Common substring (DP — Strings Sub-pattern)

// Longest common substring: dp[j] = length of the common run ending at a[i - 1] and b[j - 1].
// A mismatch breaks the run (0). j goes high -> low so dp[j - 1] is still the previous row.
int longestCommonSubstring(const string& a, const string& b) {
    int m = b.size(), best = 0;
    vector<int> dp(m + 1, 0);
    for (size_t i = 1; i <= a.size(); i++)
        for (int j = m; j >= 1; j--) {
            dp[j] = a[i - 1] == b[j - 1] ? dp[j - 1] + 1 : 0;
            best = max(best, dp[j]);                 // the answer can end anywhere
        }
    return best;
}