class Solution:
    # import itertools
    # def permute(self, nums):
    #     """
    #     :type nums: List[int]
    #     :rtype: List[List[int]]
    #     """
    #     result = itertools.permutations(nums)
    #     result = [list(t) for t in result]
    #     return result

    def permute(self, nums):
        # DPS with swapping
        res = []
        if len(nums) == 0:
            return res
        self.get_permute(res, nums, 0)
        return res

    def get_permute(self, res, nums, index):
        if index == len(nums):
            res.append(list(nums))
            return
        for i in range(index, len(nums)):
            nums[i], nums[index] = nums[index], nums[i]
            # s(n) = 1 + s(n-1)
            self.get_permute(res, nums, index + 1)
            nums[i], nums[index] = nums[index], nums[i]

    # def permute(self, nums):
    #     # iterative solution
    #     res = [[]]
    #     for i in range(len(nums)):
    #         cache = set()
    #         while len(res[0]) == i:
    #             curr = res.pop(0)
    #             for j in range(len(curr) + 1):
    #                 # generate new n permutations from n -1 permutations
    #                 new_perm = curr[:j] + [nums[i]] + curr[j:]
    #                 stemp = ''.join(map(str, new_perm))
    #                 if stemp not in cache:
    #                     cache.add(stemp)
    #                     res.append(new_perm)
    #     return res

class Solution:
    # import itertools
    # def permute(self, nums):
    #     """
    #     :type nums: List[int]
    #     :rtype: List[List[int]]
    #     """
    #     result = itertools.permutations(nums)
    #     result = [list(t) for t in result]
    #     return result

    def permute(self, nums):
        # DPS with swapping
        res = []
        if len(nums) == 0:
            return res
        self.get_permute(res, nums, 0)
        return res

    def get_permute(self, res, nums, index):
        if index == len(nums):
            res.append(list(nums))
            return
        for i in range(index, len(nums)):
            nums[i], nums[index] = nums[index], nums[i]
            # s(n) = 1 + s(n-1)
            self.get_permute(res, nums, index + 1)
            nums[i], nums[index] = nums[index], nums[i]

    # def permute(self, nums):
    #     # iterative solution
    #     res = [[]]
    #     for i in range(len(nums)):
    #         cache = set()
    #         while len(res[0]) == i:
    #             curr = res.pop(0)
    #             for j in range(len(curr) + 1):
    #                 # generate new n permutations from n -1 permutations
    #                 new_perm = curr[:j] + [nums[i]] + curr[j:]
    #                 stemp = ''.join(map(str, new_perm))
    #                 if stemp not in cache:
    #                     cache.add(stemp)
    #                     res.append(new_perm)
    #     return res

# import itertools # def permute(self, nums): #     """ #     :type nums: List[int] #     :rtype: List[List[int]] #     """ #     result = itertools.permutations(nums) #     result = [list(t) for t in result] #     return result # DPS with swapping # s(n) = 1 + s(n-1) # def permute(self, nums): #     # iterative solution #     res = [[]] #     for i in range(len(nums)): #         cache = set() #         while len(res[0]) == i: #             curr = res.pop(0) #             for j in range(len(curr) + 1): #                 # generate new n permutations from n -1 permutations #                 new_perm = curr[:j] + [nums[i]] + curr[j:] #                 stemp = ''.join(map(str, new_perm)) #                 if stemp not in cache: #                     cache.add(stemp) #                     res.append(new_perm) #     return res