3604 - Minimum Time to Reach Destination in Directed Graph.

Medium

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 <code>edgesi = u_i, v_i, start_i, end_i</code> indicates an edge from node <code>u_i</code> to <code>v_i</code> that can only be used at any integer time t such that <code>start_i<= t <= end_i</code>.

You start at node 0 at time 0.

In one unit of time, you can either:

• Wait at your current node without moving, or

• Travel along an outgoing edge from your current node if the current time t satisfies <code>start_i<= t <= end_i</code>.

Return the minimum time required to reach node n - 1. If it is impossible, return -1.

Example 1:

Input: n = 3, edges = [0,1,0,1,1,2,2,5]

Output: 3

Explanation:

The optimal path is:

• At time t = 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.

• At time ``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.

Example 2:

Input: n = 4, edges = [0,1,0,3,1,3,7,8,0,2,1,5,2,3,4,7]

Output: 5

Explanation:

The optimal path is:

• Wait at node 0 until time t = 1, then take the edge (0 → 2) which is available from 1 to 5. You arrive at node 2 at t = 2.

• Wait at node 2 until time 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.

Example 3:

Input: n = 3, edges = [1,0,1,3,1,2,3,5]

Output: \-1

Explanation:

• Since there is no outgoing edge from node 0, it is impossible to reach node 2. Hence, the output is -1.

Constraints:

• <code>1 <= n <= 10⁵</code>

• <code>0 <= edges.length <= 10⁵</code>

• <code>edgesi == u_i, v_i, start_i, end_i</code>

• <code>0 <= u_i, v_i<= n - 1</code>

• <code>u_i != v_i</code>

• <code>0 <= start_i<= end_i<= 10⁹</code>