-
Notifications
You must be signed in to change notification settings - Fork 3
Expand file tree
/
Copy path23_Graph_CriticalPath.html
More file actions
870 lines (795 loc) · 47 KB
/
23_Graph_CriticalPath.html
File metadata and controls
870 lines (795 loc) · 47 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
<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>23 图的应用：关键路径</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-accent: #22d3ee; /* Cyan */
--color-secondary: #a78bfa; /* Purple */
--color-highlight: #f472b6; /* Pink */
--color-warn: #f59e0b;
--color-success: #22c55e;
--color-danger: #ef4444;
--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 {
.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 15% 15%, rgba(34,211,238,0.08) 0%, transparent 30%), radial-gradient(circle at 85% 85%, rgba(167,139,250,0.08) 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-accent) 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-accent; }
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; }
.btn-primary { @apply px-6 py-3 bg-accent/20 border border-accent/50 rounded-xl text-accent font-bold text-[24px] cursor-pointer transition-all hover:bg-accent/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::-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="w-40 h-40 relative mb-12">
<div class="absolute inset-0 border-4 border-accent/30 rounded-full animate-[spin_10s_linear_infinite]"></div>
<div class="absolute inset-4 border-4 border-secondary/30 rounded-full animate-[spin_15s_linear_infinite_reverse]"></div>
<div class="absolute inset-0 flex items-center justify-center">
<i class="fas fa-project-diagram text-7xl text-white drop-shadow-[0_0_15px_rgba(255,255,255,0.5)]"></i>
</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 APPLICATIONS</span>
</div>
<h1>数据结构与算法</h1>
<p class="text-[56px] text-slate-300 mt-4">AOE 网与关键路径</p>
<div class="mt-12 flex gap-12 text-[32px] text-slate-400 font-mono">
<span class="flex items-center"><i class="fas fa-clock text-accent mr-3"></i> 最短工期</span>
<span class="text-slate-600">|</span>
<span class="flex items-center"><i class="fas fa-route text-secondary mr-3"></i> 最长路径</span>
</div>
</div>
</section>
<!-- P02: AOE网概念 -->
<section class="slide" data-title="AOE网概念">
<h2>AOE 网 (Activity On Edge)</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-accent">
<h3 class="text-accent text-[40px] mb-4">核心定义</h3>
<p class="text-[32px] text-white leading-relaxed">
在一个表示工程的<strong class="text-accent">有向无环图 (DAG)</strong> 中：
</p>
<ul class="space-y-6 text-[28px] text-slate-300 mt-4">
<li><i class="fas fa-circle text-secondary mr-3"></i> <strong>顶点 (Vertex)</strong>：表示<strong class="text-white">事件 (Event)</strong>。<br><span class="text-slate-400 text-[24px]">如“食材备好”、“可以开饭”。</span></li>
<li><i class="fas fa-long-arrow-alt-right text-accent mr-3"></i> <strong>有向边 (Edge)</strong>：表示<strong class="text-white">活动 (Activity)</strong>。<br><span class="text-slate-400 text-[24px]">如“打鸡蛋”、“炒菜”。</span></li>
<li><i class="fas fa-weight-hanging text-warn mr-3"></i> <strong>权值 (Weight)</strong>：表示活动持续的<strong class="text-white">时间</strong>。</li>
</ul>
</div>
<div class="card bg-slate-800/30">
<p class="text-[28px] text-slate-300">
<strong class="text-white">性质：</strong>
只有在某顶点代表的事件发生后，从该顶点出发的活动才能开始。
</p>
</div>
</div>
<div class="flex flex-col items-center justify-center relative h-full bg-slate-900/30 rounded-3xl border border-slate-700/50 p-8">
<svg width="700" height="500" viewBox="0 0 700 500" class="overflow-visible">
<defs>
<marker id="arrow-aoe" markerWidth="20" markerHeight="15" refX="58" refY="6" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 16 6, 0 12" fill="#334155" />
</marker>
<marker id="arrow-aoe-curve" markerWidth="20" markerHeight="15" refX="18" refY="6" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 16 6, 0 12" fill="#334155" />
</marker>
</defs>
<!-- Edges -->
<!-- Start -> Ingredients Ready (Parallel Edges) -->
