516. Longest Palindromic Subsequence

Description

https://leetcode.com/problems/longest-palindromic-subsequence/
题意：
给定一个字符串，寻找最长回文子序列，返回其长度。

Solving Ideas

https://www.youtube.com/watch?v=_nCsPn7_OgI&t=57s

动态规划：

State:
dp[i][j]: s.substring(i, j+1)中最长回文序列的长度

Initial State:
dp[i][i] = 1;

State Transition:
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]);

Solution

class Solution {
    /**
     * dp[i][j]: palindromic sub-sequence's length of substring(i,j+1)
     * i,j represent left, right indexes of input string
     *
     * State transition:
     *   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]);
     *
     * Initial state:
     *   dp[i][i] = 1;
     *
     * @param s string
     * @return the length of longest palindromic sub-sequence
     */
    public int longestPalindromeSubseq(String s) {
        if (s == null || s.length() == 0) return 0;

        int[][] dp = new int[s.length()][s.length()];
        for (int i = s.length() - 1; i >= 0; i--) {
            dp[i][i] = 1;
            for (int j = i + 1; j < s.length(); 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][s.length() - 1];
    }
}