1135. Connecting Cities With Minimum Cost

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. 1 <= N <= 10000
2. 1 <= connections.length <= 10000
3. 1 <= connections[i][0], connections[i][1] <= N
4. 0 <= connections[i][2] <= 10^5
5. connections[i][0] != connections[i][1]

1、题目描述¶

想象一下你是个城市基建规划者，地图上有 N 座城市，它们按以 1 到 N 的次序编号。

给你一些可连接的选项 conections，其中每个选项 conections[i] = [city1, city2, cost] 表示将城市 city1 和城市 city2 连接所要的成本。（连接是双向的，也就是说城市 city1 和城市 city2 相连也同样意味着城市 city2 和城市 city1 相连）。

返回使得每对城市间都存在将它们连接在一起的连通路径（可能长度为 1 的）最小成本。该最小成本应该是所用全部连接代价的综合。如果根据已知条件无法完成该项任务，则请你返回 -1。

示例 1：

输入：N = 3, conections = [[1,2,5],[1,3,6],[2,3,1]]
输出：6
解释：
选出任意 2 条边都可以连接所有城市，我们从中选取成本最小的 2 条。

示例 2：

输入：N = 4, conections = [[1,2,3],[3,4,4]]
输出：-1
解释： 
即使连通所有的边，也无法连接所有城市。

提示：

• 1 <= N <= 10000
• 1 <= conections.length <= 10000
• 1 <= conections[i][0], conections[i][1] <= N
• 0 <= conections[i][2] <= 10^5
• conections[i][0] != conections[i][1]