middle" fill="white" font-weight="bold" font-size="24">S</text>
<text x="100" y="255" text-anchor="middle" fill="#22c55e" font-size="20">起点</text>
<!-- A -->
<circle cx="300" cy="80" r="30" fill="#0f172a" stroke="#64748b" stroke-width="3" />
<text x="300" y="90" text-anchor="middle" fill="#94a3b8" font-size="20">A</text>
<!-- D (was B) -->
<circle cx="300" cy="200" r="30" fill="#0f172a" stroke="#f59e0b" stroke-width="4" />
<text x="300" y="210" text-anchor="middle" fill="#f59e0b" font-weight="bold" font-size="20">D</text>
<!-- C -->
<circle cx="300" cy="320" r="30" fill="#0f172a" stroke="#64748b" stroke-width="3" />
<text x="300" y="330" text-anchor="middle" fill="#94a3b8" font-size="20">C</text>
<!-- E -->
<circle cx="500" cy="200" r="30" fill="#0f172a" stroke="#ec4899" stroke-width="4" />
<text x="500" y="210" text-anchor="middle" fill="white" font-weight="bold" font-size="24">E</text>
<text x="500" y="255" text-anchor="middle" fill="#ec4899" font-size="20">终点</text>
<!-- Labels -->
<rect x="150" y="370" width="300" height="40" rx="20" fill="#f59e0b20" stroke="#f59e0b" />
<text x="300" y="398" text-anchor="middle" fill="#f59e0b" font-size="18" font-weight="bold">最短路径: S -> D -> E (Cost: 4)</text>
</svg>
</div>
</div>
</div>
</section>
<!-- P03: Dijkstra 概念 -->
<section class="slide" data-title="Dijkstra概念">
<h2>Dijkstra 核心思想</h2>
<div class="flex flex-col gap-12 flex-1 min-h-0 justify-center max-w-6xl mx-auto w-full">
<div class="flex flex-col gap-8">
<div class="card border-l-8 border-dijkstra">
<h3 class="text-dijkstra text-[40px] mb-6">由近及远，层层刷新</h3>
<ul class="space-y-6 text-[28px] text-slate-300">
<li class="flex items-start">
<span class="bg-dijkstra/20 text-dijkstra rounded-full w-10 h-10 flex items-center justify-center mr-4 mt-1 font-bold">1</span>
<span>
<strong class="text-white block mb-1">选最近</strong>
每次都在还没确定的点里，挑一个离起点最近的，直接把它的最短路“锁死”。
</span>
</li>
<li class="flex items-start">
<span class="bg-floyd/20 text-floyd rounded-full w-10 h-10 flex items-center justify-center mr-4 mt-1 font-bold">2</span>
<span>
<strong class="text-white block mb-1">做跳板</strong>
利用这个刚“锁死”的点作为中转站，去问问它的邻居们：“从我这走，会不会比你们原来的路更近？”
</span>
</li>
</ul>
</div>
<div class="bg-slate-800/50 p-6 rounded-2xl border border-slate-600 text-center">
<p class="text-[32px] text-dijkstra font-bold m-0 leading-normal text-left">
<i class="fas fa-bullseye mr-3"></i>Dijkstra 算法就是 从起点开始，像水波纹一样向外扩散，每次锁定一个离波纹中心最近的点，利用这个点作为新的波源，去触达更远的地方，直到覆盖全图。
</p>
</div>
</div>
</div>
</section>
<!-- P04: Dijkstra 演示 -->
<section class="slide" data-title="Dijkstra演示">
<h2>Dijkstra 算法演示</h2>
<div class="flex gap-4 flex-1 min-h-0 w-full">
<!-- Left: Graph -->
<div class="w-[45%] bg-slate-900/50 rounded-3xl border border-slate-700 relative flex items-center justify-center">
<svg id="dijkstra-svg" width="100%" height="100%" viewBox="0 0 800 600" class="overflow-visible">
<g id="dijkstra-edges"></g>
<g id="dijkstra-nodes"></g>
</svg>
<div class="absolute top-4 left-4 text-slate-400 font-mono">Source: 0</div>
</div>
<!-- Right: State (Table) -->
<div class="w-[55%] flex flex-col gap-4">
<!-- Table Container -->
