Java program for 0-1 knapsack #200

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	import java.util.*;


	class Knapsack
	{

	// A function to return maximum of two integers
	static int maximum(int a, int b)
	{
	if(a>b)
	return a;
	else
	return b;

	}

	// Returns the maximum value that can be put in a knapsack of capacity W
	static int knapSack(int W, int wt[], int val[], int n)
	{
	int i, w;
	int K[][] = new int[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;
	else if (wt[i-1] <= w)
	K[i][w] = maximum(val[i-1] + K[i-1][w-wt[i-1]] , K[i1][w]);
	else
	K[i][w] = K[i-1][w];
	}
	}

	Return K[n][W];
	}



	public static void main(String args[])
	{

	Scanner s=new Scanner(System.in);
	System.out.println("Enter number of objects");
	int n=s.nextInt();
	int val[]=new int[n];
	int wt[] = new int[n];
	System.out.println("Enter values of objects");


	for(int i=0;i<n;i++)
	{
	val[i]=s.nextInt();
	}

	System.out.println("Enter weights of object");
	for(int i=0;i<n;i++)
	{
	wt[i]=s.nextInt();
	}


	System.out.println("Enter the maximum weight");
	int W = s.nextInt();
	System.out.println(knapSack(W, wt, val, n));
	}
	}

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	# 0-1 Knapsack
	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.

	Time Complexity
	Time Complexity: O(nW) where n is the number of items and W is the capacity of knapsack.
	### Applications
	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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