LintCode Longest Common Substring

原题链接在这里：http://www.lintcode.com/en/problem/longest-common-substring/#

题目：

Given two strings, find the longest common substring.

Return the length of it.

The characters in substring should occur continuously in original string. This is different with subsequence.

Example

Given A = "ABCD", B = "CBCE", return 2. "BC"

Challenge

O(n x m) time and memory.

题解：

与Longest Common Subsequence相似.

DP. 参考http://www.geeksforgeeks.org/longest-common-substring/

dp[i][j]表示长度为i的str1 和 长度为j的str2 longest common substring长度.

看两个substring 的 suffix.

dp[i][j] = dp[i-1][j-1] + 1 if str1.charAt(i-1) == str2.charAt(j-1).

dp[i][j] = 0. o.w

Time Complexity: O(m*n). Space: O(m*n).

AC Java:

public class Solution {
    /**
     * @param A, B: Two string.
     * @return: the length of the longest common substring.
     */
    public int longestCommonSubstring(String A, String B) {
        if(A == null || B == null){
            return 0;
        }
        int m = A.length(); 
        int n = B.length();
        int [][] dp = new int[m+1][n+1];
        int longest = 0;
        for(int i = 1; i<=m; i++){
            for(int j = 1; j<=n; j++){
                if(A.charAt(i-1) == B.charAt(j-1)){
                    dp[i][j] = dp[i-1][j-1]+1;
                }else{
                    dp[i][j] = 0;
                }
                longest = Math.max(longest, dp[i][j]);
            }
        }
        return longest;
    }
}