Help my about the LCS.

general
,
1

First, I wanna say sorry for my awful English!

These days, i start to learning algorithms, and now i want to count the LCS of the two strings.
I wrote my code and sent it to the online judge, but it always got WA. I can find what’s wrong with it, because it succeed int my computer. I need your help, although it’s a very simple question, but i am a newbie, so i ask this question.
Here is my core code.

    string first, second;
    cin >> first >> second;
    int n = first.length(), m = second.length();
    for(int i = 0; i <= m; i++) lcs[i][0] = 0;
    for(int j = 0; j <= n; j++) lcs[0][j] = 0;
    
// index from 1 to n for
for(int i = n; i >= 1; i--) first[i] = first[i-1];
    for(int j = m; j >= 1; j--) second[j] = second[j-1];
		  
    for(int r = 1; r <= m; r++){
        for(int c = 1; c <= n; c++){
	        if(first[c] == second[r]) lcs[r][c] = lcs[r-1][c-1] + 1;
            else lcs[r][c] = max(lcs[r-1][c], lcs[r][c-1]);
        }
    }
	printf("%d\n", lcs[m][n]);
}

}

Thanks a lot for helping me with such a simple question!