KnapsackProblem.cpp

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

/*———————————————————————————————————————————————————————————————————————————*/
int knapsack_dp(int n, int M, int w[], int p[]){
    int i,j;
 
    //create a matrix to memoize the values using dynamic programming
    int knapsack[n+1][M+1];
 
    //knapsack[i][j] denotes the maximum attainable value of items in knapsack with i available items and capacity of knapsack being j
 
    //initializing knapsack[0][j]=0 for 0<=j<=M because if there is no item, no value can be attained
    for(j = 0; j <= M; j++)
        knapsack[0][j] = 0;
 
    //initializing knapsack[i][0]=0 for 0<=i<=n, because in a bag of zero capacity, no item can be placed
    for(i = 0; i <= n; i++)
        knapsack[i][0] = 0;
 
    //now, filling the matrix in bottom up manner
    for(i = 1; i <= n; i++){
        for(j = 1; j <= M; j++){
            //check if the weight of current item i is less than or equal to the capacity of sack, take maximum of once including the current item and once not including
            if(w[i-1] <= j){
                knapsack[i][j] = max(knapsack[i-1][j], p[i-1]+knapsack[i-1][j-w[i-1]]);
            }
 
            //can not include the current item in this case
            else{
                knapsack[i][j] = knapsack[i-1][j];
            }
        }
    }
    return knapsack[n][M];
}

/*———————————————————————————————————————————————————————————————————————————*/ 
int main(){
    int i, j;
    int n;  //number of items
    int M;  //capacity of knapsack
 
    cout << "Enter the no. of items : ";
    cin >> n;
 
    int w[n];  //weight of items
    int p[n];  //value of items
 
    cout << "Enter the weight and price of all items : " << endl;
    for(i = 0; i < n; i++){
        cin >> w[i] >> p[i];
    }
 
    cout << "enter the capacity of knapsack : ";
    cin >> M;
 
    int result = knapsack_dp(n, M, w, p);
 
    //the maximum value will be given by knasack[n][M], ie. using n items with capacity M
    cout << "The maximum value of items that can be put into knapsack is : " << result;
 
    return 0;
}

/*

Sample Input:
2 50
5 35
1 10
6 45
3 40
*/