<path d="M140,250 Q250,150 360,250" fill="none" stroke="#334155" stroke-width="4" marker-end="url(#arrow-aoe-curve)" />
<text x="250" y="180" text-anchor="middle" fill="#22d3ee" font-size="24" font-weight="bold">打鸡蛋 (2min)</text>
<path d="M140,250 Q250,350 360,250" fill="none" stroke="#334155" stroke-width="4" marker-end="url(#arrow-aoe-curve)" />
<text x="250" y="340" text-anchor="middle" fill="#22d3ee" font-size="24" font-weight="bold">洗番茄 (1min)</text>
<!-- Ingredients Ready -> Done -->
<line x1="400" y1="250" x2="700" y2="250" stroke="#334155" stroke-width="4" marker-end="url(#arrow-aoe)" />
<text x="550" y="230" text-anchor="middle" fill="#22d3ee" font-size="24" font-weight="bold">炒菜 (3min)</text>
<!-- Nodes -->
<!-- V1 Start -->
<circle cx="100" cy="250" r="40" fill="#1e293b" stroke="#a78bfa" stroke-width="4" />
<text x="100" y="260" text-anchor="middle" fill="#fff" font-size="24" font-weight="bold">V1</text>
<text x="100" y="320" text-anchor="middle" fill="#a78bfa" font-size="20">开始</text>
<!-- V2 Ingredients Ready -->
<circle cx="400" cy="250" r="40" fill="#1e293b" stroke="#a78bfa" stroke-width="4" />
<text x="400" y="260" text-anchor="middle" fill="#fff" font-size="24" font-weight="bold">V2</text>
<text x="400" y="320" text-anchor="middle" fill="#a78bfa" font-size="20">食材备好</text>
<!-- V3 Done (was V4) -->
<circle cx="700" cy="250" r="40" fill="#1e293b" stroke="#a78bfa" stroke-width="4" />
<text x="700" y="260" text-anchor="middle" fill="#fff" font-size="24" font-weight="bold">V3</text>
<text x="700" y="320" text-anchor="middle" fill="#a78bfa" font-size="20">Done</text>
</svg>
<div class="mt-4 p-4 bg-slate-800/80 rounded-xl border border-slate-600 backdrop-blur-sm">
<p class="text-[24px] text-slate-200 text-center m-0 leading-relaxed">
工程的总工期取决于<strong class="text-white">最长</strong>的那条路径长度，<br/>这条路径被称为<strong class="text-highlight">关键路径 (Critical Path)</strong>。
</p>
</div>
</div>
</div>
</section>
<!-- P03: 关键参数解析 -->
<section class="slide" data-title="关键参数解析">
<h2>关键参数解析</h2>
<div class="grid grid-cols-2 gap-12 flex-1 min-h-0">
<!-- Left Column: Vertex Parameters -->
<div class="flex flex-col gap-8">
<div class="card border-l-8 border-accent">
<h3 class="text-accent text-[40px] mb-4"><i class="fas fa-circle mr-3"></i>事件 (顶点) 参数</h3>
<div class="space-y-8">
<div>
<p class="text-[34px] text-white font-bold mb-2">ve(i) - 最早发生时间 <span class="text-[24px] text-slate-500 font-normal ml-2">(Earliest)</span></p>
<p class="text-[28px] text-slate-300 leading-normal">
事件 i <strong class="text-accent">最早</strong>可以在什么时候发生？
<br><span class="text-slate-400 text-[24px]">取决于所有前驱活动都完成的时间点。</span>
</p>
</div>
<div>
<p class="text-[34px] text-white font-bold mb-2">vl(i) - 最晚发生时间 <span class="text-[24px] text-slate-500 font-normal ml-2">(Latest)</span></p>
<p class="text-[28px] text-slate-300 leading-normal">
事件 i <strong class="text-secondary">最晚</strong>必须在什么时候发生？
<br><span class="text-slate-400 text-[24px]">为了不拖延整个工期，最迟不能晚于这个时间点。</span>
</p>
</div>
</div>
</div>
</div>
<!-- Right Column: Edge Parameters -->
<div class="flex flex-col gap-8">
<div class="card border-l-8 border-highlight">
<h3 class="text-highlight text-[40px] mb-4"><i class="fas fa-long-arrow-alt-right mr-3"></i>活动 (边) 参数</h3>
<div class="space-y-8">
<div>
<p class="text-[34px] text-white font-bold mb-2">e(k) - 最早开始时间 <span class="text-[24px] text-slate-500 font-normal ml-2">(Earliest)</span></p>
<p class="text-[28px] text-slate-300 leading-normal">
活动 k <strong class="text-highlight">最早</strong>什么时候能开工？
<br><span class="text-slate-400 text-[24px]">等于其起点事件的最早发生时间 ve(i)。</span>
</p>
</div>
<div>
<p class="text-[34px] text-white font-bold mb-2">l(k) - 最晚开始时间 <span class="text-[24px] text-slate-500 font-normal ml-2">(Latest)</span></p>
<p class="text-[28px] text-slate-300 leading-normal">
活动 k <strong class="text-warn">最晚</strong>必须什么时候开工？
<br><span class="text-slate-400 text-[24px]">等于终点最晚时间减去耗时：vl(j) - weight。</span>
