给出两个字符串，找到最长公共子串，并返回其长度。
注意事项
子串的字符应该连续的出现在原字符串中，这与子序列有所不同。
样例
给出A=“ABCD”，B=“CBCE”，返回 2
代码
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;
}
}
