Longest Palindromic Substring (DP)

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本文介绍了一种高效算法来找出给定字符串中的最长回文子串。通过使用布尔型表格记录子串是否为回文，该算法能够系统地检查所有可能的子串长度，并最终确定最长的回文子串。

Given a string S, find the longest palindromic substring in S. You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.

public class Solution {

public String longestPalindrome(String s) {

int n = s.length();
char[] charArray = s.toCharArray();

int longestBegin = 0;
int maxLen = 1;

boolean[][] table = new boolean[1000][1000];
for (int i = 0; i < 1000; i++) {
for (int j = 0; j < 1000; j++) {
table[i][j] = false;
}
}

for (int i = 0; i < n; i++) {
table[i][i] = true;
}

for (int i = 0; i < n - 1; i++) {
if (charArray[i] == charArray[i + 1]) {
table[i][i + 1] = true;
longestBegin = i;
maxLen = 2;
}
}

for (int len = 3; len <= n; len++) {
for (int i = 0; i <= n-1; i++) {
int j = i + len - 1;
if ( j<=n-1 && charArray[i] == charArray[j] && table[i + 1][j - 1]) {
table[i][j] = true;

if (maxLen < len) {
longestBegin = i;
maxLen = len;
}

}
}
}

return s.substring(longestBegin, longestBegin + maxLen);

}
}