Feat(Improved): Add 0/1 Knapsack Problem: Recursive and Tabulation (Bottom-Up DP) Implementations in Java along with their corresponding Tests (#6425)

* feat: Add 0/1 Knapsack and its tabulation implementation with their corresponding tests

* feat: Add 0/1 Knapsack and its tabulation implementation with their corresponding tests

* feat: Add 0/1 Knapsack and its tabulation implementation with their corresponding tests

* Feat:add 0/1knapsack and 0/1knapsacktabulation along with their tests

* Feat:add 0/1knapsack and 0/1knapsacktabulation along with their tests

* Feat:add 0/1knapsack and 0/1knapsacktabulation along with their tests

---------

Co-authored-by: Oleksandr Klymenko <alexanderklmn@gmail.com>

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

@@ -0,0 +1,69 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Tabulation (Bottom-Up) Solution for 0-1 Knapsack Problem.
+ * This method uses dynamic programming to build up a solution iteratively,
+ * filling a 2-D array where each entry dp[i][w] represents the maximum value
+ * achievable with the first i items and a knapsack capacity of w.
+ *
+ * The tabulation approach is efficient because it avoids redundant calculations
+ * by solving all subproblems in advance and storing their results, ensuring
+ * each subproblem is solved only once. This is a key technique in dynamic programming,
+ * making it possible to solve problems that would otherwise be infeasible due to
+ * exponential time complexity in naive recursive solutions.
+ *
+ * Time Complexity: O(n * W), where n is the number of items and W is the knapsack capacity.
+ * Space Complexity: O(n * W) for the DP table.
+ *
+ * For more information, see:
+ * https://en.wikipedia.org/wiki/Knapsack_problem#Dynamic_programming
+ */
+public final class KnapsackZeroOneTabulation {
+
+    private KnapsackZeroOneTabulation() {
+        // Prevent instantiation
+    }
+
+    /**
+     * Solves the 0-1 Knapsack problem using the bottom-up tabulation technique.
+     * @param values the values of the items
+     * @param weights the weights of the items
+     * @param capacity the total capacity of the knapsack
+     * @param itemCount the number of items
+     * @return the maximum value that can be put in the knapsack
+     * @throws IllegalArgumentException if input arrays are null, of different lengths,or if capacity or itemCount is invalid
+     */
+    public static int compute(final int[] values, final int[] weights, final int capacity, final int itemCount) {
+        if (values == null || weights == null) {
+            throw new IllegalArgumentException("Values and weights arrays must not be null.");
+        }
+        if (values.length != weights.length) {
+            throw new IllegalArgumentException("Values and weights arrays must be non-null and of same length.");
+        }
+        if (capacity < 0) {
+            throw new IllegalArgumentException("Capacity must not be negative.");
+        }
+        if (itemCount < 0 || itemCount > values.length) {
+            throw new IllegalArgumentException("Item count must be between 0 and the length of the values array.");
+        }
+
+        final int[][] dp = new int[itemCount + 1][capacity + 1];
+
+        for (int i = 1; i <= itemCount; i++) {
+            final int currentValue = values[i - 1];
+            final int currentWeight = weights[i - 1];
+
+            for (int w = 1; w <= capacity; w++) {
+                if (currentWeight <= w) {
+                    final int includeItem = currentValue + dp[i - 1][w - currentWeight];
+                    final int excludeItem = dp[i - 1][w];
+                    dp[i][w] = Math.max(includeItem, excludeItem);
+                } else {
+                    dp[i][w] = dp[i - 1][w];
+                }
+            }
+        }
+
+        return dp[itemCount][capacity];
+    }
+}