</p>
</div>
</div>
</div>
</div>
</div>
</section>
<section class="slide" data-title="ve计算">
<h2>1. 事件最早发生时间 ve(i)</h2>
<div class="flex gap-6 flex-1 min-h-0 w-full">
<div class="w-3/5 bg-slate-900/50 rounded-3xl border border-slate-700 relative flex items-center justify-center" id="ve-container">
<!-- SVG injected by JS -->
</div>
<div class="w-2/5 flex flex-col gap-6">
<div class="card border-l-8 border-accent flex-1">
<h3 class="text-accent text-[32px] mb-4">正向推导 (Forward)</h3>
<p class="text-[26px] text-slate-300 mb-4">
从源点开始，往后推算。
</p>
<div class="bg-black/30 p-4 rounded-xl font-mono text-[24px] text-white mb-6 border border-slate-600">
ve(j) = Max{ ve(i) + dut(<i,j>) }
</div>
<p class="text-[24px] text-slate-400">
<i class="fas fa-lightbulb text-yellow-500 mr-2"></i> 只有所有前驱活动都完成了，事件 j 才能发生，所以要取<strong class="text-white">最大值</strong>。
</p>
</div>
<div id="ve-status" class="h-30 text-[24px] text-accent font-mono p-4 bg-slate-800/50 rounded-xl border border-slate-700"></div>
<div class="flex gap-4">
<button onclick="prevStep('ve')" class="btn-secondary flex-1">上一步</button>
<button onclick="resetStep('ve')" class="btn-secondary w-16"><i class="fas fa-undo"></i></button>
<button onclick="nextStep('ve')" class="btn-primary flex-1">下一步</button>
</div>
</div>
</div>
</section>
<!-- P05: vl 计算 -->
<section class="slide" data-title="vl计算">
<h2>2. 事件最晚发生时间 vl(i)</h2>
<div class="flex gap-8 flex-1 min-h-0 w-full">
<div class="w-3/5 bg-slate-900/50 rounded-3xl border border-slate-700 relative flex items-center justify-center" id="vl-container">
<!-- SVG injected by JS -->
</div>
<div class="w-2/5 flex flex-col gap-6">
<div class="card border-l-8 border-secondary flex-1">
<h3 class="text-secondary text-[32px] mb-4">逆向推导 (Backward)</h3>
<p class="text-[26px] text-slate-300 mb-4">
从汇点开始，往前推算。
</p>
<div class="bg-black/30 p-4 rounded-xl font-mono text-[24px] text-white mb-6 border border-slate-600">
vl(i) = Min{ vl(j) - dut(<i,j>) }
</div>
<p class="text-[24px] text-slate-400">
<i class="fas fa-lightbulb text-yellow-500 mr-2"></i> 为了不耽误后续工期，必须在最晚时间前完成，所以要取<strong class="text-white">最小值</strong>。
</p>
</div>
<div id="vl-status" class="h-30 text-[24px] text-secondary font-mono p-4 bg-slate-800/50 rounded-xl border border-slate-700"></div>
<div class="flex gap-4">
<button onclick="prevStep('vl')" class="btn-secondary flex-1">上一步</button>
<button onclick="resetStep('vl')" class="btn-secondary w-16"><i class="fas fa-undo"></i></button>
<button onclick="nextStep('vl')" class="btn-primary flex-1">下一步</button>
</div>
</div>
</div>
</section>
<!-- P06: e & l 计算 -->
<section class="slide" data-title="el计算">
<h2>3. 活动最早/最晚开始时间</h2>
<div class="flex gap-8 flex-1 min-h-0 w-full">
<div class="w-3/5 bg-slate-900/50 rounded-3xl border border-slate-700 relative flex items-center justify-center" id="el-container">
<!-- SVG injected by JS -->
</div>
<div class="w-2/5 flex flex-col gap-6">
<div class="card border-l-8 border-highlight flex-1 overflow-y-auto custom-scrollbar">
<h3 class="text-highlight text-[32px] mb-4">边计算公式</h3>
<div class="space-y-6">
<div>
<p class="text-[24px] text-white font-bold mb-2">活动最早开始 e(k)</p>
<p class="text-[22px] text-slate-300 font-mono bg-black/30 p-2 rounded">e(k) = ve(i) <span class="text-slate-500">// 起点最早发生</span></p>
</div>
<div>
<p class="text-[24px] text-white font-bold mb-2">活动最晚开始 l(k)</p>
<p class="text-[22px] text-slate-300 font-mono bg-black/30 p-2 rounded">l(k) = vl(j) - weight <span class="text-slate-500">// 终点最晚 - 耗时</span></p>
</div>
<div>
<p class="text-[24px] text-white font-bold mb-2">机动时间 (Slack)</p>
<p class="text-[22px] text-slate-300 font-mono bg-black/30 p-2 rounded">slack = l(k) - e(k)</p>
</div>
</div>
</div>
<div id="el-status" class="h-40 text-[22px] text-white font-mono p-4 bg-slate-800/50 rounded-xl border border-slate-700 whitespace-pre-line"></div>
<div class="flex gap-4">
<button onclick="prevStep('el')" class="btn-secondary flex-1">上一步</button>
<button onclick="resetStep('el')" class="btn-secondary w-16"><i class="fas fa-undo"></i></button>
<button onclick="nextStep('el')" class="btn-primary flex-1">下一步</button>
</div>
</div>
</div>
</section>
<!-- P07: 关键路径 -->
<section class="slide" data-title="关键路径">
<h2>关键路径 (Critical Path)</h2>
<div class="flex gap-8 flex-1 min-h-0 w-full">
<div class="w-3/5 bg-slate-900/50 rounded-3xl border border-slate-700 relative flex items-center justify-center" id="cp-container">
<!-- SVG injected by JS -->
</div>
<div class="w-2/5 flex flex-col gap-6">
<div class="card border-l-8 border-red-500">
<h3 class="text-red-500 text-[36px] mb-4">判定条件</h3>
<p class="text-[30px] text-white mb-6">
<span class="font-mono text-highlight">e(k) == l(k)</span> 的活动为<strong class="text-red-500">关键活动</strong>。
</p>
<p class="text-[26px] text-slate-300">
由关键活动组成的从源点到汇点的路径，即为<strong class="text-white">关键路径</strong>。
</p>
</div>
<div class="bg-slate-800/50 p-6 rounded-2xl border border-slate-700">
<h4 class="text-white text-[28px] mb-4">本例结果：</h4>
<ul class="text-[26px] text-slate-300 space-y-2 font-mono" id="cp-result">
<!-- Injected -->
</ul>
</div>
<button onclick="showCriticalPath()" class="btn-primary mt-auto">显示关键路径</button>
</div>
</div>
</section>
<!-- P08: 工程应用 -->
<section class="slide" data-title="工程应用">
<h2>工程进度控制应用</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-green-500">
<h3 class="text-green-500 text-[36px] mb-4"><i class="fas fa-stopwatch mr-4"></i>缩短工期</h3>
<p class="text-[28px] text-slate-200 leading-relaxed">
要想缩短整个工程的工期，必须缩短<strong class="text-white">关键活动</strong>的持续时间。
</p>
<p class="text-[24px] text-slate-400 mt-4">
注意：缩短到一定程度，关键路径可能会发生<strong class="text-warn">变化</strong>（非关键路径变成了关键路径）。
</p>
</div>
<div class="card bg-slate-800/30">
<h3 class="text-white text-[32px] mb-4">非关键活动</h3>
<p class="text-[28px] text-slate-300">
具有<strong class="text-highlight">机动时间 (Slack)</strong>。
<br/>
在不影响总工期的前提下，可以适当推迟开始，或调配资源支援关键活动。
</p>
</div>
</div>
<div class="flex items-center justify-center">
<div class="relative w-full h-80 bg-slate-900 rounded-2xl border border-slate-700 p-8 flex flex-col justify-center gap-6">
<!-- Gantt Chart Metaphor -->
<div class="flex items-center gap-4">
<div class="w-24 text-right text-slate-400 text-xl">Critical</div>
<div class="flex-1 h-10 bg-slate-800 rounded-full overflow-hidden relative">
<div class="absolute left-0 w-full h-full bg-red-500/80"></div>
<div class="absolute left-0 w-full h-full flex items-center justify-center text-white font-bold">No Slack</div>
</div>
</div>
<div class="flex items-center gap-4">
<div class="w-24 text-right text-slate-400 text-xl">Normal</div>
<div class="flex-1 h-10 bg-slate-800 rounded-full overflow-hidden relative">
<div class="absolute left-0 w-3/4 h-full bg-blue-500/80"></div>
<div class="absolute right-0 w-1/4 h-full bg-slate-700 repeating-linear-gradient-45"></div>
<div class="absolute right-4 top-2 text-xs text-slate-400">Slack</div>
</div>
</div>
</div>
</div>
</div>
</section>
<!-- P09: 典型应用场景 -->
<section class="slide" data-title="典型应用场景">
<h2>AOE 网的典型应用场景</h2>
<div class="grid grid-cols-2 gap-16 flex-1 min-h-0 items-center">
<div class="flex flex-col gap-4">
<div class="card border-l-8 border-blue-500">
<h3 class="text-blue-500 text-[36px] mb-4"><i class="fas fa-tasks mr-4"></i>项目管理 (PERT)</h3>
<p class="text-[28px] text-slate-200">
在软件开发、建筑施工等复杂项目中，用于<strong class="text-white">估算工期</strong>、<strong class="text-white">识别瓶颈</strong>。
</p>
</div>
<div class="card border-l-8 border-purple-500">
<h3 class="text-purple-500 text-[36px] mb-4"><i class="fas fa-industry mr-4"></i>生产流程优化</h3>
<p class="text-[28px] text-slate-200">
在流水线生产中，分析各工序依赖关系，通过优化<strong class="text-white">关键工序</strong>（如增加设备、人力）来提升整体产能。
</p>
</div>
<div class="card border-l-8 border-orange-500">
<h3 class="text-orange-500 text-[36px] mb-4"><i class="fas fa-truck-moving mr-4"></i>物流与调度</h3>
