<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>

struct Node{
    int val;
    int i;
    int j;
    Node(int val,int i,int j): val(val),i(i),j(j) {};
        // Define the operator< to compare Node objects
    bool operator<(const Node& other) const {
        if (val != other.val) return val < other.val;
        if (i != other.i) return i < other.i;
        return j < other.j;
    }
};

std::ostream& operator<<(std::ostream& os, const Node& node) {
    os << "Node(val=" << node.val << ", i=" << node.i << ", j=" << node.j << ")";
    return os;
}

class Solution {
public:
    vector<vector<int>> threeSum(vector<int>& nums) {
        // vector<int> nums;
        // map<int,int> c;
        // for(auto x:p){
        //     if(c[x]>3||(x!=0&&c[x]>2))continue;
        //     c[x]++;
        //     nums.push_back(x);
        // }
        sort(nums.begin(),nums.end());
        // for(auto x:nums)cout <<x << " ";cout<<endl;
        // map<int,int> mp;
        // for(int i=0;i<nums.size();i++)mp[nums[i]]=i;
        set<Node> q;
        q.insert(Node(nums[0]+nums[1],0,1));
        for(int i=1;i<nums.size()-1;i++){
            if(nums[i-1]!=nums[i])q.insert(Node(nums[i]+nums[i+1],i,i+1));
        }
        int k = nums.size()-1;
        vector<vector<int>> ans;
        while(q.size()!=0){
            // for (const auto& node : q) {
            //     std::cout << node << std::endl;
            // }
            Node node = *q.begin();
            int c = - node.val;
            int b = nums[node.j], a = nums[node.i],i=node.i,j=node.j;
            // cout << a << " " << b << " " << c << endl;
            q.erase(q.begin());
            while(k>-1&&nums[k]>c)k--;
            if(k<0)break;
            // cout << k <<endl;
            if(nums[k]==c){
                // cout << i << "---" << j << "---" << k <<endl;
                if(j<k)ans.push_back({a,b,c});
            }
            while(j+1<nums.size()&&nums[j+1]==nums[j])j++;
            if(j+1<nums.size()) q.insert(Node(nums[i]+nums[j+1],i,j+1));
        }
        return ans;
    }
};

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