<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:
    def restoreArray(self, adjacentPairs: List[List[int]]) -> List[int]:
        # 2 -> 1, 3
        # 3 -> 2, 4
        # 1 -> 2
        # 4 -> 3

        # keep track of numbers that appear once when populating dict (start and end nums)
        # [1, 4]
        # for first num -> go to mapped of second number 
        # [1, 2, 3, 4]
        # for each number in dict[num] -> add to queue 
        # for each number in qeueu -> add neigbors to queue
        # if neighbor already in list, continue
        # if not, append num to the list


        nums = {}
        unique = set()
        ends = set()

        for u, v in adjacentPairs:
            if u in unique:
                ends.discard(u)
            else:
                ends.add(u)
                unique.add(u)
            if v in unique:
                ends.discard(v)
            else:
                ends.add(v)
                unique.add(v)
            if u in nums:
                nums[u].append(v)
            else:
                nums[u] = [v]
            if v in nums:
                nums[v].append(u)
            else:
                nums[v] = [u]
        ends = list(ends)
        #res = [ends[0]]
        res = []
        q = deque()
        q.append(ends[0])
        visited = set()

        while q:
            for i in range(len(q)):
                num = q.popleft()
                if num in visited:
                    continue
                for n in nums[num]:
                    if n in visited:
                        continue
                    q.append(n)
                    visited.add(num)
                    res.append(num)
        res.append(ends[1])
        return res


            


        
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