<p class="text-[28px] text-slate-200">
规划多阶段运输任务，确保物资在<strong class="text-white">最短时间</strong>内到达目的地，同时合理安排中转等待时间。
</p>
</div>
</div>
<div class="flex flex-col items-center justify-center bg-slate-900/30 rounded-3xl border border-slate-700/50 p-12">
<div class="text-center mb-12">
<h3 class="text-white text-[48px] font-bold">核心价值</h3>
</div>
<ul class="space-y-8 text-[36px] text-slate-300 w-full px-8">
<li class="flex items-center bg-slate-800/50 p-6 rounded-2xl border border-slate-700">
<span class="w-12 h-12 rounded-full bg-accent flex items-center justify-center text-black font-bold mr-6">1</span>
<span>预估整个工程的<strong class="text-accent">最短工期</strong></span>
</li>
<li class="flex items-center bg-slate-800/50 p-6 rounded-2xl border border-slate-700">
<span class="w-12 h-12 rounded-full bg-highlight flex items-center justify-center text-black font-bold mr-6">2</span>
<span>找出影响进度的<strong class="text-highlight">关键活动</strong></span>
</li>
<li class="flex items-center bg-slate-800/50 p-6 rounded-2xl border border-slate-700">
<span class="w-12 h-12 rounded-full bg-green-500 flex items-center justify-center text-black font-bold mr-6">3</span>
<span>合理调配资源，利用<strong class="text-green-500">机动时间</strong></span>
</li>
</ul>
</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>
// --- GRAPH DATA ---
const nodes = [
{ id: 'V1', x: 100, y: 300 },
{ id: 'V2', x: 300, y: 150 },
{ id: 'V3', x: 300, y: 450 },
{ id: 'V4', x: 500, y: 150 },
{ id: 'V5', x: 500, y: 300 },
{ id: 'V6', x: 700, y: 300 }
];
const edges = [
{ u: 0, v: 1, w: 3, id: 'a1' }, // V1->V2
{ u: 0, v: 2, w: 2, id: 'a2' }, // V1->V3
{ u: 1, v: 3, w: 2, id: 'a3' }, // V2->V4
{ u: 1, v: 4, w: 3, id: 'a4' }, // V2->V5
{ u: 2, v: 3, w: 4, id: 'a5' }, // V3->V4
{ u: 2, v: 5, w: 3, id: 'a6' }, // V3->V6
{ u: 3, v: 5, w: 2, id: 'a7' }, // V4->V6
{ u: 4, v: 5, w: 1, id: 'a8' } // V5->V6
];
// Calculated Data
const ve = [0, 3, 2, 6, 6, 8];
const vl = [0, 4, 2, 6, 7, 8];
// Edge calculations: e, l, slack
const edgeCalc = edges.map(e => {
const ek = ve[e.u];
const lk = vl[e.v] - e.w;
return { ...e, ek, lk, slack: lk - ek, isCritical: (lk - ek === 0) };
});
// --- RENDER HELPERS ---
function createSVG(type) {
const container = document.getElementById(`${type}-container`);
if (!container) return;
container.innerHTML = '';
const svg = document.createElementNS("http://www.w3.org/2000/svg", "svg");
svg.setAttribute("width", "100%");
svg.setAttribute("height", "100%");
svg.setAttribute("viewBox", "0 0 800 600");
svg.classList.add("overflow-visible");
// Defs for arrow
const defs = document.createElementNS("http://www.w3.org/2000/svg", "defs");
// Determine active color based on type
const activeColor = type === 'el' ? '#f472b6' : '#22d3ee';
defs.innerHTML = `
<marker id="arrow-${type}" markerWidth="16" markerHeight="12" refX="48" refY="6" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 16 6, 0 12" fill="#475569" />
</marker>
<marker id="arrow-active-${type}" markerWidth="16" markerHeight="12" refX="48" refY="6" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 16 6, 0 12" fill="${activeColor}" />
</marker>
<marker id="arrow-critical-${type}" markerWidth="16" markerHeight="12" refX="48" refY="6" orient="auto" markerUnits="userSpaceOnUse">
<polygon points="0 0, 16 6, 0 12" fill="#ef4444" />
</marker>
`;
svg.appendChild(defs);
// Edges
const edgesG = document.createElementNS("http://www.w3.org/2000/svg", "g");
edgesG.id = `edges-${type}`;
edges.forEach((e, i) => {
const u = nodes[e.u];
const v = nodes[e.v];
const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
g.id = `edge-${type}-${i}`;
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", "#475569");
line.setAttribute("stroke-width", "3");
line.setAttribute("marker-end", `url(#arrow-${type})`);
// Weight Label
const text = document.createElementNS("http://www.w3.org/2000/svg", "text");
// Adjust position ratio: default 0.5 (center).
