# Question

Given an array nums of n integers and an integer target, are there elements a, b, c, and d in nums such that a + b + c + d = target? Find all unique quadruplets in the array which gives the sum of target.

Note:

The solution set must not contain duplicate quadruplets.

Example:

Given array nums = [1, 0, -1, 0, -2, 2], and target = 0.

A solution set is:
[
[-1,  0, 0, 1],
[-2, -1, 1, 2],
[-2,  0, 0, 2]
]


# Solution

$$O(n^3)$$. Use double for-loops to capture all possible combinations of first two numbers, and then use the greedy method in 2Sum to find a combination of the remaining two numbers. Thus it is $$O(n^2)$$ to run the double for-loop, and $$O(n)$$ to find the combination.

class Solution:
def fourSum(self, nums, target):
"""
:type nums: List[int]
:type target: int
:rtype: List[List[int]]
"""
nums.sort()
res = set()

length = len(nums)
for i, n in enumerate(nums[:-3]):
for j in range(i+1, length-2):
m = nums[j]
if n + m + nums[j+1] + nums[j+2] <= target and n + m + nums[-1] + nums[-2] >= target:
l, r = j + 1, length - 1
while l < r:
s = n + m + nums[l] + nums[r]
if s < target:
l += 1
elif s > target:
r -= 1
else: