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Commit cc26632

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Merge pull request #200 from ManognaMutyala/master
Java program for 0-1 knapsack
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import java.util.*;
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class Knapsack
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{
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// A function to return maximum of two integers
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static int maximum(int a, int b)
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{
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if(a>b)
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return a;
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else
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return b;
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}
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// Returns the maximum value that can be put in a knapsack of capacity W
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static int knapSack(int W, int wt[], int val[], int n)
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{
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int i, w;
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int K[][] = new int[n+1][W+1];
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// Build table K[][] in bottom up manner
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for (i = 0; i <= n; i++)
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{
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for (w = 0; w <= W; w++)
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{
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if (i==0 || w==0)
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K[i][w] = 0;
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else if (wt[i-1] <= w)
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K[i][w] = maximum(val[i-1] + K[i-1][w-wt[i-1]] , K[i1][w]);
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else
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K[i][w] = K[i-1][w];
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}
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}
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Return K[n][W];
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}
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public static void main(String args[])
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{
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Scanner s=new Scanner(System.in);
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System.out.println("Enter number of objects");
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int n=s.nextInt();
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int val[]=new int[n];
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int wt[] = new int[n];
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System.out.println("Enter values of objects");
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for(int i=0;i<n;i++)
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{
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val[i]=s.nextInt();
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}
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System.out.println("Enter weights of object");
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for(int i=0;i<n;i++)
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{
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wt[i]=s.nextInt();
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}
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System.out.println("Enter the maximum weight");
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int W = s.nextInt();
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System.out.println(knapSack(W, wt, val, n));
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}
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}
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# 0-1 Knapsack
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The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
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**Time Complexity**
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Time Complexity: O(nW) where n is the number of items and W is the capacity of knapsack.
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### Applications
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Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials,[4] selection of investments and portfolios selection of assets for asset-backed securitization and generating keys for the Merkle–Hellman and other knapsack cryptosystems

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