18-4sum

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Description

Given an array nums of n integers, return an array of all the unique quadruplets [nums[a], nums[b], nums[c], nums[d]] such that:

• 0 <= a, b, c, d < n
• a, b, c, and d are distinct.
• nums[a] + nums[b] + nums[c] + nums[d] == target

You may return the answer in any order.

 

Example 1:

Input: nums = [1,0,-1,0,-2,2], target = 0
Output: [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]

Example 2:

Input: nums = [2,2,2,2,2], target = 8
Output: [[2,2,2,2]]

 

Constraints:

• 1 <= nums.length <= 200
• -109 <= nums[i] <= 109
• -109 <= target <= 109

Solution(Python)

class Solution:
    def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
	
        def kSum(nums: List[int], target: int, k: int) -> List[List[int]]:
            res = []
            
            # If we have run out of numbers to add, return res.
            if not nums:
                return res
            
            # There are k remaining values to add to the sum. The 
            # average of these values is at least target // k.
            average_value = target // k
            
            # We cannot obtain a sum of target if the smallest value
            # in nums is greater than target // k or if the largest 
            # value in nums is smaller than target // k.
            if average_value < nums[0] or nums[-1] < average_value:
                return res
            
            if k == 2:
                return twoSum(nums, target)
    
            for i in range(len(nums)):
                if i == 0 or nums[i - 1] != nums[i]:
                    for subset in kSum(nums[i + 1:], target - nums[i], k - 1):
                        res.append([nums[i]] + subset)
    
            return res

        def twoSum(nums: List[int], target: int) -> List[List[int]]:
            res = []
            s = set()
    
            for i in range(len(nums)):
                if len(res) == 0 or res[-1][1] != nums[i]:
                    if target - nums[i] in s:
                        res.append([target - nums[i], nums[i]])
                s.add(nums[i])
    
            return res

        nums.sort()
        return kSum(nums, target, 4)