<div class="flex-1 bg-slate-800/30 rounded-2xl border border-slate-700 p-4 flex flex-col overflow-hidden">
<h3 class="text-white text-[24px] mb-2 border-b border-slate-600 pb-2 flex justify-between">
<span><i class="fas fa-table mr-2 text-dijkstra"></i>迭代过程表</span>
<span class="text-sm text-slate-400 font-normal self-end">每次选距离S最近的点，然后更新</span>
</h3>
<div class="flex-1 overflow-auto custom-scrollbar relative">
<table class="w-full text-center border-collapse text-lg">
<thead class="sticky top-0 bg-slate-900 z-10">
<tr id="dijkstra-header-row" class="text-slate-400 border-b border-slate-600 text-[24px]">
<th class="p-4 border-r border-slate-700 w-[15%]">节点</th>
<th class="p-4 border-r border-slate-700 w-[15%]">标记</th>
<th class="p-4 border-r border-slate-700 w-[35%]">距离 (dist)</th>
<th class="p-4 border-slate-700 w-[35%]">前面点 (pre)</th>
</tr>
</thead>
<tbody id="dijkstra-table-body" class="font-mono text-slate-200 text-[24px]">
<!-- Rows injected dynamically -->
</tbody>
</table>
</div>
</div>
<div id="dijkstra-status" class="text-dijkstra text-[22px] font-mono h-12 leading-tight flex items-center">Ready...</div>
<!-- Controls -->
<div class="flex gap-4">
<button onclick="prevDijkstraStep()" class="btn-secondary flex-1"><i class="fas fa-step-backward mr-2"></i>上一步</button>
<button onclick="resetDijkstraStep()" class="btn-secondary w-16"><i class="fas fa-undo"></i></button>
<button onclick="nextDijkstraStep()" class="btn-primary flex-1">下一步<i class="fas fa-step-forward ml-2"></i></button>
</div>
</div>
</div>
</section>
<!-- P05: Dijkstra 代码 -->
<section class="slide" data-title="Dijkstra代码">
<h2>Dijkstra 代码实现</h2>
<div class="grid grid-cols-2 gap-8 flex-1 min-h-0">
<div class="code-block h-full custom-scrollbar text-[18px]"><span class="code-type">void</span> <span class="code-fn">dijkstra</span>(<span class="code-type">MGraph</span> G, <span class="code-type">int</span> v0, <span class="code-type">int</span> pre[], <span class="code-type">int</span> dist[]) {
<span class="code-cm">// 循环变量及最小值临时变量</span>
<span class="code-type">int</span> i, j, u, min;
<span class="code-cm">// 标记数组，visited[i]=1表示已确定</span>
<span class="code-type">int</span> visited[MAXV];
<span class="code-cm">// 1. 初始化所有节点状态</span>
<span class="code-kw">for</span>(i = 0; i < G.numVertexes; i++) {
<span class="code-cm">// 初始所有节点均未被访问</span>
visited[i] = 0;
<span class="code-cm">// 将到所有节点的距离初始化为无穷大</span>
dist[i] = INF;
<span class="code-cm">// 初始化前驱节点为 -1 (无前驱)</span>
pre[i] = -1;
}
<span class="code-cm">// 起点到自身的距离为 0</span>
dist[v0] = 0;
<span class="code-cm">// 2. 主循环：每次确定一个节点的最短路径</span>
<span class="code-kw">for</span>(i = 0; i < G.numVertexes; i++) {
<span class="code-cm">// 初始化当前最小距离为无穷大</span>
min = INF;
<span class="code-cm">// 初始化最近节点索引为无效值</span>
u = -1;
<span class="code-cm">// 2.1 贪心选择：在未标记节点中寻找距离最近的节点 u</span>
<span class="code-kw">for</span>(j = 0; j < G.numVertexes; j++) {
<span class="code-cm">// 如果节点 j 未被标记 且 距离小于当前最小值</span>
<span class="code-kw">if</span>(!visited[j] && dist[j] < min) {
<span class="code-cm">// 更新最小值</span>
min = dist[j];
