{ "data": { "question": { "questionId": "3386", "questionFrontendId": "3123", "categoryTitle": "Algorithms", "boundTopicId": 2746491, "title": "Find Edges in Shortest Paths", "titleSlug": "find-edges-in-shortest-paths", "content": "
You are given an undirected weighted graph of n
nodes numbered from 0 to n - 1
. The graph consists of m
edges represented by a 2D array edges
, where edges[i] = [ai, bi, wi]
indicates that there is an edge between nodes ai
and bi
with weight wi
.
Consider all the shortest paths from node 0 to node n - 1
in the graph. You need to find a boolean array answer
where answer[i]
is true
if the edge edges[i]
is part of at least one shortest path. Otherwise, answer[i]
is false
.
Return the array answer
.
Note that the graph may not be connected.
\n\n\n
Example 1:
\n\nInput: n = 6, edges = [[0,1,4],[0,2,1],[1,3,2],[1,4,3],[1,5,1],[2,3,1],[3,5,3],[4,5,2]]
\n\nOutput: [true,true,true,false,true,true,true,false]
\n\nExplanation:
\n\nThe following are all the shortest paths between nodes 0 and 5:
\n\n0 -> 1 -> 5
: The sum of weights is 4 + 1 = 5
.0 -> 2 -> 3 -> 5
: The sum of weights is 1 + 1 + 3 = 5
.0 -> 2 -> 3 -> 1 -> 5
: The sum of weights is 1 + 1 + 2 + 1 = 5
.Example 2:
\n\nInput: n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]
\n\nOutput: [true,false,false,true]
\n\nExplanation:
\n\nThere is one shortest path between nodes 0 and 3, which is the path 0 -> 2 -> 3
with the sum of weights 1 + 2 = 3
.
\n
Constraints:
\n\n2 <= n <= 5 * 104
m == edges.length
1 <= m <= min(5 * 104, n * (n - 1) / 2)
0 <= ai, bi < n
ai != bi
1 <= wi <= 105
给你一个 n
个节点的无向带权图,节点编号为 0
到 n - 1
。图中总共有 m
条边,用二维数组 edges
表示,其中 edges[i] = [ai, bi, wi]
表示节点 ai
和 bi
之间有一条边权为 wi
的边。
对于节点 0
为出发点,节点 n - 1
为结束点的所有最短路,你需要返回一个长度为 m
的 boolean 数组 answer
,如果 edges[i]
至少 在其中一条最短路上,那么 answer[i]
为 true
,否则 answer[i]
为 false
。
请你返回数组 answer
。
注意,图可能不连通。
\n\n\n\n
示例 1:
\n\n\n\n输入:n = 6, edges = [[0,1,4],[0,2,1],[1,3,2],[1,4,3],[1,5,1],[2,3,1],[3,5,3],[4,5,2]]
\n\n输出:[true,true,true,false,true,true,true,false]
\n\n解释:
\n\n以下为节点 0 出发到达节点 5 的 所有 最短路:
\n\n0 -> 1 -> 5
:边权和为 4 + 1 = 5
。0 -> 2 -> 3 -> 5
:边权和为 1 + 1 + 3 = 5
。0 -> 2 -> 3 -> 1 -> 5
:边权和为 1 + 1 + 2 + 1 = 5
。示例 2:
\n\n\n\n输入:n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]
\n\n输出:[true,false,false,true]
\n\n解释:
\n\n只有一条从节点 0 出发到达节点 3 的最短路 0 -> 2 -> 3
,边权和为 1 + 2 = 3
。
\n\n
提示:
\n\n2 <= n <= 5 * 104
m == edges.length
1 <= m <= min(5 * 104, n * (n - 1) / 2)
0 <= ai, bi < n
ai != bi
1 <= wi <= 105
n - 1
to all other nodes.",
"How to use the above calculated shortest paths to check if an edge is part of at least one shortest path from 0 to n - 1
?"
],
"solution": null,
"status": null,
"sampleTestCase": "6\n[[0,1,4],[0,2,1],[1,3,2],[1,4,3],[1,5,1],[2,3,1],[3,5,3],[4,5,2]]",
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