2492 - Minimum Score of a Path Between Two Cities.

Medium

You are given a positive integer n representing n cities numbered from 1 to n. You are also given a 2D array roads where <code>roadsi = a_i, b_i, distance_i</code> indicates that there is a bidirectional road between cities <code>a_i</code> and <code>b_i</code> with a distance equal to <code>distance_i</code>. The cities graph is not necessarily connected.

The score of a path between two cities is defined as the minimum distance of a road in this path.

Return the minimum possible score of a path between cities 1 and n.

Note:

• A path is a sequence of roads between two cities.

• It is allowed for a path to contain the same road multiple times, and you can visit cities 1 and n multiple times along the path.

• The test cases are generated such that there is at least one path between 1 and n.

Example 1:

Input: n = 4, roads = [1,2,9,2,3,6,2,4,5,1,4,7]

Output: 5

Explanation: The path from city 1 to 4 with the minimum score is: 1 -> 2 -> 4. The score of this path is min(9,5) = 5. It can be shown that no other path has less score.

Example 2:

Input: n = 4, roads = [1,2,2,1,3,4,3,4,7]

Output: 2

Explanation: The path from city 1 to 4 with the minimum score is: 1 -> 2 -> 1 -> 3 -> 4. The score of this path is min(2,2,4,7) = 2.

Constraints:

• <code>2 <= n <= 10⁵</code>

• <code>1 <= roads.length <= 10⁵</code>

• roads[i].length == 3

• <code>1 <= a_i, b_i<= n</code>

• <code>a_i != b_i</code>

• <code>1 <= distance_i<= 10⁴</code>

• There are no repeated edges.

• There is at least one path between 1 and n.