<span class="code-cm">// 记录该节点索引</span>
u = j;
}
}
<span class="code-cm">// 如果找不到可达节点，跳出循环</span>
<span class="code-kw">if</span>(u == -1) <span class="code-kw">break</span>;
<span class="code-cm">// 将找到的最近节点 u 标记为已确定</span>
visited[u] = 1;
<span class="code-cm">// 2.2 松弛操作：更新节点 u 的所有邻居 j</span>
<span class="code-kw">for</span>(j = 0; j < G.numVertexes; j++) {
<span class="code-cm">// 如果节点 j 未被标记 且 u 到 j 之间有边相连</span>
<span class="code-kw">if</span>(!visited[j] && G.arc[u][j] < INF) {
<span class="code-cm">// 核心判断：经过 u 到达 j 的距离是否比原来更短？</span>
<span class="code-kw">if</span>(dist[u] + G.arc[u][j] < dist[j]) {
<span class="code-cm">// 更新 j 的最短距离</span>
dist[j] = dist[u] + G.arc[u][j];
<span class="code-cm">// 更新 j 的前驱节点为 u</span>
pre[j] = u;
}
}
}
}
}</div>
<div class="flex flex-col gap-6">
<div class="card bg-slate-800/30">
<h3 class="text-white text-[32px] mb-4">关键数组</h3>
<ul class="space-y-4 text-[26px] text-slate-300">
<li><span class="font-mono text-dijkstra">dist[i]</span>：源点到顶点 i 的当前最短距离。</li>
<li><span class="font-mono text-info">pre[i]</span>：记录顶点 i 在最短路径上的前驱节点（用于还原路径）。</li>
<li><span class="font-mono text-slate-400">visited[i]</span>：标记顶点 i 的最短路径是否已确定。</li>
</ul>
</div>
<div class="card border-l-8 border-dijkstra">
<h3 class="text-white text-[32px] mb-4">复杂度分析</h3>
<ul class="space-y-4 text-[26px] text-slate-300">
<li><strong class="text-dijkstra">时间复杂度</strong>：<span class="font-mono text-warn">O(V²)</span>。</li>
<li>若使用优先队列优化（堆优化），可降至 <span class="font-mono text-green-400">O(E log V)</span>。</li>
</ul>
</div>
<div class="card bg-slate-800/30">
<h3 class="text-white text-[32px] mb-4">注意事项</h3>
<p class="text-[26px] text-slate-200">
<i class="fas fa-exclamation-triangle text-yellow-500 mr-2"></i>
Dijkstra 算法<strong class="text-red-400">不适用</strong>于包含<strong class="text-red-400">负权边</strong>的图。
<br/>
如果有负权边，需要使用 Bellman-Ford 算法。
</p>
</div>
</div>
</div>
</section>
<!-- P06: 贪心思想解读 -->
<section class="slide" data-title="贪心思想">
<h2>贪心策略深度解读</h2>
<div class="grid grid-cols-2 gap-16 flex-1 min-h-0 items-center">
<div class="flex flex-col gap-10">
<div class="card border-l-8 border-dijkstra">
<h3 class="text-dijkstra text-[40px] mb-6"><i class="fas fa-brain mr-4"></i>什么是“贪心”？</h3>
<p class="text-[32px] text-slate-200 leading-relaxed mb-6">
总是做出在<strong class="text-white">当前看来</strong>最好的选择。<br/>
不考虑长远的整体规划，而是通过<strong class="text-dijkstra">每一步的局部最优</strong>，试图达成全局最优。
</p>
</div>
<div class="card bg-slate-800/30">
<h3 class="text-white text-[32px] mb-6">Dijkstra 的“贪心时刻”</h3>
<ul class="space-y-6 text-[28px] text-slate-300">
<li class="flex items-start">
<span class="bg-dijkstra text-black font-bold rounded-full w-8 h-8 flex items-center justify-center mr-4 mt-1 shrink-0">1</span>
<div>
<strong class="text-white">选最近</strong>：在所有未确定的节点中，选离起点最近的那个。
</div>
</li>
<li class="flex items-start">
<span class="bg-dijkstra text-black font-bold rounded-full w-8 h-8 flex items-center justify-center mr-4 mt-1 shrink-0">2</span>
<div>
<strong class="text-white">不回头</strong>：一旦选定，就认为“这就是最短路了”，标记为已确定，不再更改。
</div>
</li>
</ul>
</div>
</div>
