leetcode動態規劃題目總結

Hello everyone, I am a Chinese noob programmer. I have practiced questions on leetcode.com for 2 years. During this time, I studied a lot from many Great Gods’ articles. After worship, I always wanted to write an article as they did, and now I take the courage to write my first article here.

This is an article summarizing topics related to dynamic programming. Its main inspiration comes from these two articles: Dynamic Programming Patterns and 怎樣學好動態規劃？ - 窮碼農的回答 - 知乎. DP is always a very difficult problem for me and lately, I have done dozens of questions to improve my DP skills. But the DP problem is so flexible that random practice has little effect. Therefore, I made further improvements based on these two articles and summarize some typical topics of DP problem. I hope this article can help you.

In this article, all problems come from leetcode.com and leetcode-cn.com which is a Chinese version of leetcode.com. By the way, because I am Chinese, I attached the Chinese translation after the English topics so that I can use this article more convenient in the future. Moreover, can anyone tell me how to create a table of contents? I wrote this article with VSCode and attempted many extensions to do this but all of them failed. I will be very grateful if you can tell me a way to achieve this function.

I will continue practicing DP problems on leetcode.com and will keep updating this article. If you have any better suggestions or supplements, welcome to put them in the comment area and @me. Now the main text begins.

1. Number Tower，數塔

1. 118. Pascal’s Triangle(Easy)、118. 楊輝三角(簡單)
2. 119. Pascal’s Triangle II(Easy)、119. 楊輝三角 II(簡單)
3. 120. Triangle(Medium)、120. 三角形最小路徑和(中等)
4. 64. Minimum Path Sum(Medium)、64. 最小路徑和(中等)
5. 931. Minimum Falling Path Sum(Medium)、931. 下降路徑最小和(中等)

2. Fibonacci Numbers，斐波那契數列

1. Fibonacci numbers，斐波那契數列問題
   1. 509. Fibonacci Number(Easy)、509. 斐波那契數(簡單)
   2. 1137. N-th Tribonacci Number(Easy)、1137. 第 N 個泰波那契數(簡單)
2. Staircase，爬樓梯問題
   1. 70. Climbing Stairs(Easy)、70. 爬樓梯(簡單)
   2. 746. Min Cost Climbing Stairs(Easy)、746. 使用最小花費爬樓梯(簡單)
3. House thief，偷房子問題
   1. 198. House Robber(Easy)、198. 打家劫舍(簡單)

3. 0/1 Knapsack, 0/1 揹包

1. Equal Subset Sum Partition，相等子集劃分問題
   1. 416. Partition Equal Subset Sum(Medium)、416. 分割等和子集(中等)
2. Subset Sum，子集和問題
   1. 494. Target Sum(Medium)、494. 目標和(中等)
3. Minimum Subset Sum Difference，子集和的最小差問題
   1. 1049. Last Stone Weight II(Medium)、1049. 最後一塊石頭的重量 II(中等)
4. Other，其它
   1. 474. Ones and Zeroes(Medium)、474. 一和零(中等)

4. Unbounded Knapsack，無限（完全）揹包

1. Coin Change，換硬幣問題
   1. 322. Coin Change(Medium)、322. 零錢兌換(中等)
   2. 518. Coin Change 2(Medium)、518. 零錢兌換 II(中等)
2. Others，其它
   1. 377. Combination Sum IV(Medium)、377. 組合總和 Ⅳ(中等)
   2. 1449. Form Largest Integer With Digits That Add up to Target(Hard)、1449. 數位成本和爲目標值的最大數字(困難)

5. Counting DP，計數 DP

5.1. Total Number of Solutions，方案總數

1. 62. Unique Paths(Medium)、62. 不同路徑(中等)
2. 63. Unique Paths II(Medium)、63. 不同路徑 II(中等)
3. 1155. Number of Dice Rolls With Target Sum(Medium)、1155. 擲骰子的N種方法(中等)
4. 1223. Dice Roll Simulation(Medium)、1223. 擲骰子模擬(中等)
5. 935. Knight Dialer(Medium)、935. 騎士撥號器(中等)
6. 576. Out of Boundary Paths(Medium)、576. 出界的路徑數(中等)
7. 790. Domino and Tromino Tiling(Medium)、790. 多米諾和托米諾平鋪(中等)
8. 91. Decode Ways(Medium)、91. 解碼方法(中等)

5.2. Probability，概率

1. 688. Knight Probability in Chessboard(Medium)、688-cn. “馬”在棋盤上的概率(中等)
2. 808. Soup Servings(Medium)、808. 分湯(中等)

6. Decision Making，決策問題

6.1. Buy and Sell Stock，買賣股票問題

1. 309. Best Time to Buy and Sell Stock with Cooldown(Medium)、309. 最佳買賣股票時機含冷凍期(中等)
2. 714. Best Time to Buy and Sell Stock with Transaction Fee(Medium)、714. 買賣股票的最佳時機含手續費(中等)
3. 123. Best Time to Buy and Sell Stock III(Hard)、123. 買賣股票的最佳時機 III(困難)
4. 188. Best Time to Buy and Sell Stock IV(Hard)、188. 買賣股票的最佳時機 IV(困難)

6.2. Can I Win? 遊戲勝負問題

1. 464. Can I Win(Medium)、464. 我能贏嗎(中等)
2. 877. Stone Game(Medium)、877. 石子游戲(中等)
3. 1140. Stone Game II(Medium)、1140. 石子游戲 II(中等)
4. 1406. Stone Game III(Hard)、1406. 石子游戲 III(困難)

