【Leetcode】647. Palindromic Substrings

Description

Given a string, your task is to count how many palindromic substrings in this string.

The substrings with different start indexes or end indexes are counted as different substrings even they consist of same characters.

Example 1:

Input: "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".

Example 2:

Input: "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".

Note:

1. The input string length won't exceed 1000.

Discusss

回文字符串可以分为长度为1,2,3来分别讨论。dp[i][j]为回文字符串时，dp[i-1][j+1]是否为回文字符串只需判断i-1和j+1处的字符串是否相等。

所以可得状态方程dp[i][j] = dp[i + 1][j - 1] && c[i] == c[j] ? true : false;

Code

class Solution {
    public int countSubstrings(String s) {
        if (s == null || s.length() == 0) { return 0; }
        int n = s.length();
        boolean[][] f = new boolean[n][n];
        f[0][0] = true;
        char[] c = s.toCharArray();
        int count = 1;
        for (int i = 1; i < n; i++) {
            f[i][i] = true;
            count++;
            if (c[i] == c[i-1]) {
                f[i-1][i] = true;
                count++;
            }
        }

        for (int i = 2; i < n; i++) {
            for (int j = 0; j < i - 1; j++) {
                f[j][i] = f[j + 1][i - 1] && (c[j] == c[i] ? true : false);
                if (f[j][i]) {
                    count++;
                }
            }
        }
        return count;
    }
}