<div class="flex flex-col items-center justify-center h-full relative">
<!-- 贪心逻辑可视化 -->
<div class="bg-slate-900/50 p-6 rounded-3xl border border-slate-700 w-full h-[550px] flex flex-col items-center justify-center relative overflow-hidden">
<h3 class="absolute top-6 left-8 text-slate-400 text-[24px]">为什么“只看眼前”是正确的？</h3>
<svg width="600" height="420" viewBox="0 0 600 420" class="overflow-visible mt-4">
<defs>
<!-- refX=10 ensures the tip of the arrow (at x=10) touches the end coordinate -->
<marker id="arrow-greedy" markerWidth="10" markerHeight="7" refX="10" refY="3.5" orient="auto">
<polygon points="0 0, 10 3.5, 0 7" fill="#64748b" />
</marker>
<marker id="arrow-greedy-highlight" markerWidth="10" markerHeight="7" refX="10" refY="3.5" orient="auto">
<polygon points="0 0, 10 3.5, 0 7" fill="#f59e0b" />
</marker>
</defs>
<!-- Logic Text Block (Top) -->
<foreignObject x="20" y="30" width="560" height="110">
<div xmlns="http://www.w3.org/1999/xhtml" class="text-slate-200 text-[22px] bg-slate-800/40 p-4 rounded-xl border border-slate-600/50 backdrop-blur-sm">
既然 <strong>U</strong> 是当前最近的 (dist[U] < dist[V])，<br/>
那么 <span class="text-dijkstra font-bold">dist[V] + weight</span> 必然大于 <span class="text-dijkstra font-bold">dist[U]</span>。
</div>
</foreignObject>
<!-- Graph Elements (Bottom) -->
<g transform="translate(0, 40)">
<!-- Edges (Draw first to be behind nodes) -->
<!-- S -> U (Direct) -->
<!-- S(80,180) r=30 -> U(500,180) r=40 -->
<!-- Start: 80+30=110. End: 500-40=460 -->
<line x1="110" y1="180" x2="460" y2="180" stroke="#f59e0b" stroke-width="4" marker-end="url(#arrow-greedy-highlight)" />
<text x="290" y="160" text-anchor="middle" fill="#f59e0b" font-size="20" font-weight="bold" stroke="#030712" stroke-width="8" paint-order="stroke">dist[U] (min)</text>
<!-- S -> V (Indirect Start) -->
<!-- S(80,180) r=30 -> V(290,360) r=30 -->
<path d="M 103 199 Q 160 310 267 341" fill="none" stroke="#64748b" stroke-width="2" stroke-dasharray="6,6" marker-end="url(#arrow-greedy)" />
<text x="140" y="310" text-anchor="end" fill="#64748b" font-size="18" stroke="#030712" stroke-width="8" paint-order="stroke">dist[V] > dist[U]</text>
<!-- V -> U (Indirect End) -->
<!-- V(290,360) r=30 -> U(500,180) r=40 -->
<!-- Start on V edge (top-right): 290+21=311, 360-21=339 -->
<!-- End on U edge (bottom-left): 500-25=475, 180+31=211 -->
<path d="M 311 359 Q 400 320 475 211" fill="none" stroke="#64748b" stroke-width="2" marker-end="url(#arrow-greedy)" stroke-dasharray="6,6"/>
<text x="420" y="310" text-anchor="start" fill="#64748b" font-size="18" stroke="#030712" stroke-width="8" paint-order="stroke">weight ≥ 0</text>
<!-- Nodes -->
<!-- S -->
<circle cx="80" cy="180" r="30" fill="#0f172a" stroke="#22c55e" stroke-width="4"/>
<text x="80" y="190" text-anchor="middle" fill="white" font-weight="bold" font-size="20">S</text>
<!-- U (Target) -->
<circle cx="500" cy="180" r="40" fill="#0f172a" stroke="#f59e0b" stroke-width="4"/>
<text x="500" y="175" text-anchor="middle" fill="white" font-weight="bold" font-size="24">U</text>
<text x="500" y="205" text-anchor="middle" fill="#f59e0b" font-size="16">当前最近</text>
