{ "data": { "question": { "questionId": "3326", "questionFrontendId": "3067", "boundTopicId": null, "title": "Count Pairs of Connectable Servers in a Weighted Tree Network", "titleSlug": "count-pairs-of-connectable-servers-in-a-weighted-tree-network", "content": "
You are given an unrooted weighted tree with n
vertices representing servers numbered from 0
to n - 1
, an array edges
where edges[i] = [ai, bi, weighti]
represents a bidirectional edge between vertices ai
and bi
of weight weighti
. 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
.c
to a
is divisible by signalSpeed
.c
to b
is divisible by signalSpeed
.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
.
\n
Example 1:
\n\n\nInput: edges = [[0,1,1],[1,2,5],[2,3,13],[3,4,9],[4,5,2]], signalSpeed = 1\nOutput: [0,4,6,6,4,0]\nExplanation: Since signalSpeed is 1, count[c] is equal to the number of pairs of paths that start at c and do not share any edges.\nIn the case of the given path graph, count[c] is equal to the number of servers to the left of c multiplied by the servers to the right of c.\n\n\n
Example 2:
\n\n\nInput: edges = [[0,6,3],[6,5,3],[0,3,1],[3,2,7],[3,1,6],[3,4,2]], signalSpeed = 3\nOutput: [2,0,0,0,0,0,2]\nExplanation: Through server 0, there are 2 pairs of connectable servers: (4, 5) and (4, 6).\nThrough server 6, there are 2 pairs of connectable servers: (4, 5) and (0, 5).\nIt can be shown that no two servers are connectable through servers other than 0 and 6.\n\n\n
\n
Constraints:
\n\n2 <= n <= 1000
edges.length == n - 1
edges[i].length == 3
0 <= ai, bi < n
edges[i] = [ai, bi, weighti]
1 <= weighti <= 106
1 <= signalSpeed <= 106
edges
represents a valid tree.i
, the number of nodes in the subtree rooted at i
whose distance to the root is divisible by signalSpeed
.",
"If the root has m
children named c1, c2, …, cm
that respectively have num[c1], num[c2], …, num[cm]
nodes in their subtrees whose distance is divisible by signalSpeed. Then, there are ((S - num[ci]) * num[ci]) / 2
that are connectable through the root that we have fixed, where S
is the sum of num[ci]
."
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"sampleTestCase": "[[0,1,1],[1,2,5],[2,3,13],[3,4,9],[4,5,2]]\n1",
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