DMOJ · dmopc16c1p3

Shoe Shopping

This C++ solution uses dynamic programming for DMOJ dmopc16c1p3 Shoe Shopping. Read the reasoning, inspect the code, or try your own test case below.

dmopc16c1p3Dynamic programmingC++24 lines
Solution184of 248
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Approach

Dynamic programming

Shoe Shopping matches the ordered prices, grouping discounts, and 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

P_3_Shoe_Shopping.cpp

C++

    #include <bits/stdc++.h>
    using namespace std;
    using ll = long long;
    using i128 = __int128;
    const int inf = 1e9;
    const ll INF = 1e18; //❄️
    int main() {
        ios::sync_with_stdio(0); cin.tie(0); 
        int n; cin >> n;
        vector<long double> v(n);
        for (int i = 0; i < n; i++) cin >> v[i];
        vector<long double> dp(n + 1);
        dp[1] = v[0];
        for (int i = 1; i <= n; i++) {
            if (i >= 2) dp[i] = min(dp[i - 1] + v[i - 1], dp[i - 2] + max(v[i - 1], v[i - 2]) + min(v[i - 1], v[i - 2]) * (long double) 0.5);
            if (i >= 3) {
                vector<long double> a = {v[i - 1], v[i - 2], v[i - 3]};
                sort(a.begin(), a.end());
                dp[i] = min(dp[i], dp[i - 3] + a[2] + a[1]);
            }
        }
        cout << fixed << setprecision(1) << dp[n] << '\n';
        return 0;
    }
        

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