MEX Tree codeforces solution 2021 - You are given a tree with nn nodes, numerated from 00 to n−1n−1.

  

MEX Tree codeforces solution 2021

SOLUTION

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You are given a tree with n$n$ nodes, numerated from 0$0$ to n−1$n-1$. For each k$k$ between 0$0$ and n$n$, inclusive, you have to count the number of unordered pairs (u,v)$(u,v)$, u≠v$u\ne v$, such that the MEX of all the node labels in the shortest path from u$u$ to v$v$ (including end points) is k$k$.

The MEX of a sequence of integers is the smallest non-negative integer that does not belong to the sequence.

Input MEX Tree codeforces solution 2021

The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases.

The first line of each test case contains a single integer n$n$ (2≤n≤2⋅105$2\le n\le 2\cdot {10}^5$).

The next n−1$n-1$ lines of each test case describe the tree that has to be constructed. These lines contain two integers u$u$ and v$v$ (0≤u,v≤n−1$0\le u,v\le n-1$) denoting an edge between u$u$ and v$v$ (u≠v$u\ne v$).

It is guaranteed that the given edges form a tree.

It is also guaranteed that the sum of n$n$ for all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Output MEX Tree codeforces solution 2021

For each test case, print n+1$n+1$ integers: the number of paths in the tree, such that the MEX of all the node labels in that path is k$k$ for each k$k$ from 0$0$ to n$n$.

Example MEX Tree codeforces solution 2021

input

Copy

2
4
0 1
0 2
2 3
2
1 0

output

Copy

1 2 1 1 1 
0 0 1 

Note

1. In example case 1$1$,
   • For k=0$k=0$, there is 1$1$ path that is from 2$2$ to 3$3$ as MEX([2,3])=0$MEX([2,3])=0$.
   • For k=1$k=1$, there are 2$2$ paths that is from 0$0$ to 2$2$ as MEX([0,2])=1$MEX([0,2])=1$ and 0$0$ to 3$3$ as MEX([0,2,3])=1$MEX([0,2,3])=1$.
   • For k=2$k=2$, there is 1$1$ path that is from 0$0$ to 1$1$ as MEX([0,1])=2$MEX([0,1])=2$.
   • For k=3$k=3$, there is 1$1$ path that is from 1$1$ to 2$2$ as MEX([1,0,2])=3$MEX([1,0,2])=3$
   • For k=4$k=4$, there is 1$1$ path that is from 1$1$ to 3$3$ as MEX([1,0,2,3])=4$MEX([1,0,2,3])=4$.
2. In example case 2$2$,
   • For k=0$k=0$, there are no such paths.
   • For k=1$k=1$, there are no such paths.
   • For k=2$k=2$, there is 1$1$ path that is from 0$0$ to 1$1$ as MEX([0,1])=2$MEX([0,1])=2$.

SOLUTION

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codeforces

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