/*
Dynamic programming approach to 0-1 knapsack problem - O(mn)
Two cases arises for each nd every item - include or discard - 0-1
n This should be the f$ckin rule of life too :P
Max value is obtained from n items is max of the following -
1 - max value obtained from n-1 items with W as weight
(excluding nth item).
2- value of nth item plus max value oobtained by n-1 items and weight as (W - weight(nth) ) item
(including nth item)
If weight of nth > W then only case left is 1st , 0-1 hence
*/
#include<stdio.h>
int max(int a, int b) { return (a > b) ? a : b; };
//returns max value to be sacked in a knapsack of capacity W
int knapSack(int W,int wt[], int val[], int n)
{
int i, w;
int K[n + 1][W + 1];
//build table K[][] in bottom up manner
for (i = 0; i <= n; ++i)
{
for (w = 0; w <= W; ++w)
{
if (i == 0 || w == 0)
K[i][w] = 0;
//include
else if (wt[i - 1] <= w)
K[i][w] = max(val[i - 1] + K[i - 1][w - wt[i - 1] ], K[i - 1][w]);
else
//discard
K[i][w] = K[i - 1][w];
}
}
return K[n][W];
}
int main()
{
int val[] = { 60, 100, 120 };
int wt[] = { 10, 20, 30 };
int W = 50;
int n = sizeof(val) / sizeof(val[0]);
printf("%d", knapSack(W, wt, val, n));
getchar();
return 0;
}
Dynamic programming approach to 0-1 knapsack problem - O(mn)
Two cases arises for each nd every item - include or discard - 0-1
n This should be the f$ckin rule of life too :P
Max value is obtained from n items is max of the following -
1 - max value obtained from n-1 items with W as weight
(excluding nth item).
2- value of nth item plus max value oobtained by n-1 items and weight as (W - weight(nth) ) item
(including nth item)
If weight of nth > W then only case left is 1st , 0-1 hence
*/
#include<stdio.h>
int max(int a, int b) { return (a > b) ? a : b; };
//returns max value to be sacked in a knapsack of capacity W
int knapSack(int W,int wt[], int val[], int n)
{
int i, w;
int K[n + 1][W + 1];
//build table K[][] in bottom up manner
for (i = 0; i <= n; ++i)
{
for (w = 0; w <= W; ++w)
{
if (i == 0 || w == 0)
K[i][w] = 0;
//include
else if (wt[i - 1] <= w)
K[i][w] = max(val[i - 1] + K[i - 1][w - wt[i - 1] ], K[i - 1][w]);
else
//discard
K[i][w] = K[i - 1][w];
}
}
return K[n][W];
}
int main()
{
int val[] = { 60, 100, 120 };
int wt[] = { 10, 20, 30 };
int W = 50;
int n = sizeof(val) / sizeof(val[0]);
printf("%d", knapSack(W, wt, val, n));
getchar();
return 0;
}
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