{ "data": { "question": { "questionId": "2171", "questionFrontendId": "2045", "categoryTitle": "Algorithms", "boundTopicId": 1048465, "title": "Second Minimum Time to Reach Destination", "titleSlug": "second-minimum-time-to-reach-destination", "content": "

A city is represented as a bi-directional connected graph with n vertices where each vertex is labeled from 1 to n (inclusive). The edges in the graph are represented as a 2D integer array edges, where each edges[i] = [ui, vi] denotes a bi-directional edge between vertex ui and vertex vi. Every vertex pair is connected by at most one edge, and no vertex has an edge to itself. The time taken to traverse any edge is time minutes.

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Each vertex has a traffic signal which changes its color from green to red and vice versa every change minutes. All signals change at the same time. You can enter a vertex at any time, but can leave a vertex only when the signal is green. You cannot wait at a vertex if the signal is green.

\n\n

The second minimum value is defined as the smallest value strictly larger than the minimum value.

\n\n\n\n

Given n, edges, time, and change, return the second minimum time it will take to go from vertex 1 to vertex n.

\n\n

Notes:

\n\n\n\n

 

\n

Example 1:

\n\"\"        \"\"\n
\nInput: n = 5, edges = [[1,2],[1,3],[1,4],[3,4],[4,5]], time = 3, change = 5\nOutput: 13\nExplanation:\nThe figure on the left shows the given graph.\nThe blue path in the figure on the right is the minimum time path.\nThe time taken is:\n- Start at 1, time elapsed=0\n- 1 -> 4: 3 minutes, time elapsed=3\n- 4 -> 5: 3 minutes, time elapsed=6\nHence the minimum time needed is 6 minutes.\n\nThe red path shows the path to get the second minimum time.\n- Start at 1, time elapsed=0\n- 1 -> 3: 3 minutes, time elapsed=3\n- 3 -> 4: 3 minutes, time elapsed=6\n- Wait at 4 for 4 minutes, time elapsed=10\n- 4 -> 5: 3 minutes, time elapsed=13\nHence the second minimum time is 13 minutes.      \n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 2, edges = [[1,2]], time = 3, change = 2\nOutput: 11\nExplanation:\nThe minimum time path is 1 -> 2 with time = 3 minutes.\nThe second minimum time path is 1 -> 2 -> 1 -> 2 with time = 11 minutes.
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "到达目的地的第二短时间", "translatedContent": "

城市用一个 双向连通 图表示，图中有 n 个节点，从 1 到 n 编号（包含 1 和 n）。图中的边用一个二维整数数组 edges 表示，其中每个 edges[i] = [ui, vi] 表示一条节点 ui 和节点 vi 之间的双向连通边。每组节点对由 最多一条 边连通，顶点不存在连接到自身的边。穿过任意一条边的时间是 time 分钟。

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每个节点都有一个交通信号灯，每 change 分钟改变一次，从绿色变成红色，再由红色变成绿色，循环往复。所有信号灯都 同时 改变。你可以在 任何时候 进入某个节点，但是 只能 在节点 信号灯是绿色时 才能离开。如果信号灯是  绿色 ，你 不能 在节点等待，必须离开。

\n\n

第二小的值 是 严格大于 最小值的所有值中最小的值。

\n\n\n\n

给你 n、edges、time 和 change ，返回从节点 1 到节点 n 需要的 第二短时间 。

\n\n

注意：

\n\n\n\n

 

\n\n

示例 1：

\n\n

\"\"        \"\"

\n\n
\n输入：n = 5, edges = [[1,2],[1,3],[1,4],[3,4],[4,5]], time = 3, change = 5\n输出：13\n解释：\n上面的左图展现了给出的城市交通图。\n右图中的蓝色路径是最短时间路径。\n花费的时间是：\n- 从节点 1 开始，总花费时间=0\n- 1 -> 4：3 分钟，总花费时间=3\n- 4 -> 5：3 分钟，总花费时间=6\n因此需要的最小时间是 6 分钟。\n\n右图中的红色路径是第二短时间路径。\n- 从节点 1 开始，总花费时间=0\n- 1 -> 3：3 分钟，总花费时间=3\n- 3 -> 4：3 分钟，总花费时间=6\n- 在节点 4 等待 4 分钟，总花费时间=10\n- 4 -> 5：3 分钟，总花费时间=13\n因此第二短时间是 13 分钟。      \n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 2, edges = [[1,2]], time = 3, change = 2\n输出：11\n解释：\n最短时间路径是 1 -> 2 ，总花费时间 = 3 分钟\n第二短时间路径是 1 -> 2 -> 1 -> 2 ，总花费时间 = 11 分钟
\n\n

 

\n\n

提示：

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