AtCoder · dp_d

D - Knapsack 1

This C++ solution uses weight-indexed dynamic programming for AtCoder dp_d D - Knapsack 1. Read the reasoning, inspect the code, or try your own test case below.

dp_dDynamic programmingWeight-indexed dynamic programmingC++31 lines
Solution120of 248
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Approach

Weight-indexed dynamic programming

Educational DP Contest Knapsack 1 constraints and weight-indexed DP match.

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

knapsack.cpp

C++

    #include <bits/stdc++.h>
     
    using namespace std;
     
    typedef long long ll;
     
    int main(){
        ios::sync_with_stdio(0);
        cin.tie(0);
        int n, w;
        cin >> n >> w;
        vector<ll> wt(n), val(n);
        for(int i = 0; i < n; i++){
            cin >> wt[i]; cin >> val[i];
        }
        vector<vector<ll>> dp(wt.size() + 1, vector<ll>(w + 1));
        for(int i = 0; i <= wt.size(); i++){
            for(int j = 0; j <= w; j++){
                if(j == 0 || i == 0) dp[i][j] = 0;
                else {
                    ll pick = 0;
                    if(wt[i - 1] <= j){
                        pick = max(dp[i][j], dp[i - 1][j - wt[i - 1]] + val[i - 1]);
                    }
                    ll not_pick = dp[i - 1][j];
                    dp[i][j] = max(pick, not_pick);
                }
            }
        }
        cout << dp[wt.size()][w] << '\n';
    }
        

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