c_cpp 0-1Knapsack

Posted 2021-05-14

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

// #DynamicProgramming #StandardProblem
// https://codingblocks.com/resources/dp-webinar/

// Testcase:
// 1
// 3
// 6 10 12
// 1 2 3
// 5
// Output: 22

// ===============( Recursion last item to first (Right to Left) )===============
int maxValueTD(vector<int> wt, vector<int> val, int cap, int lastIndex){
    if(lastIndex<0){
        return 0; // no items
    }
    if(cap==0){
        return 0; // no capacity left
    }
    int with=0; // if wt > cap cant pickup, profit 0
    if(wt[lastIndex]<=cap){
        with=val[lastIndex] + maxValueTD(wt,val,cap-wt[lastIndex],lastIndex-1);
    }
    int without=maxValueTD(wt,val,cap,lastIndex-1);
    return max(with,without);
}
int maxValueTD(vector<int> wt, vector<int> val, int cap){
    int lastIndex=wt.size()-1;
    return maxValueTD(wt, val, cap, lastIndex);
}

//=====================( BottomUp )=====================
int maxValueBU(vector<int> wt, vector<int> val, int cap){
    int n=wt.size();
    vector<vector<int>> dp(n+1,vector<int>(cap+1));
    // i-> numOfItems( NOT index ), c->capacity
    // bases cases
    for(int i=0;i<=n;i++){
        dp[i][0]=0; // capacity 0
    }
    for(int c=0;c<=cap;c++){
        dp[0][c]=0; // no items
    }

    for(int i=1;i<=n;i++){
        for(int c=1;c<=cap;c++){
            int prev=dp[i-1][c];
            int with=0;
            // NOTE: wt and val have ranges [0,n-1]
            // Here i denotes number of items NOT index
            if(c>=wt[i-1]){ // if obj is picked up
                with=val[i-1]+dp[i-1][c-wt[i-1]];
            }
            int without=prev; // if object is not picked stays same as for prev
            dp[i][c]=max(with,without);
        }
    }
    cout<<"BottomUp Table: "<<endl;
    for(int i=0;i<=n;i++){
        for(int c=0;c<=cap;c++){
            cout<<dp[i][c]<<" ";
        }
        cout<<endl;
    }
    return dp[n][cap];
}

//=====================( TopDown (Left to Right) )=====================
int maxValue(vector<int> wt, vector<int> val, int cap, int index){
    if(index>=wt.size()){
        return 0; // no items left
    }
    if(cap<=0){
        return 0; // no space left
    }
    int with=0;
    if(wt[index]<=cap){
        with=val[index]+maxValue(wt,val,cap-wt[index],index+1);
    }
    int without=maxValue(wt,val,cap,index+1);
    // decide if picking/without picking gives max profit
    return max(with,without);
}

int maxValue(vector<int> wt, vector<int> val, int cap){
    return maxValue(wt,val,cap,0); // starting from 0 index
}

int main(){
    freopen("ip.txt","r",stdin);
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector<int> val(n);
        vector<int> wt(n);
        for(int i=0;i<n;i++){
            cin>>val[i];
        }
        for(int i=0;i<n;i++){
            cin>>wt[i];
        }
        int cap;
        cin>>cap;
        cout<<"Memoization: "<<maxValue(wt,val,cap)<<endl;
        cout<<"BottomUp: "<<maxValueBU(wt,val,cap)<<endl;
        cout<<"TopDown: "<<maxValueTD(wt,val,cap)<<endl;
    }
    return 0;
}