short java solution,beats 99%,with explanation

  • 7

    It is a typical DP problem. let's use a[i][j] represent the longest Palindromic Subsequence of S[i:j] (i,j inclusive).
    So a[i][j]=
    (1) a[i+1][j-1]+2 if S[i] == S[j]
    (2) Max( a[i+1][j], a[i][j-1] ) if S[i]! = S[j]

    public class Solution {
        public int longestPalindromeSubseq(String s) {
            int n=s.length();
            int[][] a=new int[n][n];
            for(int i=0;i<n;i++) a[i][i]=1;
            return helper(a,0,n-1,s);
        private int helper(int[][] a,int i,int j,String s){
            if(i>j || a[i][j]!=0) return a[i][j];
            if(s.charAt(i)==s.charAt(j)) a[i][j]=helper(a,i+1,j-1,s)+2;
            else a[i][j]=Math.max(helper(a,i,j-1,s),helper(a,i+1,j,s) );
            return a[i][j];

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