refactor: redesign ArrayCombination (#5181)

* Related to #5164 (Redesign of ArrayCombination)

* Checkstyle fix

* Clang_format

* refactor: cleanup

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>
Co-authored-by: vil02 <vil02@o2.pl>

src/main/java/com/thealgorithms/backtracking/ArrayCombination.java

@@ -1,32 +1,42 @@
 package com.thealgorithms.backtracking;
 
+import java.util.ArrayList;
 import java.util.List;
-import java.util.TreeSet;
 
 /**
- * Finds all permutations of 1...n of length k
- * @author TheClerici (<a href="https://github.com/TheClerici">git-TheClerici</a>)
+ * Finds all combinations of 0...n-1 of length k
  */
 public final class ArrayCombination {
     private ArrayCombination() {
     }
-    private static int length;
 
     /**
-     * Find all combinations of 1..n by creating an array and using backtracking in Combination.java
-     * @param n max value of the array.
-     * @param k length of combination
-     * @return a list of all combinations of length k. If k == 0, return null.
+     * Finds all combinations of length k of 0..n-1 using backtracking.
+     *
+     * @param n Number of the elements.
+     * @param k Length of the combination.
+     * @return A list of all combinations of length k.
      */
-    public static List<TreeSet<Integer>> combination(int n, int k) {
-        if (n <= 0) {
-            return null;
+    public static List<List<Integer>> combination(int n, int k) {
+        if (n < 0 || k < 0 || k > n) {
+            throw new IllegalArgumentException("Wrong input.");
         }
-        length = k;
-        Integer[] arr = new Integer[n];
-        for (int i = 1; i <= n; i++) {
-            arr[i - 1] = i;
+
+        List<List<Integer>> combinations = new ArrayList<>();
+        combine(combinations, new ArrayList<>(), 0, n, k);
+        return combinations;
+    }
+
+    private static void combine(List<List<Integer>> combinations, List<Integer> current, int start, int n, int k) {
+        if (current.size() == k) { // Base case: combination found
+            combinations.add(new ArrayList<>(current)); // Copy to avoid modification
+            return;
+        }
+
+        for (int i = start; i < n; i++) {
+            current.add(i);
+            combine(combinations, current, i + 1, n, k);
+            current.removeLast(); // Backtrack
         }
-        return Combination.combination(arr, length);
     }
 }