Add combinations function for array inputs

data_structures/arrays/new_combination.py

@@ -0,0 +1,68 @@
+from itertools import combinations
+
+
+def permute_recursive(nums: list[int]) -> list[list[int]]:
+    """
+    Return all permutations.
+
+    >>> permute_recursive([1, 2, 3])
+    [[3, 2, 1], [2, 3, 1], [1, 3, 2], [3, 1, 2], [2, 1, 3], [1, 2, 3]]
+    """
+    result: list[list[int]] = []
+    if len(nums) == 0:
+        return [[]]
+    for _ in range(len(nums)):
+        n = nums.pop(0)
+        permutations = permute_recursive(nums.copy())
+        for perm in permutations:
+            perm.append(n)
+        result.extend(permutations)
+        nums.append(n)
+    return result
+
+
+def permute_backtrack(nums: list[int]) -> list[list[int]]:
+    """
+    Return all permutations of the given list.
+
+    >>> permute_backtrack([1, 2, 3])
+    [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1], [3, 1, 2]]
+    """
+
+    def backtrack(start: int) -> None:
+        if start == len(nums) - 1:
+            output.append(nums[:])
+        else:
+            for i in range(start, len(nums)):
+                nums[start], nums[i] = nums[i], nums[start]
+                backtrack(start + 1)
+                nums[start], nums[i] = nums[i], nums[start]  # backtrack
+
+    output: list[list[int]] = []
+    backtrack(0)
+    return output
+
+
+def get_combinations(nums: list[int], r: int) -> list[list[int]]:
+    """
+    Return all combinations of the given list of length r.
+
+    >>> get_combinations([1, 2, 3], 2)
+    [[1, 2], [1, 3], [2, 3]]
+    """
+    return [list(comb) for comb in combinations(nums, r)]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    # Test permutations
+    result_permute = permute_backtrack([1, 2, 3])
+    print("Permutations:", result_permute)
+
+    # Test combinations
+    result_combinations = get_combinations([1, 2, 3], 2)
+    print("Combinations of length 2:", result_combinations)
+
+    # Run doctests
+    doctest.testmod()