_516_LongestPalindromicSubsequence.java

package dynamicProgramming;

/**
 * 
 * Problem:
 * 
 * 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".
 *
 */
public class _516_LongestPalindromicSubsequence {
	public int longestPalindromeSubseq(String s) {
		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];
	}
}