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/***************************************************************
* Name: Prof. Rafael Orta
* Course: Computer Science & Programming
* Class: CS04225
*****************************************************************
* Purpose: Demonstrate the use of Dynamic programming to resolve the
* knapsack problem
*****************************************************************/
#include <iostream>
using namespace std;
// Function protocol
int knapsack_dp (int n, int M, int w[], int p[]);
int executions = 0; // Variable used to measure the number of executions
int main () {
int i, j; // variables control for the matrix
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;
cout << "\nThe function gets executed: " << executions << " times" << endl;
return 0;
}
int knapsack_dp (int n, int M, int w[], int p[])
{
executions++;
//cout << "\nWeight: " << w[n] << " Value: " << p[n] << " Items: " << n << " Capacity: " << M << endl;
int i, j;
//create a matrix to memoize the values using dynamic programming
int knapsack[n + 1][M + 1];
//cout << "\nRow n+1: " << n+1 << " Col M+1: " << M+1 << endl;
//knapsack[i][j] denotes the maximum attainable value of items in knpasack 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]]);
//cout << "\n Max: " << max (knapsack[i - 1][j], p[i - 1] + knapsack[i - 1][j - w[i - 1]]) << " Row: " << i << " Col: " << j << endl;
}
//can not include the current item in this case
else
{
knapsack[i][j] = knapsack[i - 1][j];
}
}
}
return knapsack[n][M];
}
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