<p>There is an integer array <code>nums</code> that consists of <code>n</code> <strong>unique </strong>elements, but you have forgotten it. However, you do remember every pair of adjacent elements in <code>nums</code>.</p>

<p>You are given a 2D integer array <code>adjacentPairs</code> of size <code>n - 1</code> where each <code>adjacentPairs[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that the elements <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> are adjacent in <code>nums</code>.</p>

<p>It is guaranteed that every adjacent pair of elements <code>nums[i]</code> and <code>nums[i+1]</code> will exist in <code>adjacentPairs</code>, either as <code>[nums[i], nums[i+1]]</code> or <code>[nums[i+1], nums[i]]</code>. The pairs can appear <strong>in any order</strong>.</p>

<p>Return <em>the original array </em><code>nums</code><em>. If there are multiple solutions, return <strong>any of them</strong></em>.</p>

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

<pre>
<strong>Input:</strong> adjacentPairs = [[2,1],[3,4],[3,2]]
<strong>Output:</strong> [1,2,3,4]
<strong>Explanation:</strong> This array has all its adjacent pairs in adjacentPairs.
Notice that adjacentPairs[i] may not be in left-to-right order.
</pre>

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

<pre>
<strong>Input:</strong> adjacentPairs = [[4,-2],[1,4],[-3,1]]
<strong>Output:</strong> [-2,4,1,-3]
<strong>Explanation:</strong> There can be negative numbers.
Another solution is [-3,1,4,-2], which would also be accepted.
</pre>

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

<pre>
<strong>Input:</strong> adjacentPairs = [[100000,-100000]]
<strong>Output:</strong> [100000,-100000]
</pre>

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

<ul>
	<li><code>nums.length == n</code></li>
	<li><code>adjacentPairs.length == n - 1</code></li>
	<li><code>adjacentPairs[i].length == 2</code></li>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i], u<sub>i</sub>, v<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li>There exists some <code>nums</code> that has <code>adjacentPairs</code> as its pairs.</li>
</ul>

class Solution {
    
public:
    vector<int> restoreArray(const vector<vector<int>>& adjacentPairs) 
    {
        unordered_map<int, pair<int,int>> m;
        for (const auto& p : adjacentPairs)
        {
            auto [i0, u0] = m.insert({p[0], {INT_MAX, INT_MAX}});
            if (i0->second.first==INT_MAX) i0->second.first  = p[1];
            else                           i0->second.second = p[1]; 

            auto [i1, u1] = m.insert({p[1], {INT_MAX, INT_MAX}});
            if (i1->second.first==INT_MAX) i1->second.first  = p[0];
            else                           i1->second.second = p[0]; 
        }

        int f = INT_MAX, prev = INT_MAX;
        for (auto [v, p] : m)
        {
            if (p.second==INT_MAX) { f = v; break; }
        }

        int n = adjacentPairs.size()+1;
        vector<int> r(n);
        for (int i=0; i<n; i++)
        {
            r[i] = f;
            auto p = m[f];
            if (p.first!=INT_MAX && p.first!=prev) { prev = f; f = p.first;  }
            else                                   { prev = f; f = p.second; }
        }
        return r;
    }
};
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