Merge pull request #6 from tttson/Knapsack

adding 0 1 Knapsack problem

Author: darpanjbora

Dynamic Programming/Knapsack.java

@@ -0,0 +1,65 @@
+import java.util.HashMap;
+import java.util.Map;
+
+// Time complexity: O(nW) where n is the number of items in the input and W is the Knapsack capacity.
+// Auxilary space: O(nW)
+
+class KnapSack
+{
+    // Values (stored in array v)
+    // Weights (stored in array w)
+    // Number of distinct items (n)
+    // Knapsack capacity W
+    public static int knapSack(int[] v, int[] w, int n, int W,
+                            Map<String, Integer> lookup)
+    {
+        // base case: Negative capacity
+        if (W < 0) {
+            return Integer.MIN_VALUE;
+        }
+
+        // base case: no items left or capacity becomes 0
+        if (n < 0 || W == 0) {
+            return 0;
+        }
+
+        // construct a unique map key from dynamic elements of the input
+        String key = n + "|" + W;
+
+        // if sub-problem is seen for the first time, solve it and
+        // store its result in a map
+        if (!lookup.containsKey(key))
+        {
+            // Case 1. include current item n in knapSack (v[n]) & recur
+            // for remaining items (n-1) with decreased capacity (W - w[n])
+            int include = v[n] + knapSack(v, w, n - 1, W - w[n], lookup);
+
+            // Case 2. exclude current item n from knapSack and recur for
+            // remaining items (n-1)
+            int exclude = knapSack(v, w, n - 1, W, lookup);
+
+            // assign max value we get by including or excluding current item
+            lookup.put(key, Integer.max(include, exclude));
+        }
+
+        // return solution to current sub-problem
+        return lookup.get(key);
+    }
+
+    // 0-1 Knapsack problem
+    public static void main(String[] args)
+    {
+        // Input: set of items each with a weight and a value
+        int[] v = { 20, 5, 10, 40, 15, 25 };
+        int[] w = {  1, 2,  3,  8,  7, 4 };
+
+        // Knapsack capacity
+        int W = 10;
+
+        // create a map to store solutions of subproblems
+        Map<String, Integer> lookup = new HashMap<>();
+
+        System.out.println("Knapsack value is " +
+                knapSack(v, w, v.length - 1, W, lookup));
+    }
+}