<p>Given an integer array nums, return all the triplets <code>[nums[i], nums[j], nums[k]]</code> such that <code>i != j</code>, <code>i != k</code>, and <code>j != k</code>, and <code>nums[i] + nums[j] + nums[k] == 0</code>.</p>

<p>Notice that the solution set must not contain duplicate triplets.</p>

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

<pre>
<strong>Input:</strong> nums = [-1,0,1,2,-1,-4]
<strong>Output:</strong> [[-1,-1,2],[-1,0,1]]
<strong>Explanation:</strong> 
nums[0] + nums[1] + nums[2] = (-1) + 0 + 1 = 0.
nums[1] + nums[2] + nums[4] = 0 + 1 + (-1) = 0.
nums[0] + nums[3] + nums[4] = (-1) + 2 + (-1) = 0.
The distinct triplets are [-1,0,1] and [-1,-1,2].
Notice that the order of the output and the order of the triplets does not matter.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,1,1]
<strong>Output:</strong> []
<strong>Explanation:</strong> The only possible triplet does not sum up to 0.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,0,0]
<strong>Output:</strong> [[0,0,0]]
<strong>Explanation:</strong> The only possible triplet sums up to 0.
</pre>

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

<ul>
	<li><code>3 &lt;= nums.length &lt;= 3000</code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

#include <set>
using namespace std;
class Solution {
public:
    int binarySearch(int toFind, vector<int>& nums, int start){
        if(start < 0){
            start = 0;
        }

        int end = nums.size() - 1;
        while(start <= end){
            int index = start + (end - start) / 2;
            if(nums[index] < toFind){
                start = index + 1;
            }else if(nums[index] > toFind){
                end = index - 1;
            }
            else{
                return index;
            }
        }
        return -1;
    }


    vector<vector<int>> twoSum(int index, int num, vector<int>& nums, int min_value, int max_value){
        vector<vector<int>> pairs;
        for(int i=0; i<nums.size(); i++){
            if(i == index){
                continue;
            }

            int number = nums[i];
            int needed = num - number;
            if (needed < min_value || needed > max_value){
                continue;
            }
            
            int start_index = binarySearch(needed, nums, 0);
            if(start_index == -1){
                continue;
            }

            if(start_index == index){
                start_index = binarySearch(needed, nums, start_index+1);
                if(start_index == -1){
                    continue;
                }
            }

            while(true){
                if(nums[start_index] == needed){
                    if(start_index != i){
                        vector<int> pair = {number, nums[start_index]};
                        pairs.push_back(pair);
                    }
                    start_index++;
                }
                break;
            }       
        }

        return pairs;
    }

    vector<vector<int>> threeSum(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int min_value = nums[0];
        int max_value = nums[nums.size()-1];
        set<vector<int>> triplets;
        int current_num = min_value;
        bool success = false;

        for(int i=0; i<nums.size(); i++){
            int num = nums[i];
            if(num == current_num && success){
                continue;
            }
            current_num = num;
            success = false;
            vector<vector<int>> pairs = twoSum(i, -num, nums, min_value, max_value);
            if(pairs.size() > 0){
                for(int j=0; j<pairs.size(); j++){
                    vector<int> pair = pairs[j];
                    vector<int> triplet = {num, pair[0], pair[1]};
                    sort(triplet.begin(), triplet.end());
                    triplets.insert(triplet);
                    success = true;
                }
            }

        }

        vector<vector<int>> ret;
        for(vector<int> triplet: triplets){
            ret.push_back(triplet);
        }
        return ret;
    }
};
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