Add 0/1 Knapsack Algorithm implementation using Dynamic Programming

Author: Madhu696969

src/main/java/dynamicprogramming/Knapsack.java

@@ -0,0 +1,52 @@
+package dynamicprogramming;
+/**
+ * Implementation of the 0/1 Knapsack Problem using Dynamic Programming.
+ *
+ * Given weights and values of n items, put these items in a knapsack of capacity W
+ * to get the maximum total value in the knapsack.
+ */
+public class Knapsack {
+
+    /**
+     * Returns the maximum value that can be put in a knapsack of capacity W.
+     *
+     * @param W    capacity of the knapsack
+     * @param wt   array of weights of the items
+     * @param val  array of values of the items
+     * @param n    number of items
+     * @return maximum value achievable with given capacity
+     */
+    public static int knapSack(int W, int[] wt, int[] val, int n) {
+        int[][] dp = new int[n + 1][W + 1];
+
+        // Build table dp[][] in bottom-up manner
+        for (int i = 0; i <= n; i++) {
+            for (int w = 0; w <= W; w++) {
+                if (i == 0 || w == 0) {
+                    dp[i][w] = 0; // Base case: no items or zero capacity
+                } else if (wt[i - 1] <= w) {
+                    // Include the item or exclude it, choose max value
+                    dp[i][w] = Math.max(val[i - 1] + dp[i - 1][w - wt[i - 1]],
+                                        dp[i - 1][w]);
+                } else {
+                    // Item can't be included because it weighs more than capacity
+                    dp[i][w] = dp[i - 1][w];
+                }
+            }
+        }
+
+        return dp[n][W];
+    }
+
+    // Example usage and simple test case
+    public static void main(String[] args) {
+        int[] values = { 60, 100, 120 };
+        int[] weights = { 10, 20, 30 };
+        int capacity = 50;
+        int n = values.length;
+
+        int maxValue = knapSack(capacity, weights, values, n);
+        System.out.println("Maximum value in Knapsack = " + maxValue);
+        // Expected output: 220
+    }
+}