7. Design and implement C/C++ Program to solve discrete Knapsack and continuous Knapsack problems using greedy approximation method.
#include <stdio.h>
#define MAX 50
int p[MAX], w[MAX], x[MAX];
double maxprofit;
int n, m, i;
void greedyKnapsack(int n, int w[], int p[], int m)
{
double ratio[MAX];
// Calculate the ratio of profit to weight for each item
for (i = 0; i < n; i++)
{
ratio[i] = (double)p[i] / w[i];
}
// Sort items based on the ratio in non-increasing order
for (i = 0; i < n - 1; i++)
{
for (int j = i + 1; j < n; j++)
{
if (ratio[i] < ratio[j])
{
double temp = ratio[i];
ratio[i] = ratio[j];
ratio[j] = temp;
int temp2 = w[i];
w[i] = w[j];
w[j] = temp2;
temp2 = p[i];
p[i] = p[j];
p[j] = temp2;
}
}
}
int currentWeight = 0;
maxprofit = 0.0;
// Fill the knapsack with items
for (i = 0; i < n; i++)
{
if (currentWeight + w[i] <= m)
{
x[i] = 1; // Item i is selected
currentWeight += w[i];
maxprofit += p[i];
}
else
{
// Fractional part of item i is selected
x[i] = (m - currentWeight) / (double)w[i];
maxprofit += x[i] * p[i];
break;
}
}
printf("Optimal solution for greedy method: %.1f\n", maxprofit);
printf("Solution vector for greedy method: ");
for (i = 0; i < n; i++)
printf("%d\t", x[i]);
}
int main()
{
printf("Enter the number of objects: ");
scanf("%d", &n);
printf("Enter the objects' weights: ");
for (i = 0; i < n; i++)
scanf("%d", &w[i]);
printf("Enter the objects' profits: ");
for (i = 0; i < n; i++)
scanf("%d", &p[i]);
printf("Enter the maximum capacity: ");
scanf("%d", &m);
greedyKnapsack(n, w, p, m);
return 0;
}
Enter the number of objects: 4
Enter the objects' weights: 56 78 98 78
Enter the objects' profits: 23 45 76 78
Enter the maximum capacity: 100
Optimal solution for greedy method: 78.0
Solution vector for greedy method: 1 0 0 0