<!-- V (Other) -->
<circle cx="290" cy="360" r="30" fill="#0f172a" stroke="#64748b" stroke-width="3" stroke-dasharray="4 2"/>
<text x="290" y="370" text-anchor="middle" fill="#94a3b8" font-size="20">V</text>
<text x="290" y="415" text-anchor="middle" fill="#64748b" font-size="16">更远的点</text>
</g>
</svg>
</div>
</div>
</div>
</section>
<!-- Page Number -->
<div id="page-number" class="absolute bottom-6 right-8 text-slate-400 text-[24px] font-mono z-50"></div>
</div>
<script>
// --- SLIDESHOW SYSTEM ---
let currentSlide = 0;
const pageNumberEl = document.getElementById('page-number');
const urlParams = new URLSearchParams(window.location.search);
if (urlParams.has('page')) {
const page = parseInt(urlParams.get('page'));
if (!isNaN(page) && page > 0) currentSlide = page - 1;
}
function updateSlide() {
const slides = document.querySelectorAll('.slide');
if (currentSlide >= slides.length) currentSlide = slides.length - 1;
if (currentSlide < 0) currentSlide = 0;
slides.forEach((slide, index) => {
slide.classList.remove('active');
if (index === currentSlide) {
slide.classList.add('active');
const title = slide.getAttribute('data-title');
// Lazy Init
if (title === 'Dijkstra演示' && document.getElementById('dijkstra-nodes').children.length === 0) {
initDijkstraDemo();
}
}
});
if(pageNumberEl) pageNumberEl.textContent = `${currentSlide + 1} / ${slides.length}`;
try {
const url = new URL(window.location.href);
url.searchParams.set('page', currentSlide + 1);
window.history.replaceState(null, '', url.href);
} catch (e) {}
}
function nextSlide() {
if (currentSlide < document.querySelectorAll('.slide').length - 1) {
currentSlide++;
updateSlide();
}
}
function prevSlide() {
if (currentSlide > 0) {
currentSlide--;
updateSlide();
}
}
function resizeApp() {
const app = document.getElementById('app');
const scale = Math.min(window.innerWidth / 1920, window.innerHeight / 1080);
app.style.transform = `scale(${scale})`;
}
window.addEventListener('resize', resizeApp);
window.addEventListener('load', () => { resizeApp(); updateSlide(); });
document.addEventListener('keydown', (e) => {
if (['ArrowRight', ' ', 'Enter'].includes(e.key)) nextSlide();
else if (e.key === 'ArrowLeft') prevSlide();
});
// --- SHARED CONSTANTS ---
const INF = 99;
// --- DIJKSTRA DEMO ---
// Graph Data from User Image
const dNodes = [
{id: '0', x: 50, y: 300},
{id: '1', x: 200, y: 150},
{id: '7', x: 200, y: 450},
{id: '2', x: 400, y: 150},
{id: '8', x: 400, y: 300},
{id: '6', x: 400, y: 450},
{id: '3', x: 600, y: 150},
{id: '5', x: 600, y: 450},
{id: '4', x: 750, y: 300}
];
// Edges based on visual analysis of the image
const dEdges = [
{u: '0', v: '1', w: 4},
{u: '0', v: '7', w: 8},
{u: '1', v: '7', w: 11},
{u: '1', v: '2', w: 8},
{u: '7', v: '8', w: 7},
{u: '7', v: '6', w: 1},
{u: '6', v: '8', w: 6},
{u: '6', v: '5', w: 2},
{u: '2', v: '8', w: 2},
{u: '2', v: '5', w: 4},
{u: '2', v: '3', w: 7},
{u: '3', v: '5', w: 14},
{u: '3', v: '4', w: 9},
{u: '5', v: '4', w: 10}
];
let dSteps = [];
let dCurrentStep = -1;
function generateDijkstraSteps() {
dSteps = [];
const n = dNodes.length;