// For a5/a6, move closer to start node (0.35) to avoid overlap
let ratio = 0.5;
if (e.id === 'a5' || e.id === 'a6') ratio = 0.35;
const midX = u.x + (v.x - u.x) * ratio;
const midY = u.y + (v.y - u.y) * ratio;
// Calculate angle
const dx = v.x - u.x;
const dy = v.y - u.y;
let angle = Math.atan2(dy, dx) * 180 / Math.PI;
// Adjust angle to prevent upside down text
if (angle > 90 || angle < -90) {
angle += 180;
}
text.setAttribute("x", midX);
text.setAttribute("y", midY - 10);
text.setAttribute("fill", "#94a3b8");
text.setAttribute("font-size", "20");
text.setAttribute("text-anchor", "middle");
text.setAttribute("transform", `rotate(${angle}, ${midX}, ${midY})`);
text.textContent = `${e.id}=${e.w}`;
g.appendChild(line);
g.appendChild(text);
edgesG.appendChild(g);
});
svg.appendChild(edgesG);
// Nodes
const nodesG = document.createElementNS("http://www.w3.org/2000/svg", "g");
nodesG.id = `nodes-${type}`;
nodes.forEach((n, i) => {
const g = document.createElementNS("http://www.w3.org/2000/svg", "g");
g.id = `node-${type}-${i}`;
const circle = document.createElementNS("http://www.w3.org/2000/svg", "circle");
circle.setAttribute("cx", n.x); circle.setAttribute("cy", n.y);
circle.setAttribute("r", "30");
circle.setAttribute("fill", "#1e293b");
circle.setAttribute("stroke", "#475569");
circle.setAttribute("stroke-width", "3");
const text = document.createElementNS("http://www.w3.org/2000/svg", "text");
text.setAttribute("x", n.x); text.setAttribute("y", n.y + 8);
text.setAttribute("text-anchor", "middle");
text.setAttribute("fill", "#fff");
text.setAttribute("font-weight", "bold");
text.setAttribute("font-size", "20");
text.textContent = n.id;
// Value Label (ve/vl)
const valText = document.createElementNS("http://www.w3.org/2000/svg", "text");
valText.id = `val-${type}-${i}`;
valText.setAttribute("x", n.x); valText.setAttribute("y", n.y + 55);
valText.setAttribute("text-anchor", "middle");
valText.setAttribute("fill", "#22d3ee");
valText.setAttribute("font-size", "24");
valText.setAttribute("font-weight", "bold");
valText.textContent = ""; // Init empty
g.appendChild(circle);
g.appendChild(text);
g.appendChild(valText);
nodesG.appendChild(g);
});
svg.appendChild(nodesG);
container.appendChild(svg);
}
// --- ANIMATION STATE ---
const states = {
ve: { step: -1, max: 6 }, // 0..5 nodes + finish
vl: { step: -1, max: 6 },
el: { step: -1, max: 8 } // 8 edges
};
function updateVisuals(type) {
const s = states[type];
const containerId = type === 'el' ? 'el-container' : (type === 'cp' ? 'cp-container' : `${type}-container`);
const statusEl = document.getElementById(`${type}-status`);
if (type === 've') {
// Reset
nodes.forEach((_, i) => {
const val = document.getElementById(`val-ve-${i}`);
const node = document.getElementById(`node-ve-${i}`).querySelector('circle');
if (i <= s.step) {
val.textContent = `ve=${ve[i]}`;
node.setAttribute("stroke", "#22d3ee");
} else {
val.textContent = "";
node.setAttribute("stroke", "#475569");
}
});
if (s.step === -1) statusEl.textContent = "准备开始计算...";
else if (s.step < 6) {
const curr = s.step;
// Find incoming edges to explain max
const incoming = edges.filter(e => e.v === curr);
if (incoming.length === 0) {
statusEl.textContent = `源点 V1: ve(0) = 0`;
} else {
const calcs = incoming.map(e => `ve(${e.u}) + ${e.w} = ${ve[e.u] + e.w}`);
statusEl.textContent = `V${curr+1}: Max{ ${calcs.join(', ')} } = ${ve[curr]}`;
}
}
} else if (type === 'vl') {
// Reset
nodes.forEach((_, i) => {
const val = document.getElementById(`val-vl-${i}`);
const node = document.getElementById(`node-vl-${i}`).querySelector('circle');
// Reverse logic for display? No, just check if node index is >= n-1-step
// But we step 0..5. Let's map step to node index.
