Longest Common Substring

Problem Statement

Given two strings. The task is to find the length of the longest common substring.

Example 1:

Input: S1 = "ABCDGH", S2 = "ACDGHR", n = 6, m = 6
Output: 4
Explanation: The longest common substring
is "CDGH" which has length 4.

Example 2:

Input: S1 = "ABC", S2 "ACB", n = 3, m = 3
Output: 1
Explanation: The longest common substrings
are "A", "B", "C" all having length 1.

Your Task: You don't need to read input or print anything. Your task is to complete the function longestCommonSubstr() which takes the string S1, string S2 and their length n and m as inputs and returns the length of the longest common substring in S1 and S2.

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

Constraints: 1<=n, m<=1000

Intuition

Approach:

We cannot memoize this, as this will boil down to LCS problem, Because if no
match we will have to return and cannot match earlier elements

So, We check for every character matching using bootom up and update the count

Video Links

Approach 1:

C++

int longestCommonSubstr (string s1, string s2, int n, int m){
        int maxi=0;
        vector<vector<int>>dp(n+1,vector<int>(m+1,0));
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                if(s1[i-1] == s2[j-1]){
                    dp[i][j]=dp[i-1][j-1]+1;
                    maxi=max(maxi,dp[i][j]);
                }
                
            }
        }
        return maxi;
    }

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++