const dist = new Array(n).fill(INF);
const path = new Array(n).fill(-1); // -1 means None/Start
const visited = new Array(n).fill(false);
// Init
dist[0] = 0;
path[0] = 0; // Self as prev for start
// Helper to snapshot state
const snapshot = (desc, activeU = -1, activeV = -1, type = 'step') => {
return {
type: type,
desc: desc,
dist: [...dist],
path: [...path],
visited: [...visited],
activeU: activeU,
activeV: activeV
};
};
dSteps.push(snapshot('初始化：出发点 0 距离设为 0，其他为 ∞', -1, -1, 'init'));
for (let i = 0; i < n; i++) {
// 1. Select Min Unvisited
let u = -1;
let minVal = INF;
for (let j = 0; j < n; j++) {
if (!visited[j] && dist[j] < minVal) {
minVal = dist[j];
u = j;
}
}
if (u === -1) break; // Should not happen if graph is connected
// Mark
visited[u] = true;
dSteps.push(snapshot(`选择距离最近的未标记节点 ${dNodes[u].id} (dist=${minVal})，标记为已确定`, u, -1, 'select'));
// 2. Relax Neighbors
// Find neighbors of u
const neighbors = [];
dEdges.forEach(e => {
if (e.u === dNodes[u].id) neighbors.push({vIdx: dNodes.findIndex(n=>n.id===e.v), w: e.w});
else if (e.v === dNodes[u].id) neighbors.push({vIdx: dNodes.findIndex(n=>n.id===e.u), w: e.w});
});
for (let neighbor of neighbors) {
const v = neighbor.vIdx;
const w = neighbor.w;
if (!visited[v]) {
const newDist = dist[u] + w;
let updateDesc = `检查邻居 ${dNodes[v].id}：${dist[u]} + ${w} = ${newDist}`;
if (newDist < dist[v]) {
const oldDistVal = dist[v] === INF ? '∞' : dist[v];
dist[v] = newDist;
path[v] = u;
updateDesc += ` < ${oldDistVal}，更新距离和前驱`;
dSteps.push(snapshot(updateDesc, u, v, 'relax'));
} else {
// Optional: show check even if no update?
// The user image implies we just update. Let's skip non-updates to keep it clean, or show briefly.
// dSteps.push(snapshot(updateDesc + ` >= ${dist[v]}，不更新`, u, v, 'check'));
}
}
}
}
dSteps.push(snapshot('所有节点标记完成，最短路径计算结束', -1, -1, 'finish'));
// Backtrack Path
const targetIdx = dNodes.findIndex(n => n.id === '4');
if (targetIdx !== -1) {
let curr = targetIdx;
const pathNodes = [curr];
const pathEdges = [];
let pathStr = dNodes[curr].id;
while (curr !== 0) { // 0 is source index
const prev = path[curr];
if (prev === -1) break; // Should not happen if connected
pathEdges.push({u: dNodes[prev].id, v: dNodes[curr].id});
pathNodes.push(prev);
pathStr = dNodes[prev].id + ' -> ' + pathStr;
curr = prev;
}
dSteps.push({
...snapshot(`最终最短路径: ${pathStr}`, -1, -1, 'show_path'),
pathNodes: pathNodes,
pathEdges: pathEdges
});
}
}
function initDijkstraDemo() {
generateDijkstraSteps();
const svgEdges = document.getElementById('dijkstra-edges');
const svgNodes = document.getElementById('dijkstra-nodes');
svgEdges.innerHTML = '';
svgNodes.innerHTML = '';
// Defs
const defs = document.createElementNS("http://www.w3.org/2000/svg", "defs");
defs.innerHTML = `<marker id="arrow-d" markerWidth="10" markerHeight="10" refX="28" refY="3" orient="auto"><path d="M0,0 L0,6 L9,3 z" fill="#334155" /></marker>`;
svgEdges.appendChild(defs);
// Edges
dEdges.forEach(e => {
const u = dNodes.find(n => n.id === e.u);
const v = dNodes.find(n => n.id === e.v);
// Draw undirected lines for graph structure, but logic is directed?
