Sahil ada practical - 5

FACULTY OF ENGINEERING
Information technology
Analysis and Design of Algorithms
Practical 5
AIM: Implementation of a knapsack problem using dynamic programming.
Code:
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
int W, n;
int main() {
int w, i, l = 0, p, j;
time_t start, end;
double tc;
printf("Enter number of Items \n");
scanf("%d", &n);
printf("Enter maximum weight \n");
scanf("%d", &W);
int k[n + 1][W + 1], a[W], v[W], ks[W];
printf("Enter weights of Items \n");
a[0] = 0;
for (i = 1; i < n + 1; i++) {
printf("w[%d] = ", i);
scanf("%d", &a[i]);
}
printf("Enter profits/values of Items \n");
v[0] = 0;
start = clock();
for (i = 1; i < n + 1; i++) {
printf("p[%d] = ", i);
scanf("%d", &v[i]);
}
k[0][0] = 0;
for (w = 1; w <= W; w++)
k[0][w] = 0;
for (i = 1; i <= n + 1; i++)
k[i][0] = 0;
for (i = 1; i <= n; i++) {
for (w = 1; w <= W; w++) {
if (a[i] <= w) {
if (v[i] + k[i - 1][w - a[i]] > k[i - 1][w]) {
k[i][w] = v[i] + k[i - 1][w - a[i]];
} else {
k[i][w] = k[i - 1][w];
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FACULTY OF ENGINEERING
Information technology
Analysis and Design of Algorithms
}
} else {
k[i][w] = k[i - 1][w];
}
}
}
printf("\n\nP W i \t0 ");
for (i = 1; i <= W; i++) {
printf("%d ", i);
}
printf("\n_____________________\n");
for (i = 0; i < n + 1; i++) {
printf("%d %d %d |\t", v[i], a[i], i);
for (j = 0; j <= W; j++) {
printf("%d ", k[i][j]);
}
printf("\n");
}
i = n;
p = W;
int u = 0, x = 0;
while (i >= 0 && p >= 0) {
if (k[i][W] != k[i - 1][W]) {
ks[++l] = i;
p = p - a[i];
u = u + i;
x += v[i];
i = i - 1;
} else
i = i - 1;
}
ks[++l] = '\0';
l = 1;
printf("\nThe individual weights are ");
while (ks[l] != '\0') {
printf("%d ", ks[l]);
l++;
}
end = clock();
printf("\n\n");
printf("\n\nTotal weight to be carried in knapsack is %d \n\n", u);
printf("Total profit in knapsack is %d \n\n", x);
tc = (difftime(end, start) / CLOCKS_PER_SEC);
printf("\ntime efficiency is %lf", tc);
}
210570116504 Batch A Page no. 2

FACULTY OF ENGINEERING
Information technology
Analysis and Design of Algorithms
O/P
Time Complexity:
O(N*W)
210570116504 Batch A Page no. 3