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;
}
}