// Dijkstra works on directed or undirected. Image implies undirected (lines, no arrows).
// But standard Dijkstra usually directed. Let's assume undirected for this "map" style.
// I will use lines without arrows for the base graph.
const line = document.createElementNS("http://www.w3.org/2000/svg", "line");
line.setAttribute('x1', u.x); line.setAttribute('y1', u.y);
line.setAttribute('x2', v.x); line.setAttribute('y2', v.y);
line.setAttribute('stroke', '#334155');
line.setAttribute('stroke-width', '2');
line.id = `d-edge-${dNodes.indexOf(u)}-${dNodes.indexOf(v)}`; // Use indices for ID to match logic
// Actually, logic uses ID string in some places, but indices in others.
// Let's stick to indices for IDs to be safe: d-edge-uIdx-vIdx
// But dEdges uses string IDs.
// Let's use string IDs for simplicity: d-edge-0-1
line.id = `d-edge-${u.id}-${v.id}`;
svgEdges.appendChild(line);
// Weight
const text = document.createElementNS("http://www.w3.org/2000/svg", "text");
text.setAttribute('x', (u.x + v.x)/2);
text.setAttribute('y', (u.y + v.y)/2 - 5);
text.setAttribute('fill', '#94a3b8');
text.setAttribute('font-size', '18');
text.setAttribute('text-anchor', 'middle');
text.textContent = e.w;
svgEdges.appendChild(text);
});
// Nodes
dNodes.forEach((n, i) => {
const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
g.id = `d-node-${i}`;
g.innerHTML = `
<circle r="20" cx="${n.x}" cy="${n.y}" fill="#1e293b" stroke="#334155" stroke-width="3" />
<text x="${n.x}" y="${n.y+7}" text-anchor="middle" fill="#94a3b8" font-size="20" font-weight="bold">${n.id}</text>
`;
svgNodes.appendChild(g);
});
// Init Table Structure (Rows)
const tbody = document.getElementById('dijkstra-table-body');
tbody.innerHTML = '';
dNodes.forEach((n, i) => {
const tr = document.createElement('tr');
tr.id = `d-row-${i}`;
tr.className = 'border-b border-slate-700 hover:bg-slate-800/30 transition-colors';
// Init cells
tr.innerHTML = `
<td class="p-4 border-r border-slate-700 font-bold text-white">${n.id}</td>
<td class="p-4 border-r border-slate-700 text-slate-500"><i class="fas fa-check opacity-0"></i></td>
<td class="p-4 border-r border-slate-700 font-mono text-slate-400">∞</td>
<td class="p-4 border-slate-700 font-mono text-slate-400">-</td>
`;
tbody.appendChild(tr);
});
resetDijkstraStep();
}
function updateDijkstraVisuals() {
const status = document.getElementById('dijkstra-status');
if(dCurrentStep < 0) {
status.textContent = "Ready...";
// Reset visuals
dNodes.forEach((n, i) => {
const row = document.getElementById(`d-row-${i}`);
if(row) {
row.children[1].innerHTML = '<i class="fas fa-check opacity-0"></i>';
row.children[2].textContent = i === 0 ? '0' : '∞';
row.children[2].className = 'p-4 border-r border-slate-700 font-mono ' + (i===0?'text-white':'text-slate-400');
row.children[3].textContent = i === 0 ? '0' : '-';
row.className = 'border-b border-slate-700 hover:bg-slate-800/30 transition-colors';
}
const g = document.getElementById(`d-node-${i}`);
if(g) {
g.querySelector('circle').setAttribute('stroke', '#334155');
g.querySelector('circle').setAttribute('fill', '#1e293b');
g.querySelector('text').setAttribute('fill', '#94a3b8');
}
});
document.querySelectorAll('line').forEach(l => {
l.setAttribute('stroke', '#334155'); l.setAttribute('stroke-width', '2');
