{ "data": { "question": { "questionId": "3916", "questionFrontendId": "3604", "categoryTitle": "Algorithms", "boundTopicId": 3714015, "title": "Minimum Time to Reach Destination in Directed Graph", "titleSlug": "minimum-time-to-reach-destination-in-directed-graph", "content": "
You are given an integer n
and a directed graph with n
nodes labeled from 0 to n - 1
. This is represented by a 2D array edges
, where edges[i] = [ui, vi, starti, endi]
indicates an edge from node ui
to vi
that can only be used at any integer time t
such that starti <= t <= endi
.
You start at node 0 at time 0.
\n\nIn one unit of time, you can either:
\n\nt
satisfies starti <= t <= endi
.Return the minimum time required to reach node n - 1
. If it is impossible, return -1
.
\n
Example 1:
\n\nInput: n = 3, edges = [[0,1,0,1],[1,2,2,5]]
\n\nOutput: 3
\n\nExplanation:
\n\nThe optimal path is:
\n\nt = 0
, take the edge (0 → 1)
which is available from 0 to 1. You arrive at node 1 at time t = 1
, then wait until t = 2
.t = 2
, take the edge (1 → 2)
which is available from 2 to 5. You arrive at node 2 at time 3.Hence, the minimum time to reach node 2 is 3.
\nExample 2:
\n\nInput: n = 4, edges = [[0,1,0,3],[1,3,7,8],[0,2,1,5],[2,3,4,7]]
\n\nOutput: 5
\n\nExplanation:
\n\nThe optimal path is:
\n\nt = 1
, then take the edge (0 → 2)
which is available from 1 to 5. You arrive at node 2 at t = 2
.t = 4
, then take the edge (2 → 3)
which is available from 4 to 7. You arrive at node 3 at t = 5
.Hence, the minimum time to reach node 3 is 5.
\nExample 3:
\n\nInput: n = 3, edges = [[1,0,1,3],[1,2,3,5]]
\n\nOutput: -1
\n\nExplanation:
\n\n\n
Constraints:
\n\n1 <= n <= 105
0 <= edges.length <= 105
edges[i] == [ui, vi, starti, endi]
0 <= ui, vi <= n - 1
ui != vi
0 <= starti <= endi <= 109
给你一个整数 n
和一个 有向 图,图中有 n
个节点,编号从 0 到 n - 1
。图由一个二维数组 edges
表示,其中 edges[i] = [ui, vi, starti, endi]
表示从节点 ui
到 vi
的一条边,该边 只能 在满足 starti <= t <= endi
的整数时间 t
使用。
你在时间 0 从在节点 0 出发。
\n\n在一个时间单位内,你可以:
\n\nt
满足 starti <= t <= endi
,则从当前节点沿着出边的方向移动。返回到达节点 n - 1
所需的 最小 时间。如果不可能,返回 -1
。
\n\n
示例 1:
\n\n输入:n = 3, edges = [[0,1,0,1],[1,2,2,5]]
\n\n输出:3
\n\n解释:
\n\n最佳路径为:
\n\nt = 0
,走边 (0 → 1)
,该边在 0 到 1 的时间段内可用。你在时间 t = 1
到达节点 1,然后等待直到 t = 2
。t = 2
,走边 (1 → 2)
,该边在 2 到 5 的时间段内可用。你在时间 3 到达节点 2。因此,到达节点 2 的最小时间是 3。
\n示例 2:
\n\n输入: n = 4, edges = [[0,1,0,3],[1,3,7,8],[0,2,1,5],[2,3,4,7]]
\n\n输出: 5
\n\n解释:
\n\n最佳路径为:
\n\nt = 1
,然后走边 (0 → 2)
,该边在 1 到 5 的时间段内可用。你在 t = 2
到达节点 2。t = 4
,然后走边 (2 → 3)
,该边在 4 到 7 的时间段内可用。你在 t = 5
到达节点 3。因此,到达节点 3 的最小时间是 5。
\n示例 3:
\n\n输入: n = 3, edges = [[1,0,1,3],[1,2,3,5]]
\n\n输出: -1
\n\n解释:
\n\n\n\n
提示:
\n\n1 <= n <= 105
0 <= edges.length <= 105
edges[i] == [ui, vi, starti, endi]
0 <= ui, vi <= n - 1
ui != vi
0 <= starti <= endi <= 109
Dijkstra
algorithm over states (node, time).",
"At node u
with current time t
, you can only use an edge [u, v, start, end]
if t <= end
.",
"If t < start
, wait until start
, then traverse (arriving at start + 1
)."
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