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May 18, 2013 01:03
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Knapsack Algorithm in Java. Source: http://introcs.cs.princeton.edu/java/96optimization/Knapsack.java.html
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/************************************************************************* | |
* Compilation: javac Knapsack.java | |
* Execution: java Knapsack N W | |
* | |
* Generates an instance of the 0/1 knapsack problem with N items | |
* and maximum weight W and solves it in time and space proportional | |
* to N * W using dynamic programming. | |
* | |
* For testing, the inputs are generated at random with weights between 0 | |
* and W, and profits between 0 and 1000. | |
* | |
* % java Knapsack 6 2000 | |
* item profit weight take | |
* 1 874 580 true | |
* 2 620 1616 false | |
* 3 345 1906 false | |
* 4 369 1942 false | |
* 5 360 50 true | |
* 6 470 294 true | |
* | |
*************************************************************************/ | |
public class Knapsack { | |
public static void main(String[] args) { | |
int N = Integer.parseInt(args[0]); // number of items | |
int W = Integer.parseInt(args[1]); // maximum weight of knapsack | |
int[] profit = new int[N+1]; | |
int[] weight = new int[N+1]; | |
// generate random instance, items 1..N | |
for (int n = 1; n <= N; n++) { | |
profit[n] = (int) (Math.random() * 1000); | |
weight[n] = (int) (Math.random() * W); | |
} | |
// opt[n][w] = max profit of packing items 1..n with weight limit w | |
// sol[n][w] = does opt solution to pack items 1..n with weight limit w include item n? | |
int[][] opt = new int[N+1][W+1]; | |
boolean[][] sol = new boolean[N+1][W+1]; | |
for (int n = 1; n <= N; n++) { | |
for (int w = 1; w <= W; w++) { | |
// don't take item n | |
int option1 = opt[n-1][w]; | |
// take item n | |
int option2 = Integer.MIN_VALUE; | |
if (weight[n] <= w) option2 = profit[n] + opt[n-1][w-weight[n]]; | |
// select better of two options | |
opt[n][w] = Math.max(option1, option2); | |
sol[n][w] = (option2 > option1); | |
} | |
} | |
// determine which items to take | |
boolean[] take = new boolean[N+1]; | |
for (int n = N, w = W; n > 0; n--) { | |
if (sol[n][w]) { take[n] = true; w = w - weight[n]; } | |
else { take[n] = false; } | |
} | |
// print results | |
System.out.println("item" + "\t" + "profit" + "\t" + "weight" + "\t" + "take"); | |
for (int n = 1; n <= N; n++) { | |
System.out.println(n + "\t" + profit[n] + "\t" + weight[n] + "\t" + take[n]); | |
} | |
} | |
} |
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