Edge Deletion 2

AtCoder

IDarc170_f

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices numbered $1$ to $N$. The $i$\-th edge of the tree connects vertices $u_i$ and $v_i$ bidirectionally. For a permutation $P=(P_1,\ldots,P_N)$ of $(1,2,\ldots,N)$, we define the sequence $A(P)$ as follows: * $A(P)$ is initially empty. Write $P_i$ on each vertex $i$. * For $i=1,2,\ldots,N$ in this order, perform the following: * If vertex $i$ is an isolated vertex, append $0$ to the end of $A(P)$. Otherwise, select the adjacent vertex with the smallest written integer. Append the integer written on the selected vertex to the end of $A(P)$ and remove the edge connecting vertex $i$ and the selected vertex. Find the lexicographically smallest sequence among all possible $A(P)$. Solve each of the $T$ given test cases. ## Constraints * $1 \leq T \leq 10^5$ * $2 \leq N \leq 2 \times 10^5$ * $1\leq u_i,v_i\leq N$ * The given graph is a tree. * All input numbers are integers. * The sum of $N$ over all test cases in a single input is at most $2 \times 10^5$. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each case is given in the following format: $N$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_{N-1}$ $v_{N-1}$ [samples]

Samples

Input #1

Output #1

1 2 0 1 3
1 2 2 3 1 4 0 0
1 2 2 0 3 0 4

In the first test case, for $P=(4,1,2,3,5)$, one can obtain $A(P)=(1,2,0,1,3)$ as follows:

*   The vertex adjacent to vertex $1$ with the smallest written integer is vertex $2$. Append $P_2=1$ to the end of $A(P)$ and remove the edge connecting vertices $1$ and $2$.
    
*   The vertex adjacent to vertex $2$ with the smallest written integer is vertex $3$. Append $P_3=2$ to the end of $A(P)$ and remove the edge connecting vertices $2$ and $3$.
    
*   Vertex $3$ is an isolated vertex, so append $0$ to the end of $A(P)$.
    
*   The vertex adjacent to vertex $4$ with the smallest written integer is vertex $2$. Append $P_2=1$ to the end of $A(P)$ and remove the edge connecting vertices $4$ and $2$.
    
*   The vertex adjacent to vertex $5$ with the smallest written integer is vertex $4$. Append $P_4=3$ to the end of $A(P)$ and remove the edge connecting vertices $5$ and $4$.
    

It can be proved that this is the lexicographically smallest sequence among all possible $A(P)$.

API Response (JSON)

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    "name": "Edge Deletion 2",
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      "content": "You are given a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of the tree connects vertices $u_i$ and $v_i$ bidirectionally. For a permutation $P=(P_1,\\ldots,P_N)$ of $(1,2,\\ldots,N)$, ",
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    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of the tree connects vertices $u_i$ and $v_i$ bidirectionally.\nFor a permutation $P=(P_1,\\ldots,P_N)$ of $(1,2,\\ldots,N)$, ...",
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