// Step 0 -> Node 5. Step 1 -> Node 4...
const nodeIdx = 5 - s.step;
if (s.step > -1 && i >= nodeIdx) {
val.textContent = `vl=${vl[i]}`;
node.setAttribute("stroke", "#a78bfa");
} else {
val.textContent = "";
node.setAttribute("stroke", "#475569");
}
});
if (s.step === -1) statusEl.textContent = "准备开始计算...";
else if (s.step < 6) {
const curr = 5 - s.step;
// Find outgoing edges
const outgoing = edges.filter(e => e.u === curr);
if (outgoing.length === 0) {
statusEl.textContent = `汇点 V6: vl(5) = ve(5) = ${ve[5]}`;
} else {
const calcs = outgoing.map(e => `vl(${e.v}) - ${e.w} = ${vl[e.v] - e.w}`);
statusEl.textContent = `V${curr+1}: Min{ ${calcs.join(', ')} } = ${vl[curr]}`;
}
}
} else if (type === 'el') {
// Highlight current edge
edges.forEach((e, i) => {
const g = document.getElementById(`edge-el-${i}`);
const line = g.querySelector('line');
if (i === s.step) {
line.setAttribute("stroke", "#f472b6");
line.setAttribute("marker-end", `url(#arrow-active-${type})`);
// line.setAttribute("stroke-width", "6"); // 不加粗
} else {
line.setAttribute("stroke", "#475569");
line.setAttribute("stroke-width", "3");
line.setAttribute("marker-end", `url(#arrow-${type})`);
}
});
if (s.step > -1) {
const e = edgeCalc[s.step];
statusEl.innerHTML = `活动 <span class="text-highlight font-bold">${e.id}</span> (<span class="text-accent">V${e.u+1}</span> -> <span class="text-secondary">V${e.v+1}</span>):
<span class="text-blue-400 font-bold">e(${e.id})</span> = ve(${e.u+1}) = <span class="text-blue-400 font-bold">${e.ek}</span>
<span class="text-pink-400 font-bold">l(${e.id})</span> = vl(${e.v+1}) - ${e.w} = <span class="text-pink-400 font-bold">${e.lk}</span>
Slack = ${e.slack} ${e.isCritical ? '<span class="text-red-500 font-bold ml-2">★ 关键活动</span>' : ''}`;
} else {
statusEl.textContent = "点击下一步逐个计算活动参数";
}
}
}
function nextStep(type) {
if (states[type].step < states[type].max - 1) {
states[type].step++;
updateVisuals(type);
}
}
function prevStep(type) {
if (states[type].step > -1) {
states[type].step--;
updateVisuals(type);
}
}
function resetStep(type) {
states[type].step = -1;
updateVisuals(type);
}
function showCriticalPath() {
const containerId = 'cp';
// Highlight nodes and edges
edgeCalc.forEach((e, i) => {
if (e.isCritical) {
const line = document.querySelector(`#edge-${containerId}-${i} line`);
line.setAttribute("stroke", "#ef4444");
// line.setAttribute("stroke-width", "6"); // 不加粗
line.setAttribute("marker-end", `url(#arrow-critical-${containerId})`);
}
});
// List result
const res = document.getElementById('cp-result');
const path = edgeCalc.filter(e => e.isCritical).map(e => e.id).join(' -> ');
const len = ve[5];
res.innerHTML = `
<li>关键活动：${edgeCalc.filter(e => e.isCritical).map(e => e.id).join(', ')}</li>
<li>路径长度：${len}</li>
<li class="text-red-400">V1 -> V3 -> V4 -> V6</li>
`;
}
// --- SLIDE LOGIC ---
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');
// Init SVGs if needed
const title = slide.getAttribute('data-title');
if (title === 've计算' && document.getElementById('ve-container').children.length === 0) {
createSVG('ve');
// Pre-fill nodes for context
} else if (title === 'vl计算' && document.getElementById('vl-container').children.length === 0) {
createSVG('vl');
// Show ve values as context? Maybe not to avoid clutter
} else if (title === 'el计算' && document.getElementById('el-container').children.length === 0) {
createSVG('el');
// Show ve/vl on nodes
nodes.forEach((_, i) => {
const t = document.getElementById(`val-el-${i}`);
if (t) {
t.textContent = ''; // Clear
