pls give potimize and correct small code in c++.

Use this optimized DP code inside the given function:

cpp
int getMinimumTime(int sameTime, int partitionTime, string s) {
    int n = s.size();
    const long long INF = 4e18;

    vector<long long> dp(n + 1, INF);
    dp[0] = 0;

    for (int i = 1; i <= n; i++) {
        vector<long long> freq(256, 0);
        long long extraCost = 0;

        // Try every possible last partition: s[j ... i-1]
        for (int j = i - 1; j >= 0; j--) {
            unsigned char ch = s[j];

            // Adding s[j] creates freq[ch] new matching pairs
            extraCost += freq[ch] * 1LL * sameTime;
            freq[ch]++;

            long long cutCost = (j == 0 ? 0 : partitionTime);
            dp[i] = min(dp[i], dp[j] + cutCost + extraCost);
        }
    }

    return (int)dp[n];
}

Logic: dp[i] = minimum extra time for prefix s[0...i-1].

For every ending position i, we move j backward and compute the matching-pair cost of substring s[j...i-1] on the fly.
Time complexity is O(n^2), which is fine for n <= 2500.