Connecting Cities With Minimum Cost
Difficulty: Medium
Category: DSA
Topics: Union Find, Graph
Asked at: Amazon, Uber
There are `N` cities numbered from 1 to `N`.
You are given `connections`, where each `connections[i] = [city1, city2, cost]` represents the cost to connect `city1` and `city2` together. (A connection is bidirectional: connecting `city1` and `city2` is the same as connecting `city2` and `city1`.)
Return the minimum cost so that for every pair of cities, there exists a path of connections (possibly of length 1) that connects those two cities together. The cost is the sum of the connection costs used. If the task is impossible, return -1.
Example 1:
Input: N = 3, connections = [[1,2,5],[1,3,6],[2,3,1]]
Output: 6
Explanation:
Choosing any 2 edges will connect all cities so we choose the minimum 2.
Example 2:
Input: N = 4, connections = [[1,2,3],[3,4,4]]
Output: -1
Explanation:
There is no way to connect all cities even if all edges are used.
Note:
`1 <= N <= 10000`
`1 <= connections.length <= 10000`
`1 <= connections[i][0], connections[i][1] <= N`
`0 <= connections[i][2] <= 10^5`
`connections[i][0] != connections[i][1]`