[2018-12-23] [LeetCode-Week16] 516. Longest Palindromic Subsequence 动态规划

https://leetcode.com/problems/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".

---

d[i][len] = 以 i 开头且长度为 len 的字符串中最长回文串的长度

d[i][len] = max(   d[i][len-1],               (包含前面一个字符)
                   d[i+1][len-1],             (包含后面一个字符)
                   d[i][len-2] + 2,           (如果 前后字符相等)   )

图中的三条箭头分别对应了这三种子情况。

初始条件
d[i][1] = 1;
d[i][2] = 1 (如果不是回文) OR 2 (如果是回文)

---

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int n = s.size();
        int d[1005][1005];
        for (int i = 0; i < n; i++) {
            d[i][1] = 1;
        }
        
        for (int i = 0; i < n; i++) {
            if (i + 1 >= n) break;
            d[i][2] = (s[i] == s[i+1]) ? 2 : 1;
        }
        
        for (int len = 3; len <= n; len++) {
            for (int i = 0; i < n; i++) {
                if (i + 1 >= n) break;
                if (i + len -1 >= n) break;
                d[i][len] = max(d[i + 1][len - 1], d[i][len - 1]);
                if (s[i] == s[i + len - 1]) {
                    d[i][len] = max(d[i][len], d[i + 1][len - 2] + 2);
                }
            }
        }
        return d[0][n];
    }
};