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65 lines
2.2 KiB
C++
65 lines
2.2 KiB
C++
/*This is a C++ Program to knapsack problem using dynamic programming. The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass 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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// A Dynamic Programming based solution for 0-1 Knapsack problem
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#include <iostream>
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using namespace std;
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// A utility function that returns maximum of two integers
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int max(int a, int b)
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{
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return (a > b) ? a : 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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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[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]
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= max(val[i - 1] + K[i - 1][w - wt[i - 1]], K[i - 1][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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int main()
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{
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cout << "Enter the number of items in a Knapsack:";
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int n, W;
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cin >> n;
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int val[n], wt[n];
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for (int i = 0; i < n; i++)
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{
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cout << "Enter value and weight for item " << i << ":";
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cin >> val[i];
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cin >> wt[i];
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}
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// int val[] = { 60, 100, 120 };
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// int wt[] = { 10, 20, 30 };
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// int W = 50;
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cout << "Enter the capacity of knapsack";
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cin >> W;
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cout << knapSack(W, wt, val, n);
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return 0;
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}
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/*
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Enter the number of items in a Knapsack:5
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Enter value and weight for item 0:11 111
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Enter value and weight for item 1:22 121
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Enter value and weight for item 2:33 131
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Enter value and weight for item 3:44 141
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Enter value and weight for item 4:55 151
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Enter the capacity of knapsack 300
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99
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