<p>Given an array <code>nums</code> of <code>n</code> integers, return <em>an array of all the <strong>unique</strong> quadruplets</em> <code>[nums[a], nums[b], nums[c], nums[d]]</code> such that:</p>

<ul>
	<li><code>0 &lt;= a, b, c, d&nbsp;&lt; n</code></li>
	<li><code>a</code>, <code>b</code>, <code>c</code>, and <code>d</code> are <strong>distinct</strong>.</li>
	<li><code>nums[a] + nums[b] + nums[c] + nums[d] == target</code></li>
</ul>

<p>You may return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,0,-1,0,-2,2], target = 0
<strong>Output:</strong> [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,2,2,2,2], target = 8
<strong>Output:</strong> [[2,2,2,2]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= target &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    # my twoSum assumes sorted nums array and returns unique set of pairs that sum to target target
    def twoSum(self, sortedNums: List[int], left, right, target: int) -> Set[Tuple[int, int]]:
        if len(sortedNums) < 2:
            return set()
        resultSet = set()

        while left < right:
            currSum = sortedNums[left] + sortedNums[right]
            if currSum == target:
                resultSet.add((sortedNums[left], sortedNums[right]))
                left += 1
                right -= 1
            elif currSum < target:
                left += 1
            else:
                right -= 1
        return resultSet
        
    def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
        nums.sort()
        resultSet = set()
        listLen = len(nums)

        for i in range(listLen - 3):
            firstFixed = nums[i]
            for j in range(i+1, listLen - 2):
                secondFixed = nums[j]
                complement = target - firstFixed - secondFixed
                rightArrayPairSet = self.twoSum(nums, left=(j+1), right=(listLen-1), target=complement)
                
                for pair in rightArrayPairSet:
                    resultSet.add((firstFixed, secondFixed, pair[0], pair[1]))

        return resultSet

        
16800