Form1_DP/Knapsack+Solution_Reconstruction.cpp at main · rahulpaul-07/Form1_DP · GitHub

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#include <bits/stdc++.h>
using namespace std;

int n;
int w[3003];
int v[3003];
int W;

int dp[3003][3003];

vector<int> solution;

int rec(int i,int x){

    // basecase
    if(i==n){
        return 0;
    }

    // cache check
    if(dp[i][x]!=-1){
        return dp[i][x];
    }

    // transition
    int ans = rec(i+1,x);

    if(w[i] <= x){
        ans = max(ans, rec(i+1,x-w[i]) + v[i]);
    }

    // save and return
    dp[i][x] = ans;
    return ans;
}

void generate(int i,int x){

    if(i==n){
        return;
    }

    int donttake = rec(i+1,x);

    if(w[i] <= x){

        int take = rec(i+1,x-w[i]) + v[i];

        if(donttake >= take){
            generate(i+1,x);
        }
        else{
            solution.push_back(i);
            generate(i+1,x-w[i]);
        }
    }
    else{
        generate(i+1,x);
    }
}

void solve(){

    cin>>n;

    for(int i=0;i<n;i++){
        cin>>w[i];
    }

    for(int i=0;i<n;i++){
        cin>>v[i];
    }

    cin>>W;

    memset(dp,-1,sizeof(dp));

    cout<<"Maximum value = "<<rec(0,W)<<endl;

    generate(0,W);

    cout<<"Items taken:"<<endl;

    for(int x:solution){
        cout<<x<<" ";
    }

    cout<<endl;
}

int main(){
    solve();
}