});
return;
}
const step = dSteps[dCurrentStep];
status.textContent = step.desc;
// Update Table & Graph Nodes
step.dist.forEach((d, i) => {
const row = document.getElementById(`d-row-${i}`);
const g = document.getElementById(`d-node-${i}`);
const circle = g.querySelector('circle');
const text = g.querySelector('text');
// 1. Update Dist & Path
const distStr = d === INF ? '∞' : d;
const pathStr = step.path[i] === -1 ? '-' : dNodes[step.path[i]].id;
// Highlight changes if this is a relax step and this node is v
if (step.type === 'relax' && step.activeV === i) {
row.children[2].innerHTML = `<span class="text-dijkstra font-bold animate-pulse">${distStr}</span>`;
row.children[3].innerHTML = `<span class="text-dijkstra font-bold animate-pulse">${pathStr}</span>`;
} else {
row.children[2].textContent = distStr;
row.children[3].textContent = pathStr;
}
// 2. Update Marked Status
if (step.visited[i]) {
row.children[1].innerHTML = '<i class="fas fa-check text-green-500"></i>';
row.className = 'border-b border-slate-700 bg-slate-800/50'; // Dim visited rows
circle.setAttribute('stroke', '#22c55e');
circle.setAttribute('fill', '#064e3b');
text.setAttribute('fill', '#fff');
} else {
row.children[1].innerHTML = '<i class="fas fa-check opacity-0"></i>';
row.className = 'border-b border-slate-700 hover:bg-slate-800/30';
circle.setAttribute('stroke', '#334155');
circle.setAttribute('fill', '#1e293b');
text.setAttribute('fill', '#94a3b8');
}
// 3. Highlight Active Node (u)
if (i === step.activeU) {
circle.setAttribute('stroke', '#f59e0b');
circle.setAttribute('stroke-width', '4');
circle.setAttribute('fill', '#451a03');
text.setAttribute('fill', '#fff');
row.classList.add('bg-dijkstra/10');
}
});
// Update Edges
document.querySelectorAll('line').forEach(l => {
l.setAttribute('stroke', '#334155');
l.setAttribute('stroke-width', '2');
});
if (step.activeU !== -1 && step.activeV !== -1) {
// Find edge
const uId = dNodes[step.activeU].id;
const vId = dNodes[step.activeV].id;
let line = document.getElementById(`d-edge-${uId}-${vId}`);
if (!line) line = document.getElementById(`d-edge-${vId}-${uId}`);
if (line) {
line.setAttribute('stroke', '#f59e0b');
line.setAttribute('stroke-width', '4');
}
}
// Highlight Final Path
if (step.type === 'show_path') {
if (step.pathEdges) {
step.pathEdges.forEach(e => {
let line = document.getElementById(`d-edge-${e.u}-${e.v}`);
if (!line) line = document.getElementById(`d-edge-${e.v}-${e.u}`);
if (line) {
line.setAttribute('stroke', '#ec4899'); // Pink/Magenta for final path
line.setAttribute('stroke-width', '5');
line.classList.add('animate-pulse');
}
});
}
if (step.pathNodes) {
step.pathNodes.forEach(i => {
const g = document.getElementById(`d-node-${i}`);
if(g) {
g.querySelector('circle').setAttribute('stroke', '#ec4899');
g.querySelector('circle').setAttribute('fill', '#831843');
g.querySelector('text').setAttribute('fill', '#fff');
}
});
}
}
}
function nextDijkstraStep() {
if(dCurrentStep < dSteps.length - 1) {
dCurrentStep++;
updateDijkstraVisuals();
}
}
function prevDijkstraStep() {
if(dCurrentStep > -1) {
dCurrentStep--;
updateDijkstraVisuals();
}
}
function resetDijkstraStep() {
dCurrentStep = -1;
updateDijkstraVisuals();
}
</script>
</body>
</html>