## 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:6Explanation: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:-1Explanation: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]`

## Rust Solution

```
struct Solution;
struct UnionFind {
parent: Vec<usize>,
n: usize,
}
impl UnionFind {
fn new(n: usize) -> Self {
let parent = (0..n).collect();
UnionFind { parent, n }
}
fn find(&mut self, i: usize) -> usize {
let j = self.parent[i];
if j == i {
i
} else {
let k = self.find(j);
self.parent[i] = k;
k
}
}
fn union(&mut self, i: usize, j: usize) {
let i = self.find(i);
let j = self.find(j);
if i != j {
self.parent[i] = j;
}
self.n -= 1;
}
}
type Connection = (i32, usize, usize);
impl Solution {
fn minimum_cost(n: i32, connections: Vec<Vec<i32>>) -> i32 {
let n = n as usize;
let mut uf = UnionFind::new(n);
let mut connections: Vec<Connection> = connections
.into_iter()
.map(|v| (v[2], v[0] as usize - 1, v[1] as usize - 1))
.collect();
connections.sort_unstable();
let mut res = 0;
for connection in connections {
let u = connection.1;
let v = connection.2;
let i = uf.find(u);
let j = uf.find(v);
if i != j {
uf.union(i, j);
res += connection.0;
}
}
if uf.n == 1 {
res
} else {
-1
}
}
}
#[test]
fn test() {
let n = 3;
let connections = vec_vec_i32![[1, 2, 5], [1, 3, 6], [2, 3, 1]];
let res = 6;
assert_eq!(Solution::minimum_cost(n, connections), res);
let n = 4;
let connections = vec_vec_i32![[1, 2, 3], [3, 4, 4]];
let res = -1;
assert_eq!(Solution::minimum_cost(n, connections), res);
}
```

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