【索引】 Volume 5. Dynamic Programming

本文精选了一系列动态规划领域的经典算法竞赛题目,涵盖了从基础到进阶的多个难度级别。每道题目都附带了尝试解决该题目的人数及成功解决的比例,为读者提供了一个全面了解动态规划解题技巧的机会。

AOAPC I: Beginning Algorithm Contests (Rujia Liu)


Volume 5. Dynamic Programming




FILE111 - History Grading21158
40.59%
8764
72.44%
FILE103 - Stacking Boxes35001
22.94%
9022
60.94%
FILE10405 - Longest Common Subsequence28440
36.08%
7882
88.72%
FILE674 - Coin Change22415
47.91%
7462
90.39%
FILE10003 - Cutting Sticks23255
42.59%
6814
87.53%
FILE116 - Unidirectional TSP38836
19.34%
7449
63.39%
FILE10131 - Is Bigger Smarter?19643
38.30%
5793
85.45%
FILE10066 - The Twin Towers14200
45.51%
5429
87.94%
FILE10192 - Vacation16113
36.57%
4897
88.77%
FILE147 - Dollars35335
23.01%
7636
65.98%
FILE357 - Let Me Count The Ways25857
29.81%
7288
71.97%
FILE562 - Dividing coins22363
30.91%
5203
82.59%
FILE348 - Optimal Array Multiplication Sequence11226
40.01%
3338
86.61%
FILE624 - CD12478
43.90%
4038
88.39%
FILE10130 - SuperSale11809
49.54%
4079
92.84%
FILE531 - Compromise13217
27.14%
3543
72.31%
FILE10465 - Homer Simpson11424
35.61%
3035
83.06%
FILE10285 - Longest Run on a Snowboard6140
56.45%
2547
94.19%
FILE437 - The Tower of Babylon4814
53.12%
2181
90.65%
FILE10404 - Bachet's Game5684
55.23%
2071
93.38%
FILE620 - Cellular Structure2846
51.30%
1412
86.12%
FILE825 - Walking on the Safe Side8765
26.56%
2041
80.01%
FILE10069 - Distinct Subsequences11724
26.83%
2499
71.79%
FILE10534 - Wavio Sequence7839
37.12%
1953
81.36%
FILE10051 - Tower of Cubes5535
32.57%
1581
81.28%
FILE10651 - Pebble Solitaire2852
68.48%
1506
95.55%
FILE590 - Always on the run2862
45.14%
1153
86.30%
FILE10306 - e-Coins3224
51.95%
1257
93.64%
FILE10739 - String to Palindrome3051
64.01%
1494
95.45%
FILE10304 - Optimal Binary Search Tree4657
43.18%
1258
82.83%
FILE10271 - Chopsticks6706
32.31%
1515
78.09%
FILE10617 - Again Palindrome2687
47.30%
985
93.30%
FILE11137 - Ingenuous Cubrency4084
70.15%
2227
97.53%
FILE10154 - Weights and Measures15134
19.72%
2513
53.36%
FILE10201 - Adventures in Moving - Part IV6719
20.66%
1316
66.95%
FILE10453 - Make Palindrome5442
33.08%
1178
81.58%
FILE10029 - Edit Step Ladders11076
17.33%
1634
53.43%
FILE10313 - Pay the Price5214
26.74%
1058
81.10%
FILE10401 - Injured Queen Problem2482
38.72%
753
91.24%
FILE10891 - Game of Sum3438
52.44%
1320
90.53%
FILE11151 - Longest Palindrome8538
30.26%
1992
85.09%
FILE10911 - Forming Quiz Teams4086
48.36%
1337
90.20%
FILE10635 - Prince and Princess4170
35.20%
1202
80.45%
FILE10564 - Paths through the Hourglass2807
27.79%
628
80.73%
FILE662 - Fast Food2420
31.53%
652
77.15%
FILE10626 - Buying Coke3321
27.73%
818
72.49%
FILE10118 - Free Candies1414
41.09%
499
78.96%
FILE607 - Scheduling Lectures4967
19.93%
1111
54.19%
FILE10604 - Chemical Reaction2502
23.90%
451
74.28%
FILE10913 - Walking on a Grid2086
34.56%
621
81.16%
FILE11008 - Antimatter Ray Clearcutting2932
24.22%
495
77.58%
FILE10723 - Cyborg Genes990
40.51%
346
92.49%
FILE11258 - String Partition1948
48.51%
658
91.34%
FILE10599 - Robots(II)1530
25.29%
373
73.19%
FILE10817 - Headmaster's Headache2098
29.93%
453
83.89%
FILE10163 - Storage Keepers1289
30.88%
354
76.84%
FILE709 - Formatting Text1694
16.29%
347
57.35%
FILE10280 - Old Wine Into New Bottles1516
27.57%
344
63.66%
FILE10558 - A Brief Gerrymander732
32.65%
204
79.90%
FILE11081 - Strings1802
29.63%
466
70.17%


内容概要:本文系统介绍了算术优化算法(AOA)的基本原理、核心思想及Python实现方法,并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法,其核心思想来源于四则运算,利用乘除运算进行全局勘探,加减运算进行局部开发,通过数学优化器加速函数(MOA)和数学优化概率(MOP)动态控制搜索过程,在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略,并提供了完整的Python代码实现,结合Rastrigin函数进行测试验证。进一步地,以Flask框架搭建前后端分离系统,将AOA应用于图像分割任务,展示了其在实际工程中的可行性与高效性。最后,通过收敛速度、寻优精度等指标评估算法性能,并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群:具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员,尤其适合从事人工智能、图像处理、智能优化等领域的从业者;; 使用场景及目标:①理解元启发式算法的设计思想与实现机制;②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法;③学习如何将优化算法集成到Web系统中实现工程化应用;④为算法性能评估与改进提供实践参考; 阅读建议:建议读者结合代码逐行调试,深入理解算法流程中MOA与MOP的作用机制,尝试在不同测试函数上运行算法以观察性能差异,并可进一步扩展图像分割模块,引入更复杂的预处理或后处理技术以提升分割效果。
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