#### Min Cost To Add New Roads

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 city2together. (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]

Solution:

Try to connect cities with minimum cost, then find small cost edge first, if two cities connected by the edge do no have same ancestor, then union them.

When number of unions equal to 1, all cities are connected.

Time Complexity: O(mlogm + mlogN). sort takes O(mlogm). find takes O(logN). With path compression and unino by weight, amatorize O(1).

Space: O(N).

##### Solve the problem:

Python3#### Get one-to-one training from Google Facebook engineers

##### Top-notch Professionals

Learn from Facebook and Google senior engineers interviewed 100+ candidates.

Most recent interview questions and system design topics gathered from aonecode alumnus.

One-to-one online classes. Get feedbacks from real interviewers.

##### Customized Private Class

Already a coding expert? - Advance straight to hard interview topics of your interest.

New to the ground? - Develop basic coding skills with your own designated mentor.

Days before interview? - Focus on most important problems in target company question bank.