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0-1 Knapsack
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0-1 Knapsack
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0-1 Knapsack
Given weights and values of n items, put these items in a knapsack of
capacity W to get the maximum total value in the knapsack.
In other words, given two integer arrays val[0..n-1] and wt[0..n-1]
which represent values and weights associated with n items respectively.
Also given an integer W which represents knapsack capacity, find out the maximum
value subset of val[] such that sum of the weights of this subset is smaller than
or equal to W. You cannot break an item, either pick the complete item, or don’t pick it (0-1 property).
import java.util.*;
public class Knapsack_0_1 {
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
int n=sc.nextInt();
int wt[]=new int[n];
int val[]=new int[n];
for(int i=0;i<n;i++)
wt[i]=sc.nextInt();
for(int i=0;i<n;i++)
val[i]=sc.nextInt();
int W=sc.nextInt();
int ans=Max_Profit(W,wt,val,n);
System.out.println(ans);
}
static int Max_Profit(int W, int wt[], int val[], int n)
{
int i, w;
int K[][] = new int[n+1][W+1];
for (i = 0; i <= n; i++)
{
for (w = 0; w <= W; w++)
{
if (i==0 || w==0)
K[i][w] = 0;
else if (wt[i-1] <= w)
K[i][w] = Math.max(val[i-1] + K[i-1][w-wt[i-1]], K[i-1][w]);
else
K[i][w] = K[i-1][w];
}
}
return K[n][W];
}