The longest sub-string length in a character array

longest_substring.c

int longest_substring(char* s)
{
    int string_length = strlen(s);
    if (string_length == 0)
    {
        return 0;
    }

    // form the string matrix
    int string_matrix[string_length][string_length];
    for (int i = 0; i < string_length; i++)
    {
        for (int j = 0; j < string_length; j++)
        {
            string_matrix[i][j] = 0;
        }
    }
    for (int i = 0; i < string_length; i++)
    {
        int temp = 0;
        for (int j = i + 1; j < string_length; j++)
        {
            if (*(s + i) == *(s + j))
            {
                string_matrix[i][j] = ++temp;
            }
            else
            {
                string_matrix[i][j] = temp;
            }
        }
    }

    // form the concatenation matrix
    int concatenation_matrix[string_length][string_length];
    for (int i = 0; i < string_length; i++)
    {
        for (int j = 0; j < string_length; j++)
        {
            concatenation_matrix[i][j] = 0;
        }
    }
    for (int i = 0; i < string_length; i++)
    {
        for (int j = i; j < string_length; j++)
        {
            // add the jth row to the ith row
            for (int k = 0; k < string_length; k++)
            {
                concatenation_matrix[i][k] += string_matrix[j][k];
            }
            // check if concetenation is redundant
            bool redundant = false;
            for (int k = 0; k < string_length - 1; k++)
            {
                if ((concatenation_matrix[i][k + 1] - concatenation_matrix[i][k]) > 1)
                {
                    redundant = true;
                    break;
                }
            }
            // subtract the jth row from the ith row if redundant
            if (redundant)
            {
                for (int k = 0; k < string_length; k++)
                {
                    concatenation_matrix[i][k] -= string_matrix[j][k];
                }
            }
        }
    }

    // find the row with the most zeros
    int index = 0;
    int length = 0;
    for (int i = 0; i < string_length; i++)
    {
        int count = 0;
        for (int j = i; j < string_length; j++)
        {
            if (concatenation_matrix[i][j] == 0)
            {
                count++;
            }
            else
            {
                break;
            }
        }
        if (count > length)
        {
            length = count;
            index = i;
        }
    }

    return length;
}