018--4Sum.md

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]
]

# 思路比较简单，在三个数求和的基础上进行迭代。
class Solution(object):
    def fourSum(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: List[List[int]]
        """
        res = []
        nums_length = len(nums)
        if nums_length<4: return res
        nums = sorted(nums)
        
        for i in range(nums_length-3):
            if i>0 and nums[i-1]==nums[i]:
                continue
            nums_tmp = nums[i+1:]
            r = self.threeSum(nums_tmp, target-nums[i])
            for per_r in r:
                per_r.insert(0,nums[i])
                res.append(per_r)
        return res
    
    def threeSum(self, nums, target):
        """
        :type nums: List[int]
        :rtype: List[List[int]]
        """

        res = []
        nums = sorted(nums)
        nums_length = len(nums)

        for i in range(nums_length-2):

            if i>0 and nums[i-1]==nums[i]:
                continue
            a = nums[i]
            low = i + 1
            high = nums_length - 1
            while (low < high):
                b = nums[low]
                c = nums[high]
                if a+b+c==target:
                    res.append([a,b,c])
                    while(low<nums_length-1 and nums[low]==nums[low+1]):
                        low += 1
                    while(high>0 and nums[high]==nums[high-1]):
                        high -= 1
                    low += 1
                    high -= 1
                elif (a+b+c)>target:
                    while(high>0 and nums[high]==nums[high-1]):
                        high -= 1
                    high -= 1
                else:
                    while(low<nums_length-1 and nums[low]==nums[low+1]):
                        low += 1
                    low += 1
        return res