Minimum Score of a Path Between Two Cities
You are given a positive integer n representing n cities numbered from 1 to n. You are also given a 2D array roads where roads[i] = [ai, bi, distancei] indicates that there is a bidirectional road between cities ai and bi with a distance equal to distancei. 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
1andnmultiple times along the path. - The test cases are generated such that there is at least one path between
1andn.
Example 1
Input
n = 4, roads = [[1,2,9],[2,3,6],[2,4,5],[1,4,7]]Output
5The path from city 1 to 4 with the minimum score is 1 -> 2 -> 4, whose score is min(9, 5) = 5, and no other path has a lower score.
Example 2
Input
n = 4, roads = [[1,2,2],[1,3,4],[3,4,7]]Output
2The path from city 1 to 4 with the minimum score is 1 -> 2 -> 1 -> 3 -> 4, whose score is min(2, 2, 4, 7) = 2.
Constraints
- 2 <= n <= 10^5
- 1 <= roads.length <= 10^5
- roads[i].length == 3
- 1 <= ai, bi <= n
- ai != bi
- 1 <= distancei <= 10^4
- There are no repeated edges.
- There is at least one path between
1andn.