516. Longest Palindromic Subsequence

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".

Approach #1: DP. [Java]

class Solution {
    public int longestPalindromeSubseq(String s) {
        int len = s.length();
        int[][] dp = new int[len+1][len+1];

        for (int l = 1; l <= len; ++l) {
            for (int i = 0; i <= len - l; ++i) {
                int j = i + l - 1;
                if (i == j) {
                    dp[i][j] = 1;
                    continue;
                } else 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][len-1];
    }
}

　　

Analysis:

This problem is similar with 486. Predict the Winner.

dp[i][j] : the longest palindromic subsequence from i to j.

stage: length of substring.

for len = 1 to n:

　　for i = 0 to n-len:

　　　　j = i + len - 1;

　　　　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]);

ans : dp[0][len-1].

Approach #2: optimization. [C++]

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int len = s.length();
        vector<int> dp0(len, 0);
        vector<int> dp1(len, 0);
        vector<int> dp2(len, 0);

        for (int l = 1; l <= len; ++l) {
            for (int i = 0; i <= len - l; ++i) {
                int j = i + l - 1;
                if (i == j) {
                    dp0[i] = 1;
                    continue;
                } else if (s[i] == s[j]) {
                    dp0[i] = dp2[i+1] + 2;
                } else {
                    dp0[i] = max(dp1[i+1], dp1[i]);
                }
            }
            dp0.swap(dp1);
            dp2.swap(dp0);
        }
        return dp1[0];
    }
};

　　

Reference:

http://zxi.mytechroad.com/blog/dynamic-programming/leetcode-516-longest-palindromic-subsequence/