递归+交换

class Solution:
    def permute(self, nums: List[int]) -> List[List[int]]:
        self.count = 0
        res = []
        end = len(nums)
        self.exchange(nums,0,end,res)
        return res
        
    def exchange(self,nums,begin,nums_length,res):
        if begin == nums_length-1:
            self.count += 1
            res.append(nums[:])
            print('count{0}:{1}'.format(self.count,nums[:]))
        for i in range(begin,nums_length):
            nums[i],nums[begin] = nums[begin],nums[i]
            self.exchange(nums,begin+1,nums_length,res)
            nums[i],nums[begin] = nums[begin],nums[i]
   

递归+跳过已选数字

class Solution:
    def permute(self, nums: List[int]) -> List[List[int]]:
        res = []
        if not nums: return []
        if len(nums)==1: return [nums]
        for i in range(len(nums)):
            for j in self.permute(nums[:i]+nums[i+1:]):   #跳过了已选数字
                res.append([nums[i]]+j)
        return res

第一种方法的图解，有空补