6.3. Minimum Cost，最少花費問題

1. 983. Minimum Cost For Tickets(Medium)、983. 最低票價(中等)
2. 650. 2 Keys Keyboard(Medium)、650. 只有兩個鍵的鍵盤(中等)
3. 279. Perfect Squares(Medium)、279. 完全平方數(中等)
4. 801. Minimum Swaps To Make Sequences Increasing(Medium)、801. 使序列遞增的最小交換次數(中等)
5. 256. Paint House(Easy)、256. 粉刷房子(簡單)
6. 265. Paint House II(Hard)、265. 粉刷房子 II(困難)
7. 1473. Paint House III(Hard)、1473. 給房子塗色 III(困難)

7. Interval DP，區間 DP

1. Intervals Merge，區間合併
   1. 1130. Minimum Cost Tree From Leaf Values(Medium)、1130. 葉值的最小代價生成樹(中等)
   2. 96. Unique Binary Search Trees(Medium)、96. 不同的二叉搜索樹(中等)
2. Triangulation，三角剖分
   1. 1039. Minimum Score Triangulation of Polygon(Medium)、1039. 多邊形三角剖分的最低得分(中等)
3. Rectangle Segmentation，矩形分割
   1. 221. Maximal Square(Medium)、221. 最大正方形(中等)
   2. 1277. Count Square Submatrices with All Ones(Medium)、1277. 統計全爲 1 的正方形子矩陣(中等)
   3. 85. Maximal Rectangle(Hard)、85. 最大矩形(困難)
4. Others，其它
   1. 1478. Allocate Mailboxes(Hard)、1478. 安排郵筒(困難)

8. Subsequence/Substring，子序列/子字符串

8.1. Longest Subsequence/Substring，最長子序列/子字符串

1. Longest Common Substring，最長公共子串
   1. 718. Maximum Length of Repeated Subarray(Medium)、718. 最長重複子數組(中等)
2. Longest Common Subsequence，最長公共子序列
   1. 1143. Longest Common Subsequence(Medium)、1143. 最長公共子序列(中等)
   2. 1035. Uncrossed Lines(Medium)、1035. 不相交的線(中等)
   3. 1458. Max Dot Product of Two Subsequences(Hard)、1458. 兩個子序列的最大點積(困難)
3. Longest Increasing Subsequence，最長上升子序列
   1. 674. Longest Continuous Increasing Subsequence(Easy)、674. 最長連續遞增序列(簡單)
   2. 300. Longest Increasing Subsequence(Medium)、300. 最長上升子序列(中等)
   3. 673. Number of Longest Increasing Subsequence(Medium)、673. 最長遞增子序列的個數(中等)
4. Shortest Common Super-sequence，最短公共超級子序列
   1. 1092. Shortest Common Supersequence(Hard)、1092. 最短公共超序列(困難)
5. Others，其它
   1. 368. Largest Divisible Subset(Medium)、368. 最大整除子集(中等)

8.2. Palindromic Subsequence/Substring，迴文子序列/子字符串

1. Longest Palindromic Subsequence，最長迴文子序列
   1. 516. Longest Palindromic Subsequence(Medium)、516. 最長迴文子序列(中等)
2. Longest Palindromic Substring，最長迴文子字符串
   1. 5. Longest Palindromic Substring(Medium)、5. 最長迴文子串(中等)
3. Count Palindromic Subsequences/Substrings，迴文子序列/子字符串的個數
   1. 647. Palindromic Substrings(Medium)、647. 迴文子串(中等)
   2. 730. Count Different Palindromic Subsequences(Hard)、730. 統計不同迴文子字符串(困難)
4. Palindromic Partitioning，迴文分割
   1. 131. Palindrome Partitioning(Medium)、131. 分割回文串(中等)
   2. 132. Palindrome Partitioning II(Hard)、132. 分割回文串 II(困難)

9. String，字符串上的動態規劃

9.1. String Transform，字符串變換

1. 583. Delete Operation for Two Strings(Medium)、583. 兩個字符串的刪除操作(中等)
2. 712. Minimum ASCII Delete Sum for Two Strings(Medium)、712. 兩個字符串的最小ASCII刪除和(中等)
3. 72. Edit Distance(Hard)、72. 編輯距離(困難)

9.2. Regular Expression Matching，正則表達式匹配

1. 678. Valid Parenthesis String(Medium)、678. 有效的括號字符串(中等)
2. 10. Regular Expression Matching(Hard)、10. 正則表達式匹配(困難)
3. 44. Wildcard Matching(Hard)、44. 通配符匹配(困難)
4. 639. Decode Ways II(Hard)、639. 解碼方法 2(困難)

10. Multi-start state，多起始狀態

1. 741. Cherry Pickup(Hard)、741. 摘櫻桃(困難)
2. 1463. Cherry Pickup II(Hard)、1463. 摘櫻桃 II(困難)

11. DP Optimizition，DP優化

1. 1434. Number of Ways to Wear Different Hats to Each Other(Hard)、1434. 每個人戴不同帽子的方案數(困難)
2. 1425. Constrained Subset Sum(Hard)、1425. 帶限制的子序列和(困難)
3. 1444. Number of Ways of Cutting a Pizza(Hard)、1444. 切披薩的方案數(困難)
4. 837. New 21 Game(Medium)、837. 新21點(中等)

Thanks for your browsing and best wishes to you.