// ve (Blue)
const tspanVe = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanVe.textContent = ve[i];
tspanVe.setAttribute("fill", "#22d3ee"); // accent (cyan/blue)
tspanVe.setAttribute("font-weight", "bold");
// Separator
const tspanSep = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanSep.textContent = " / ";
tspanSep.setAttribute("fill", "#94a3b8");
// vl (Pink)
const tspanVl = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanVl.textContent = vl[i];
tspanVl.setAttribute("fill", "#f472b6"); // highlight (pink)
tspanVl.setAttribute("font-weight", "bold");
t.appendChild(tspanVe);
t.appendChild(tspanSep);
t.appendChild(tspanVl);
t.setAttribute("font-size", "22");
}
});
} else if (title === '关键路径' && document.getElementById('cp-container').children.length === 0) {
createSVG('cp');
// Populate Vertex Table for CP page
const tableContainer = document.getElementById('vertex-params-list-cp');
if (tableContainer) {
let html = `
<div class="bg-slate-800/50 p-4 rounded-xl border border-slate-700">
<h4 class="text-white text-[24px] mb-3 border-b border-slate-600 pb-2">顶点参数表</h4>
<div class="grid grid-cols-3 gap-y-2 text-[22px] font-mono text-center">
<div class="text-slate-500 text-[20px]">Vertex</div>
<div class="text-accent text-[20px]">ve(i)</div>
<div class="text-secondary text-[20px]">vl(i)</div>`;
nodes.forEach((n, i) => {
html += `
<div class="text-slate-300">${n.id}</div>
<div class="text-accent">${ve[i]}</div>
<div class="text-secondary">${vl[i]}</div>
`;
});
html += `</div></div>`;
tableContainer.innerHTML = html;
}
// Show ve/vl on nodes for Critical Path
nodes.forEach((_, i) => {
const t = document.getElementById(`val-cp-${i}`);
if (t) {
t.textContent = ''; // Clear
// ve (Blue)
const tspanVe = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanVe.textContent = ve[i];
tspanVe.setAttribute("fill", "#22d3ee"); // accent
tspanVe.setAttribute("font-weight", "bold");
// Separator
const tspanSep = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanSep.textContent = " / ";
tspanSep.setAttribute("fill", "#94a3b8");
// vl (Pink)
const tspanVl = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
tspanVl.textContent = vl[i];
tspanVl.setAttribute("fill", "#f472b6"); // highlight
tspanVl.setAttribute("font-weight", "bold");
t.appendChild(tspanVe);
t.appendChild(tspanSep);
t.appendChild(tspanVl);
t.setAttribute("font-size", "22");
}
});
}
}
});
if(pageNumberEl) pageNumberEl.textContent = `${currentSlide + 1} / ${slides.length}`;
try {
const url = new URL(window.location.href);
url.searchParams.set('page', currentSlide + 1);
window.history.replaceState(null, '', url.href);
} catch (e) {}
}
function nextSlide() {
const slides = document.querySelectorAll('.slide');
if (currentSlide < slides.length - 1) {
currentSlide++;
updateSlide();
}
}
function prevSlide() {
if (currentSlide > 0) {
currentSlide--;
updateSlide();
}
}
document.addEventListener('keydown', (e) => {
if (['ArrowRight', ' ', 'Enter'].includes(e.key)) nextSlide();
else if (e.key === 'ArrowLeft') prevSlide();
});
// Init
window.addEventListener('load', () => {
const app = document.getElementById('app');
const scale = Math.min(window.innerWidth / 1920, window.innerHeight / 1080);
app.style.transform = `scale(${scale})`;
updateSlide();
});
window.addEventListener('resize', () => {
const app = document.getElementById('app');
const scale = Math.min(window.innerWidth / 1920, window.innerHeight / 1080);
app.style.transform = `scale(${scale})`;
});
</script>
</body>
</html>