<p>Given an array <code>nums</code> of <code>n</code> integers, return <em>an array of all the <strong>unique</strong> quadruplets</em> <code>[nums[a], nums[b], nums[c], nums[d]]</code> such that:</p>

<ul>
	<li><code>0 &lt;= a, b, c, d&nbsp;&lt; n</code></li>
	<li><code>a</code>, <code>b</code>, <code>c</code>, and <code>d</code> are <strong>distinct</strong>.</li>
	<li><code>nums[a] + nums[b] + nums[c] + nums[d] == target</code></li>
</ul>

<p>You may return the answer in <strong>any order</strong>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,0,-1,0,-2,2], target = 0
<strong>Output:</strong> [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,2,2,2,2], target = 8
<strong>Output:</strong> [[2,2,2,2]]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= target &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    
    #define lli long long int
    
    /*
    method(1): use any of 3-sum like techiques to find quads
    then sort the quad vector and in uset for uniqueness
    t=o(n^3*(size of set))
    */
    
    vector<vector<int>> fourSum(vector<int>& a, int sum) {
        
        lli n=a.size();
        unordered_map<lli,lli> cnt;
        for(auto x:a) cnt[x]++;
        
        set<vector<int>> s;
        for(int i=0;i<n;i++) {            
            for(int j=i+1;j<n;j++) {                
                for(int k=j+1;k<n;k++) {
                    lli x=a[i], y=a[j], z=a[k];
                    lli req=sum;
                    req-=x;
                    req-=y;
                    req-=z;
                    bool good=false;
                    if(req==x && req==y && req==z) {
                        if(cnt[req]>=4) good=true;
                    } 
                    
                    else if((req!=x && req==y && req==z) ||(req==x && req!=y && req==z) || (req==x && req==y && req!=z)) {
                        if(cnt[req]>=3) good=true;
                    } 
                    
                    else if((req!=x && req!=y && req==z) ||(req!=x && req==y && req!=z) || (req==x && req!=y && req!=z)) {
                        if(cnt[req]>=2) good=true;
                    } 
                    
                    else {
                        if(cnt[req]>=1) good=true;
                    }
            
                    if(good) {
                       vector<int> curr;
                       curr.push_back((int)(x));
                       curr.push_back((int)(y));
                       curr.push_back((int)(z));
                       curr.push_back((int)(req));
                       sort(curr.begin(),curr.end()); // imp
                       s.insert(curr);
                   }
                }
            }
        }
        
        
        vector<vector<int>> ans;
        for(auto x:s)
        ans.push_back(x);
        return ans;
    }
};
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