Find the longest palindromic substring in a string

palidromic_substring.c

char *longest_palindrome(char *s)
{
    int n = strlen(s);
    if (n < 2) return s; // Every string of length 1 or 0 is a palindrome

    bool p[n][n];
    memset(p, 0, sizeof(p));

    int start  = 0;
    int length = 1;

    /* The base cases */
    for (int i = 0; i < n; i++)
    {
        p[i][i] = true;
    }
    for (int i = 0; i < n - 1; i++)
    {
        p[i][i + 1] = (s[i] == s[i + 1]);
        if (p[i][i + 1])
        {
            start  = i;
            length = 2;
        }
    }

    /* p[i, j] = true,  if the substring s[i] ... s[j] is a palindrome
       p[i, j] = false, otherwise. */
    for (int k = 3; k < n + 1; k++)
    {
        for (int i = 0; i < n - k + 1; i++)
        {
            int j = i + k - 1;
            p[i][j] = (p[i + 1][j - 1] && s[i] == s[j]);
            if (p[i][j] && (k > length))
            {
                start  = i;
                length = k;
            }
        }
    }

    if (s[start + length]) s[start + length] = NULL;
    return &s[start];
}