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Longest common substring problem


Dynamic programming :



\mathit{LCSuff}(S_{1..p}, T_{1..q}) =
\begin{cases}
       \mathit{LCSuff}(S_{1..p-1}, T_{1..q-1}) + 1  & \mathrm{if } \; S[p] = T[q] \\
       0                                            & \mathrm{otherwise}.
\end{cases}

For the example strings "ABAB" and "BABA":
ABAB
00000
B00101
A01020
B00203
A01030

/* Returns length of longest common substring of X[0..m-1] and Y[0..n-1] */

int LCSubStr(char *X, char *Y, int m, int n)
{
  
    int LCSuff[m+1][n+1];
    int result = 0; 
   
    for (int i=0; i<=m; i++)
    {
        for (int j=0; j<=n; j++)
        {
            if (i == 0 || j == 0)
                LCSuff[i][j] = 0;
            else if (X[i-1] == Y[j-1])
            {
                LCSuff[i][j] = LCSuff[i-1][j-1] + 1;
                result = max(result, LCSuff[i][j]);
            }
            else LCSuff[i][j] = 0;
        }
    }
    return result;
}


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