Title description:
Given a string s, find the longest palindrome subsequence, and return the length of the sequence. It can be assumed that the maximum length of s is 1000.
prompt:
- 1 <= s.length <= 1000
- s contains only lowercase English letters
Example 1:
Input:
"bbbab"
Output:
4
The longest possible palindrome subsequence is "bbbb".
Example 2:
Input:
"cbbd"
Output:
2
The longest possible palindrome subsequence is "bb".
Problem-solving ideas:
- The state f[i][j] indicates the length of the longest palindrome sequence in the substring composed of the ith character to the jth character of s
- Transfer equation
If the ith character of s and the jth character are the same, then f[i][j] = f[i + 1][j-1] + 2
If the ith character of s is different from the jth character If f[i][j] = max(f[i + 1][j], f[i][j-1]) - Then pay attention to the traversal order, i traverses from the last character forward, and j traverses from i + 1 backwards, so as to ensure that each sub-problem has been calculated.
- Initialize f[i][i] = 1 The longest palindrome sequence of a single character is 1
- Result f[0][n-1]
The JAVA code is as follows:
class Solution {
public int longestPalindromeSubseq(String s) {
int n = s.length();
char[] ch = s.toCharArray();
int[][] dp = new int[n][n];
for (int i = 0; i < n; i++) {
dp[i][i] = 1;
}
for (int i = n - 2; i >= 0; i--) {
for (int j = i + 1; j < n; j++) {
if (ch[i] == ch[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][n-1];
}
}
Results of the:
