给你一个包含 n 个整数的数组 nums，判断 nums 中是否存在三个元素 a，b，c ，使得 a + b + c = 0 ？请你找出所有满足条件且不重复的三元组。

注意：答案中不可以包含重复的三元组。

示例：

给定数组 nums = [-1, 0, 1, 2, -1, -4]，

满足要求的三元组集合为：
[
  [-1, 0, 1],
  [-1, -1, 2]
]

Solution

参考：《算法小抄》4.6

• 双指针
• 三数之和转化为两数之和子问题

# @lc code=start
class Solution:
    def threeSum(self, nums: List[int]) -> List[List[int]]:
        nums = sorted(nums)
        length = len(nums)
        res = []
        
        def twoSum(nums, start, target):
            low, high = start, len(nums)-1
            res = []
            while low<high:
                sumLR = nums[low]+nums[high]
                left, right = nums[low], nums[high]
                if sumLR<target:
                    while low<high and nums[low]==left: low+=1
                elif sumLR>target:
                    while low<high and nums[high]==right: high-=1
                else:
                    res.append([left, right])
                    while low<high and nums[low]==left: low+=1
                    while low<high and nums[high]==right: high-=1
            return res
        
        i=0
        while i< length:
            subRes = twoSum(nums, i+1, 0-nums[i])
            for sub in subRes:
                sub.append(nums[i])
                res.append(sub)
            while i<length-1 and nums[i]==nums[i+1]:
                i+=1
            i+=1
        return res
# @lc code=end

cpp

// @lc code=start
class Solution {
public:
    vector<vector<int>> threeSum(vector<int>& nums) {
        vector<vector<int>> res;
        if(nums.size()<3) return res;

        sort(nums.begin(), nums.end());
        if(nums[0]>0) return res;

        for(int i=0; i<nums.size(); ++i){
            vector<vector<int>> subRes;
            
            subRes = twoSum(nums, i+1, 0-nums[i]);
            for(auto sub : subRes){
                sub.push_back(nums[i]);
                res.push_back(sub);
            }

            while(i<nums.size()-1 && nums[i]==nums[i+1])
                i += 1;
        }
        return res;
    }
private:
    vector<vector<int>> twoSum(vector<int>& nums, int start, int target) {
        vector<vector<int>> result;
        int left=start, right=nums.size()-1;
        while(left<right){
            int sum = nums[left]+nums[right];
            int low = nums[left], high = nums[right];
            if(sum <target){
                while(left<right && nums[left]==low) left+=1;
            }
            else if(sum>target){
                while(left<right && nums[right]==high) right-=1;
            }
            else{
                result.push_back({nums[left], nums[right]});
                while(left<right && nums[left]==low) left+=1;
                while(left<right && nums[right]==high) right-=1;
            }
        }
        return result;
    }
};