knapsack Algorithm
The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The name" knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.
//
// A Dynamic Programming based solution for 0-1 Knapsack problem
//
// The All ▲lgorithms library for python
//
// https://allalgorithms.com/dynamic-programming/
// https://github.com/allalgorithms/cpp
//
// Contributed by: Unknown
// Github: Unknown
//
#include<bits/stdc++.h>
// A utility function that returns maximum of two integers
int max(int a, int b) { return (a > b)? a : b; }
// Returns the maximum value that can be put 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;
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
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]);
cout << knapSack(W, wt, val, n);
return 0;
}
