AtCoder · dp_e

E - Knapsack 2

This C++ solution uses value-indexed dynamic programming for AtCoder dp_e E - Knapsack 2. Read the reasoning, inspect the code, or try your own test case below.

dp_eDynamic programmingValue-indexed dynamic programmingC++31 lines
Solution121of 248
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Approach

Value-indexed dynamic programming

Educational DP Contest Knapsack 2 constraints require value-indexed DP, exactly as implemented.

Dynamic programming

Problem and code

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

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Implementation

knapsack2.cpp

C++

    #include <bits/stdc++.h>
     
    using namespace std;
     
    //❄️
    #define int long long 
    signed main(){
        ios::sync_with_stdio(0);
        cin.tie(0);
        int n, w;
        cin >> n >> w;
        vector<int> wt(n), val(n);
        int mx = 0;
        for(int i = 0; i < n; i++){
            cin >> wt[i] >> val[i];
            mx += val[i];
        }
        vector<int> dp(mx + 1, 0x3f3f3f3f);
        dp[0] = 0;
        for(int i = 1; i <= wt.size(); i++){
            for(int j = mx; j >= val[i - 1]; j--){
                dp[j] = min(dp[j], dp[j - val[i - 1]] + wt[i - 1]);
            }
        }
        int ans = 0;
        for(int i = 0; i <= mx; i++){
            if(dp[i] <= w) ans = i;
        }
        cout << ans << '\n';
        return 0;
    }
        

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