LeetCode 516. Longest Palindromic Subsequence (Java版; Meidum)

淩亂°似流年 2023-05-28 14:21 8阅读 0赞

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## LeetCode 516. Longest Palindromic Subsequence (Java版; Meidum) ##

#### 题目描述 ####

Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000.
    
    Example 1:
    Input:
    
    "bbbab"
    Output:
    4
    One possible longest palindromic subsequence is "bbbb".
    Example 2:
    Input:
    
    "cbbd"
    Output:
    2
    One possible longest palindromic subsequence is "bb".

#### 第一次做, 动态规划 核心:1) dp\[i\]\[j\]表示\[i,j\]上的最长回文子串 2) 根据递推公式中的依赖关系可知, 需要从下往上, 从左往右遍历 ####

class Solution { 
        public int longestPalindromeSubseq(String s) { 
            /* dp[i][j]表示s[i,j]上的最长回文子序列长度 i相当于左边界, j相当于右边界 dp[i][j] = dp[i+1][j-1] + (s[i]==s[j]?1:0) */
            int n = s.length();
            int[][] dp = new int[n][n];
            for (int i = 0; i < n; i++) { 
                dp[i][i] = 1;
            }
            for (int i = n - 1; i >= 0; i--) { 
                for (int j = i + 1; j < n; j++) { 
                    if (s.charAt(i) == s.charAt(j)) { 
                        dp[i][j] = dp[i + 1][j - 1] + 2;
                    } else { 
                        dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
                    }
                }
            }
            return dp[0][n - 1];
    
        }
    }

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