5. Longest Palindromic Substring

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.

Solution 1

static private int low, max;public static String longestPalindrome(String s) {if (s.length() < 2) {return s;}for (int i = 0; i < s.length() - 1; i++) {extend(s, i, i);extend(s, i, i + 1);}return s.substring(low, low + max);}private static void extend(String s, int start, int end) {while (start >= 0 && end < s.length() && s.charAt(start) == s.charAt(end)) {start--;end++;}if (end - start - 1 > max) {max = end - start - 1;low = start + 1;}}

Solution 2 DP

// DP/* * dp(i, j) represents whether s(i ... j) can form a palindromic substring, * dp(i, j) is true when s(i) equals to s(j) and s(i+1 ... j-1) is a * palindromic substring. When we found a palindrome, check if it's the * longest one. Time complexity O(n^2). */public static String longestPalindrome2(String s) {int n = s.length();String res = null;boolean[][] dp = new boolean[n][n];for (int i = n - 1; i >= 0; i--) {for (int j = i; j < n; j++) {dp[i][j] = s.charAt(i) == s.charAt(j) && (j - i < 3 || dp[i + 1][j - 1]);if (dp[i][j] && (res == null || j - i + 1 > res.length())) {res = s.substring(i, j + 1);}}}return res;}