給出兩個字符串，找到最長公共子串，并返回其長度。

注意事項

子串的字符應該連續(xù)的出現(xiàn)在原字符串中，這與子序列有所不同。

樣例
給出A=“ABCD”，B=“CBCE”，返回 2

代碼

public class Solution {
    /**
     * @param A, B: Two string.
     * @return: the length of the longest common substring.
     */
    public int longestCommonSubstring(String A, String B) {
        // state: f[i][j] is the length of the longest lcs
        // ended with A[i - 1] & B[j - 1] in A[0..i-1] & B[0..j-1]
        int n = A.length();
        int m = B.length();
        int[][] f = new int[n + 1][m + 1];
        
        // initialize: f[i][j] is 0 by default
        
        // function: f[i][j] = f[i - 1][j - 1] + 1 or 0
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (A.charAt(i - 1) == B.charAt(j - 1)) {
                    f[i][j] = f[i - 1][j - 1] + 1;
                } else {
                    f[i][j] = 0;
                }
            }
        }
        
        // answer: max{f[i][j]}
        int max = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                max = Math.max(max, f[i][j]);
            }
        }
        
        return max;
    }
}