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Knapsack.cpp
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Knapsack.cpp
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/***
***/
#include <bits/stdc++.h>
using namespace std;
int main()
{
int n, W;
cout << "Enter the number of items and capacity of the bag: ";
cin >> n >> W;
int cost[n+1], w[n+1];
cout << "Enter the weights : ";
for(int i=0; i<n; i++)
cin>>w[i];
cout << "Enter the costs : ";
for(int i=0; i<n; i++)
cin>>cost[i];
// Summation w_i <=W
// Some of costs = Maximum
int dp[n+1][W+1]; // dp[i][j] Stores the maximum value that can be accomodated with using first i weights in a knapsack of weight j.
for (int i=0; i<=n; i++)
for (int j=0; j<=W; j++) {
if(i==0 or j==0)
dp[i][j] = 0; //If bag has no space or no items in the house to begin with.
if(w[i-1] <= j) // If we had a weight of j
dp[i][j] = max(dp[i-1][j], cost[i-1] + dp[i-1][j-w[i-1]]);
else
dp[i][j] = dp[i-1][j];
}
cout << "Largest values possible = " << dp[n][W] << endl;
return 0;
}