## 1319. Number of Operations to Make Network Connected

There are `n`

computers numbered from `0`

to `n-1`

connected by ethernet cables `connections`

forming a network where `connections[i] = [a, b]`

represents a connection between computers `a`

and `b`

. Any computer can reach any other computer directly or indirectly through the network.

Given an initial computer network `connections`

. You can extract certain cables between two directly connected computers, and place them between any pair of disconnected computers to make them directly connected. Return the *minimum number of times* you need to do this in order to make all the computers connected. If it's not possible, return -1.

**Example 1:**

Input:n = 4, connections = [[0,1],[0,2],[1,2]]Output:1Explanation:Remove cable between computer 1 and 2 and place between computers 1 and 3.

**Example 2:**

Input:n = 6, connections = [[0,1],[0,2],[0,3],[1,2],[1,3]]Output:2

**Example 3:**

Input:n = 6, connections = [[0,1],[0,2],[0,3],[1,2]]Output:-1Explanation:There are not enough cables.

**Example 4:**

Input:n = 5, connections = [[0,1],[0,2],[3,4],[2,3]]Output:0

**Constraints:**

`1 <= n <= 10^5`

`1 <= connections.length <= min(n*(n-1)/2, 10^5)`

`connections[i].length == 2`

`0 <= connections[i][0], connections[i][1] < n`

`connections[i][0] != connections[i][1]`

- There are no repeated connections.
- No two computers are connected by more than one cable.

## 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 i == j {
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;
}
}
}
impl Solution {
fn make_connected(n: i32, connections: Vec<Vec<i32>>) -> i32 {
let n = n as usize;
let m = connections.len();
if m + 1 < n {
return -1;
}
let mut uf = UnionFind::new(n);
for connection in connections {
let i = connection[0] as usize;
let j = connection[1] as usize;
uf.union(i, j);
}
(uf.n - 1) as i32
}
}
#[test]
fn test() {
let n = 4;
let connections = vec_vec_i32![[0, 1], [0, 2], [1, 2]];
let res = 1;
assert_eq!(Solution::make_connected(n, connections), res);
let n = 6;
let connections = vec_vec_i32![[0, 1], [0, 2], [0, 3], [1, 2], [1, 3]];
let res = 2;
assert_eq!(Solution::make_connected(n, connections), res);
let n = 6;
let connections = vec_vec_i32![[0, 1], [0, 2], [0, 3], [1, 2]];
let res = -1;
assert_eq!(Solution::make_connected(n, connections), res);
let n = 5;
let connections = vec_vec_i32![[0, 1], [0, 2], [3, 4], [2, 3]];
let res = 0;
assert_eq!(Solution::make_connected(n, connections), res);
}
```

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