LN : leetcode 516 Longest Palindromic Subsequence
lc 516 Longest Palindromic Subsequence
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".
DP Accepted
此问题是求最长回文子序列,和最长回文子串的区别在于序列可以是不连续的。dp[i][j]表示从i到j能生成的最长回文子序列的长度,由定义可知dp[i][i]肯定为1,并且当dp[i]等于dp[j]时,dp[i][j]=dp[i+1][j-1] + 2,否则,dp[i][j] = max(dp[i+1][j], dp[i][j-1])。
class Solution {
public:
int longestPalindromeSubseq(string s) {
int len = s.size();
vector<vector<int>> dp(len, vector<int>(len));
for (int i = len-1; i >= 0; i--) {
dp[i][i] = 1;
for (int j = i+1; j < len; j++) {
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]);
}
}
}
return dp[0][len-1];
}
};
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