3067 - Count Pairs of Connectable Servers in a Weighted Tree Network.

Medium

You are given an unrooted weighted tree with n vertices representing servers numbered from 0 to n - 1, an array edges where <code>edgesi = a_i, b_i, weight_i</code> represents a bidirectional edge between vertices <code>a_i</code> and <code>b_i</code> of weight <code>weight_i</code>. You are also given an integer signalSpeed.

Two servers a and b are connectable through a server c if:

• a < b, a != c and b != c.

• The distance from c to a is divisible by signalSpeed.

• The distance from c to b is divisible by signalSpeed.

• The path from c to b and the path from c to a do not share any edges.

Return an integer array count of length n where count[i] is the number of server pairs that are connectable through the server i.

Example 1:

Input: edges = [0,1,1,1,2,5,2,3,13,3,4,9,4,5,2], signalSpeed = 1

Output: 0,4,6,6,4,0

Explanation: Since signalSpeed is 1, countc is equal to the number of pairs of paths that start at c and do not share any edges.

In the case of the given path graph, countc is equal to the number of servers to the left of c multiplied by the servers to the right of c.

Example 2:

Input: edges = [0,6,3,6,5,3,0,3,1,3,2,7,3,1,6,3,4,2], signalSpeed = 3

Output: 2,0,0,0,0,0,2

Explanation: Through server 0, there are 2 pairs of connectable servers: (4, 5) and (4, 6).

Through server 6, there are 2 pairs of connectable servers: (4, 5) and (0, 5).

It can be shown that no two servers are connectable through servers other than 0 and 6.

Constraints:

• 2 <= n <= 1000

• edges.length == n - 1

• edges[i].length == 3

• <code>0 <= a_i, b_i< n</code>

• <code>edgesi = a_i, b_i, weight_i</code>

• <code>1 <= weight_i<= 10⁶</code>

• <code>1 <= signalSpeed <= 10⁶</code>

• The input is generated such that edges represents a valid tree.