<p>You are given a <strong>0-indexed</strong> 2D integer array <code>pairs</code> where <code>pairs[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>. An arrangement of <code>pairs</code> is <strong>valid</strong> if for every index <code>i</code> where <code>1 &lt;= i &lt; pairs.length</code>, we have <code>end<sub>i-1</sub> == start<sub>i</sub></code>.</p>

<p>Return <em><strong>any</strong> valid arrangement of </em><code>pairs</code>.</p>

<p><strong>Note:</strong> The inputs will be generated such that there exists a valid arrangement of <code>pairs</code>.</p>

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

<pre>
<strong>Input:</strong> pairs = [[5,1],[4,5],[11,9],[9,4]]
<strong>Output:</strong> [[11,9],[9,4],[4,5],[5,1]]
<strong>Explanation:
</strong>This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 9 == 9 = start<sub>1</sub> 
end<sub>1</sub> = 4 == 4 = start<sub>2</sub>
end<sub>2</sub> = 5 == 5 = start<sub>3</sub>
</pre>

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

<pre>
<strong>Input:</strong> pairs = [[1,3],[3,2],[2,1]]
<strong>Output:</strong> [[1,3],[3,2],[2,1]]
<strong>Explanation:</strong>
This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 3 == 3 = start<sub>1</sub>
end<sub>1</sub> = 2 == 2 = start<sub>2</sub>
The arrangements [[2,1],[1,3],[3,2]] and [[3,2],[2,1],[1,3]] are also valid.
</pre>

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

<pre>
<strong>Input:</strong> pairs = [[1,2],[1,3],[2,1]]
<strong>Output:</strong> [[1,2],[2,1],[1,3]]
<strong>Explanation:</strong>
This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 2 == 2 = start<sub>1</sub>
end<sub>1</sub> = 1 == 1 = start<sub>2</sub>
</pre>

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

<ul>
	<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>
	<li><code>pairs[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub>, end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>start<sub>i</sub> != end<sub>i</sub></code></li>
	<li>No two pairs are exactly the same.</li>
	<li>There <strong>exists</strong> a valid arrangement of <code>pairs</code>.</li>
</ul>

class Solution:
    def validArrangement(self, pairs: List[List[int]]) -> List[List[int]]:
        in_degree = defaultdict(int)
        out_degree = defaultdict(int)
        graph = defaultdict(list)
        all_node = set()

        for fr, to in pairs:
            graph[fr].append(to)
            in_degree[to] += 1
            out_degree[fr] += 1
            all_node.add(fr)
            all_node.add(to)

        start = pairs[0][0]
        for node in all_node:
            if in_degree[node] < out_degree[node]:
                start = node
        # print(in_degree, out_degree)
        # print(start)

        # visited = defaultdict(int)
        ans = []
        st = [start]
        while st:
            while graph[st[-1]]:
                st.append(graph[st[-1]].pop())
            ans.append(st.pop())
        ans.reverse()
        return [[ans[i], ans[i + 1]] for i in range(len(ans) - 1)]
        # def dfs(cur: int, path: List[List[int]]) -> None:
        #     if len(path) == len(pairs):
        #         return path

        #     while len(graph[cur]) > 0:
        #         to = graph[cur].pop()
        #         return dfs(to, path + [[cur, to]])


        # ans = []
        # # visited[st] = 1
        # ans = dfs(start, ans)
        # return ans
1980