atcoder#AGC034E. [AGC034E] Complete Compress
[AGC034E] Complete Compress
Score : points
Problem Statement
You are given a tree with vertices numbered . The -th edge connects Vertex and Vertex .
You are also given a string of length consisting of 0
and 1
. The -th character of represents the number of pieces placed on Vertex .
Snuke will perform the following operation some number of times:
- Choose two pieces the distance between which is at least , and bring these pieces closer to each other by . More formally, choose two vertices and , each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from to its adjacent vertex on the path, and move one piece from to its adjacent vertex on the path.
By repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible? If the answer is yes, also find the minimum number of operations required to achieve it.
Constraints
- consists of
0
and1
, and contains at least one1
. - The edges $(a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1})$ forms a tree.
Input
Input is given from Standard Input in the following format:
Output
If it is impossible to have all the pieces on the same vertex, print -1
. If it is possible, print the minimum number of operations required.
7
0010101
1 2
2 3
1 4
4 5
1 6
6 7
3
We can gather all the pieces in three operations as follows:
- Choose the pieces on Vertex and .
- Choose the pieces on Vertex and .
- Choose the pieces on Vertex and .
7
0010110
1 2
2 3
1 4
4 5
1 6
6 7
-1
2
01
1 2
0