Leetcode: Permutations i

LC: 46 - Permutations. Fixed Length Partial Solution

class Solution:
    # 'i' is the choice for nums[i].
    # partialSolution: []
    def getSolution(self, partialSolution, nums):
        res = []
        
        for idx, num in enumerate(nums):
            if partialSolution[idx] == 1:
                res.append(num)
        return res
    def backtrack(self, idx, nums, partialSolution, result):
        if idx == len(nums):
            result.append(self.getSolution(partialSolution, nums))
            return
        
        # Choice 1: Include (1) the element or exclude (0).
        for choice in range(2):
            partialSolution[idx] = choice
            self.backtrack(idx + 1, nums, partialSolution, result)
        
    def subsets(self, nums: List[int]) -> List[List[int]]:
        result = []
        
        self.backtrack(0, nums, [0] * len(nums), result)
        
        return result

LC: 78 - Permutations. variable-length partialSolution

class Solution:
    # 'i' is the choice for nums[i].
    # partialSolution: []
    def getSolution(self, partialSolution, nums):
        res = []
        
        for idx, num in enumerate(nums):
            if partialSolution[idx] == 1:
                res.append(num)
        return res
    def backtrack(self, nums, partialSolution, result):
        # Goal (Base Case). I have made 'n' choices
        if len(partialSolution) == len(nums):
            result.append(self.getSolution(partialSolution, nums))
            # Partial solution is a complete solution.
            return
        
        # partialSolution: [{0,1}] * len(nums)
        
        # Choices -->
        
        # BF is a boolean function. BF(partialSolution, state in this problem) -> bool.
        # If a BF returns True, partialSolution is PROMISED to be valid.
        # If a BF returns False, this partialSolution is invalid. Stop exploring.

        # You can apply the BF: 
            # BEFORE placing.
                # Is board able to place a queen.
            # AFTER placing.
                # After making a choice, check to see if this choice works.
        # All depends on the problem and what is easier.
        # If I can make a choice independently of previous choices, then no BF.
        
        # Choice 1: Include the element.
        partialSolution.append(1)
        self.backtrack(nums, partialSolution, result)
        partialSolution.pop()
        
        # Choice 2: Don't include the element
        partialSolution.append(0)
        self.backtrack(nums, partialSolution, result)
        partialSolution.pop()
        
        # [1,2,3]
        # [0,1,0] -> {2}
        
    def subsets(self, nums: List[int]) -> List[List[int]]:
        
        result = []
        
        self.backtrack(nums, [], result)
        
        return result