feat: Add 0/1 Knapsack Problem: Recursive and Tabulation (Bottom-Up DP) Implementations in Java along with their corresponding Tests

src/main/java/com/thealgorithms/dynamicprogramming/ZeroOneKnapsack.java

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+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * The {@code ZeroOneKnapsack} class provides a method to solve the classic 0/1 Knapsack problem.
+ * It returns the maximum value that can be obtained by selecting items within the weight limit.
+ *
+ * Problem Description: Given weights and values of n items, put these items in a knapsack of capacity W
+ * such that the total value is maximized. You cannot break an item, either pick the complete item or don't pick it.
+ *
+ * https://en.wikipedia.org/wiki/Knapsack_problem
+ */
+public final class ZeroOneKnapsack {
+    private ZeroOneKnapsack() {
+    }
+
+    /**
+     * Solves the 0/1 Knapsack problem using recursion.
+     *
+     * @param values the array containing values of the items
+     * @param weights the array containing weights of the items
+     * @param capacity the total capacity of the knapsack
+     * @param n the number of items
+     * @return the maximum total value achievable within the given weight limit
+     */
+    public static int KnapsackCompute(int[] values, int[] weights, int capacity, int n) {
+        if (n == 0 || capacity == 0) {
+            return 0;
+        }
+
+        if (weights[n - 1] <= capacity) {
+            int include = values[n - 1] + KnapsackCompute(values, weights, capacity - weights[n - 1], n - 1);
+            int exclude = KnapsackCompute(values, weights, capacity, n - 1);
+            return Math.max(include, exclude);
+        } else {
+            return KnapsackCompute(values, weights, capacity, n - 1);
+        }
+    }
+}

src/main/java/com/thealgorithms/dynamicprogramming/ZeroOneKnapsackTab.java

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+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * The {@code ZeroOneKnapsackTab} class provides a method to solve the 0-1 Knapsack problem
+ * using dynamic programming (tabulation approach).
+ *
+ * <p>0-1 Knapsack Problem - 
+ * Given weights and values of n items, and a maximum weight W,
+ * determine the maximum total value of items that can be included in the knapsack
+ * such that their total weight does not exceed W. Each item can be picked only once.
+ * 
+ * Problem Link: https://www.geeksforgeeks.org/0-1-knapsack-problem-dp-10/
+ */
+public final class ZeroOneKnapsackTab {
+
+    private ZeroOneKnapsackTab() {
+        // prevent instantiation
+    }
+
+    /**
+     * Solves the 0-1 Knapsack problem using the bottom-up tabulation technique.
+     *
+     * @param val the values of the items
+     * @param wt the weights of the items
+     * @param W the total capacity of the knapsack
+     * @param n the number of items
+     * @return the maximum value that can be put in the knapsack
+     */
+    public static int kcompute(int[] val, int[] wt, int W, int n) {
+        int[][] dp = new int[n + 1][W + 1];
+
+        for (int i = 1; i <= n; i++) {
+            int value = val[i - 1];
+            int weight = wt[i - 1];
+
+            for (int w = 1; w <= W; w++) {
+                if (weight <= w) {
+                    int include = value + dp[i - 1][w - weight];
+                    int exclude = dp[i - 1][w];
+                    dp[i][w] = Math.max(include, exclude);
+                } else {
+                    dp[i][w] = dp[i - 1][w];
+                }
+            }
+        }
+
+        return dp[n][W];
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/ZeroOneKnapsackTabTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test class for {@code ZeroOneKnapsackTab}.
+ */
+public class ZeroOneknapsackTabTest {
+
+    /**
+     * Tests the 0-1 Knapsack tabulation approach with known values.
+     */
+    @Test
+    public void testKnownValues() {
+        int[] val = {60, 100, 120};
+        int[] wt = {10, 20, 30};
+        int W = 50;
+        int n = val.length;
+
+        // Expected result is 220 (items with weight 20 and 30)
+        assertEquals(220, ZeroOneKnapsackTab.kcompute(val, wt, W, n), "Maximum value for capacity 50 should be 220.");
+    }
+
+    @Test
+    public void testZeroCapacity() {
+        int[] val = {10, 20, 30};
+        int[] wt = {1, 1, 1};
+        int W = 0;
+        int n = val.length;
+
+        // With zero capacity, the result should be 0
+        assertEquals(0, ZeroOneKnapsackTab.kcompute(val, wt, W, n), "Maximum value for capacity 0 should be 0.");
+    }
+
+    @Test
+    public void testZeroItems() {
+        int[] val = {};
+        int[] wt = {};
+        int W = 10;
+        int n = val.length;
+
+        // With no items, the result should be 0
+        assertEquals(0, ZeroOneKnapsackTab.kcompute(val, wt, W, n), "Maximum value with no items should be 0.");
+    }
+
+    @Test
+    public void testExactFit() {
+        int[] val = {5, 10, 15};
+        int[] wt = {1, 2, 3};
+        int W = 6;
+        int n = val.length;
+
+        // All items fit exactly into capacity 6
+        assertEquals(30, ZeroOneKnapsackTab.kcompute(val, wt, W, n), "Maximum value for exact fit should be 30.");
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/ZeroOneKnapsackTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test class for {@code ZeroOneKnapsack}.
+ */
+public class ZeroOneKnapsackTest {
+
+    /**
+     * Tests the knapsack computation for a basic example.
+     */
+    @Test
+    public void testKnapsackBasic() {
+        int[] val = {15, 14, 10, 45, 30};
+        int[] wt = {2, 5, 1, 3, 4};
+        int W = 7;
+        assertEquals(75, ZeroOneKnapsack.KnapsackCompute(val, wt, W, val.length), 
+            "Expected maximum value is 75.");
+    }
+
+    /**
+     * Tests the knapsack computation when the knapsack capacity is zero.
+     */
+    @Test
+    public void testZeroCapacity() {
+        int[] val = {10, 20, 30};
+        int[] wt = {1, 1, 1};
+        int W = 0;
+        assertEquals(0, ZeroOneKnapsack.KnapsackCompute(val, wt, W, val.length), 
+            "Expected maximum value is 0 for zero capacity.");
+    }
+
+    /**
+     * Tests the knapsack computation when there are no items.
+     */
+    @Test
+    public void testNoItems() {
+        int[] val = {};
+        int[] wt = {};
+        int W = 10;
+        assertEquals(0, ZeroOneKnapsack.KnapsackCompute(val, wt, W, 0), 
+            "Expected maximum value is 0 when no items are available.");
+    }
+
+    /**
+     * Tests the knapsack computation when items exactly fit the capacity.
+     */
+    @Test
+    public void testExactFit() {
+        int[] val = {60, 100, 120};
+        int[] wt = {10, 20, 30};
+        int W = 50;
+        assertEquals(220, ZeroOneKnapsack.KnapsackCompute(val, wt, W, val.length), 
+            "Expected maximum value is 220 for exact fit.");
+    }
+}