Update permutations.py (#8102)

data_structures/arrays/permutations.py

@@ -1,7 +1,6 @@
 def permute(nums: list[int]) -> list[list[int]]:
     """
     Return all permutations.
-
     >>> from itertools import permutations
     >>> numbers= [1,2,3]
     >>> all(list(nums) in permute(numbers) for nums in permutations(numbers))
@@ -20,7 +19,32 @@ def permute(nums: list[int]) -> list[list[int]]:
     return result
 
 
+def permute2(nums):
+    """
+    Return all permutations of the given list.
+
+    >>> permute2([1, 2, 3])
+    [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1], [3, 1, 2]]
+    """
+
+    def backtrack(start):
+        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 = []
+    backtrack(0)
+    return output
+
+
 if __name__ == "__main__":
     import doctest
 
+    # use res to print the data in permute2 function
+    res = permute2([1, 2, 3])
+    print(res)
     doctest.testmod()