AtCoder · dp_n

Slimes

This C++ solution uses interval dynamic programming for AtCoder dp_n Slimes. Read the reasoning, inspect the code, or try your own test case below.

dp_nDynamic programmingInterval dynamic programmingC++28 lines
Solution193of 248
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Approach

Interval dynamic programming

Educational DP Contest Slimes matches the merge-cost objective and interval dynamic programming.

Dynamic programming

Problem and code

Useful links.

Written by benbenyaojifen. Try the problem first, then compare your approach with the code.

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Implementation

Slimes.cpp

C++

    #include <bits/stdc++.h>
    using namespace std;
    typedef long long ll;
    const ll INF = 1e17; //❄️
    #define int long long
    signed main() {
        ios::sync_with_stdio(0); cin.tie(0); 
        int n; cin >> n;
        vector<int> v(n);
        for (int i = 0; i < n; i++) cin >> v[i];
        vector<int> psa(n + 1);
        for (int i = 1; i <= n; i++) {
            psa[i] = psa[i - 1] + v[i - 1];
        }
        vector<vector<int>> dp(n, vector<int>(n));
        for (int len = 2; len <= n; len++) {
            for (int l = 0; l + len - 1 < n; l++) {
                int r = l + len - 1;
                dp[l][r] = INF;
                for (int k = l; k < r; k++) {
                    int cost = dp[l][k] + dp[k + 1][r] + psa[r + 1] - psa[l];
                    dp[l][r] = min(dp[l][r], cost);
                }
            }
        }
        cout << dp[0][n - 1] << '\n';
        return 0;
    }
        

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