{ "data": { "question": { "questionId": "1815", "questionFrontendId": "1697", "categoryTitle": "Algorithms", "boundTopicId": 524856, "title": "Checking Existence of Edge Length Limited Paths", "titleSlug": "checking-existence-of-edge-length-limited-paths", "content": "
An undirected graph of n
nodes is defined by edgeList
, where edgeList[i] = [ui, vi, disi]
denotes an edge between nodes ui
and vi
with distance disi
. Note that there may be multiple edges between two nodes.
Given an array queries
, where queries[j] = [pj, qj, limitj]
, your task is to determine for each queries[j]
whether there is a path between pj
and qj
such that each edge on the path has a distance strictly less than limitj
.
Return a boolean array answer
, where answer.length == queries.length
and the jth
value of answer
is true
if there is a path for queries[j]
is true
, and false
otherwise.
\n
Example 1:
\n\n\nInput: n = 3, edgeList = [[0,1,2],[1,2,4],[2,0,8],[1,0,16]], queries = [[0,1,2],[0,2,5]]\nOutput: [false,true]\nExplanation: The above figure shows the given graph. Note that there are two overlapping edges between 0 and 1 with distances 2 and 16.\nFor the first query, between 0 and 1 there is no path where each distance is less than 2, thus we return false for this query.\nFor the second query, there is a path (0 -> 1 -> 2) of two edges with distances less than 5, thus we return true for this query.\n\n\n
Example 2:
\n\n\nInput: n = 5, edgeList = [[0,1,10],[1,2,5],[2,3,9],[3,4,13]], queries = [[0,4,14],[1,4,13]]\nOutput: [true,false]\nExaplanation: The above figure shows the given graph.\n\n\n
\n
Constraints:
\n\n2 <= n <= 105
1 <= edgeList.length, queries.length <= 105
edgeList[i].length == 3
queries[j].length == 3
0 <= ui, vi, pj, qj <= n - 1
ui != vi
pj != qj
1 <= disi, limitj <= 109
给你一个 n
个点组成的无向图边集 edgeList
,其中 edgeList[i] = [ui, vi, disi]
表示点 ui
和点 vi
之间有一条长度为 disi
的边。请注意,两个点之间可能有 超过一条边 。
给你一个查询数组queries
,其中 queries[j] = [pj, qj, limitj]
,你的任务是对于每个查询 queries[j]
,判断是否存在从 pj
到 qj
的路径,且这条路径上的每一条边都 严格小于 limitj
。
请你返回一个 布尔数组 answer
,其中 answer.length == queries.length
,当 queries[j]
的查询结果为 true
时, answer
第 j
个值为 true
,否则为 false
。
\n\n
示例 1:
\n\n\n输入:n = 3, edgeList = [[0,1,2],[1,2,4],[2,0,8],[1,0,16]], queries = [[0,1,2],[0,2,5]]\n输出:[false,true]\n解释:上图为给定的输入数据。注意到 0 和 1 之间有两条重边,分别为 2 和 16 。\n对于第一个查询,0 和 1 之间没有小于 2 的边,所以我们返回 false 。\n对于第二个查询,有一条路径(0 -> 1 -> 2)两条边都小于 5 ,所以这个查询我们返回 true 。\n\n\n
示例 2:
\n\n\n输入:n = 5, edgeList = [[0,1,10],[1,2,5],[2,3,9],[3,4,13]], queries = [[0,4,14],[1,4,13]]\n输出:[true,false]\n解释:上图为给定数据。\n\n\n
\n\n
提示:
\n\n2 <= n <= 105
1 <= edgeList.length, queries.length <= 105
edgeList[i].length == 3
queries[j].length == 3
0 <= ui, vi, pj, qj <= n - 1
ui != vi
pj != qj
1 <= disi, limitj <= 109
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