Memoization code for "Longest Common Substring" doesn't work as expected

Question

I was able to think of a recursive solution for the problem "Longest Common Substring" but when I try to memoize it, it doesn't seem to work as I expected it to, and throws a wrong answer.

Here is the recursive code.

int lcs(string X, string Y,int i, int j, int count)
{
    if (i == 0 || j == 0)
        return count;
    if (X[i - 1] == Y[j - 1])
        count = lcs(X,Y,i - 1, j - 1, count + 1);
    count = max(count,max(lcs(X,Y,i, j-1, 0),lcs(X,Y,i - 1, j, 0)));
    return count;
}
 
int longestCommonSubstr(string S1, string S2, int n, int m)
{
    return lcs(S1,S2,n,m,0,dp);
}

And here is the memoized code.

int lcs(string X, string Y,int i, int j, int count,vector<vector<vector<int>>>& dp)
{
    if (i == 0 || j == 0)
        return count;
 
    if(dp[i - 1][j - 1][count] != -1)
        return dp[i - 1][j - 1][count];

    if (X[i - 1] == Y[j - 1])
        count = lcs(X, Y, i - 1, j - 1, count + 1, dp);
    count = max(count,max(lcs(X,Y,i, j-1, 0,dp),lcs(X,Y,i - 1, j, 0,dp)));
    return dp[i-1][j-1][count]=count;
}

int longestCommonSubstr(string S1, string S2, int n, int m)
{
    int maxSize=max(n,m);
    vector<vector<vector<int>>> dp(n,vector<vector<int>>(m,vector<int>(maxSize,-1)));
    return lcs(S1,S2,n,m,0,dp);
}

I do know that the problem can be solved using a 2D DP vector as well but my objective was to convert my original recursive solution to a memoized solution and not write a solution from scratch. And as I have 3 parameters which are changing, so it should use a 3D DP table.

Can anyone figure out what's wrong or help me out with a 3D DP solution with recursive code same or similar to mine.

Note:- An interesting observation, the max function for some reason works from left to right on my Mac system and on Ubuntu running under parallels as well, but the same function works from right to left in Windows machine and in online compilers. I do not know the reason but I would be happy to know about it. I'm running the code in an M1 Mac, I don't know if the ARM compiler is different from x86 Mac compiler or not.

Another thing, the memoized code gives different answers depending upon which recursive call is called first on the line,

count = max(count,max(lcs(X,Y,i, j-1, 0),lcs(X,Y,i - 1, j, 0)));

If I swap the positions of the function call statements then it gives a correct output but for that specific test case and probably similar cases.

This Memo solution gives TLE as well in large test cases, and I do not know why.

I recently started studying DP and this is the only question which I wasn't able to solve by just modifying the original recursive solution. It has been two days and I just can't figure out the proper reasons.

Submission Link:- https://practice.geeksforgeeks.org/problems/longest-common-substring1452/1/#

Any help in this regard would be great.

Memoization code for "Longest Common Substring" doesn't work as expected

0 Answers0