A628.codeforces-1919h

H. Tree Diameter
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
There is a hidden tree with 𝑛
vertices. The 𝑛−1
edges of the tree are numbered from 1
to 𝑛−1
. You can ask the following queries of two types:

Give the grader an array 𝑎
with 𝑛−1
positive integers. For each edge from 1
to 𝑛−1
, the weight of edge 𝑖
is set to 𝑎𝑖
. Then, the grader will return the length of the diameter†
.
Give the grader two indices 1≤𝑎,𝑏≤𝑛−1
. The grader will return the number of edges between edges 𝑎
and 𝑏
. In other words, if edge 𝑎
connects 𝑢𝑎
and 𝑣𝑎
while edge 𝑏
connects 𝑢𝑏
and 𝑣𝑏
, the grader will return min(dist(𝑢𝑎,𝑢𝑏),dist(𝑣𝑎,𝑢𝑏),dist(𝑢𝑎,𝑣𝑏),dist(𝑣𝑎,𝑣𝑏))
, where dist(𝑢,𝑣)
represents the number of edges on the path between vertices 𝑢
and 𝑣
.
Find any tree isomorphic‡
to the hidden tree after at most 𝑛
queries of type 1 and 𝑛
queries of type 2 in any order.

†
The distance between two vertices is the sum of the weights on the unique simple path that connects them. The diameter is the largest of all those distances.

‡
Two trees, consisting of 𝑛
vertices each, are called isomorphic if there exists a permutation 𝑝
containing integers from 1
to 𝑛
such that edge (𝑢
, 𝑣
) is present in the first tree if and only if the edge (𝑝𝑢
, 𝑝𝑣
) is present in the second tree.

The first and only line of input contains a single integer 𝑛
(3≤𝑛≤1000
) — the number of vertices in the tree.

The hidden tree in the example is shown above. The number on the vertices represents the vertex number while the number on the edges represents the edge number.