每日一题 day 52 (DP topic)

原创已于 2022-03-15 10:38:44 修改 · 294 阅读

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#动态规划 #leetcode #算法

于 2022-03-15 10:13:25 首次发布

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该博客讨论了如何解决LeetCode上的516题——寻找字符串中最长的回文子序列。采用动态规划的方法，通过一个二维dp数组记录以每个字符为结束或开始的回文子序列的长度，最终得到最长回文子序列的长度。示例中给出了对于输入字符串'bbbab'和'cbbd'的解题过程。

文章目录

problem
approach 1

problem

516. Longest Palindromic Subsequence
Given a string s, find the longest palindromic subsequence’s length in s.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: s = "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb".

Example 2:

Input: s = "cbbd"
Output: 2
Explanation: One possible longest palindromic subsequence is "bb".

approach 1

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int lens = s.size();
        vector<vector<int>> dp(lens, vector<int>(lens, 0));
        for(int i=0; i<lens; i++){
            dp[i][i] = 1;
            for(int j=i-1; j>=0; j--){
                if(s[i] == s[j]){
                    dp[i][j] = dp[i-1][j+1] + 2;
                }else{
                    dp[i][j] = max(dp[i-1][j], dp[i][j+1]);
                }
            }
        }
        return dp[lens-1][0];
    }
};