Question

1319. Number of Operations to Make Network Connected

中文文档

Description

There are n computers numbered from 0 to n - 1 connected by ethernet cables connections forming a network where connections[i] = [ai, bi] represents a connection between computers ai and bi. Any computer can reach any other computer directly or indirectly through the network.

You are 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 is not possible, return -1.

 

Example 1:

Input: n = 4, connections = [[0,1],[0,2],[1,2]]
Output: 1
Explanation: 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: -1
Explanation: There are not enough cables.

 

Constraints:

• 1 <= n <= 105
• 1 <= connections.length <= min(n * (n - 1) / 2, 105)
• connections[i].length == 2
• 0 <= ai, bi < n
• ai != bi
• There are no repeated connections.
• No two computers are connected by more than one cable.

Solutions

Solution 1

class Solution:
  def makeConnected(self, n: int, connections: List[List[int]]) -> int:
    def find(x):
      if p[x] != x:
        p[x] = find(p[x])
      return p[x]

    cnt, size = 0, n
    p = list(range(n))
    for a, b in connections:
      if find(a) == find(b):
        cnt += 1
      else:
        p[find(a)] = find(b)
        size -= 1
    return -1 if size - 1 > cnt else size - 1

class Solution {
  private int[] p;

  public int makeConnected(int n, int[][] connections) {
    p = new int[n];
    for (int i = 0; i < n; ++i) {
      p[i] = i;
    }
    int cnt = 0;
    for (int[] e : connections) {
      int a = e[0];
      int b = e[1];
      if (find(a) == find(b)) {
        ++cnt;
      } else {
        p[find(a)] = find(b);
        --n;
      }
    }
    return n - 1 > cnt ? -1 : n - 1;
  }

  private int find(int x) {
    if (p[x] != x) {
      p[x] = find(p[x]);
    }
    return p[x];
  }
}

class Solution {
public:
  vector<int> p;

  int makeConnected(int n, vector<vector<int>>& connections) {
    p.resize(n);
    for (int i = 0; i < n; ++i) p[i] = i;
    int cnt = 0;
    for (auto& e : connections) {
      int a = e[0], b = e[1];
      if (find(a) == find(b))
        ++cnt;
      else {
        p[find(a)] = find(b);
        --n;
      }
    }
    return n - 1 > cnt ? -1 : n - 1;
  }

  int find(int x) {
    if (p[x] != x) p[x] = find(p[x]);
    return p[x];
  }
};

func makeConnected(n int, connections [][]int) int {
  p := make([]int, n)
  for i := range p {
    p[i] = i
  }
  cnt := 0
  var find func(x int) int
  find = func(x int) int {
    if p[x] != x {
      p[x] = find(p[x])
    }
    return p[x]
  }
  for _, e := range connections {
    a, b := e[0], e[1]
    if find(a) == find(b) {
      cnt++
    } else {
      p[find(a)] = find(b)
      n--
    }
  }
  if n-1 > cnt {
    return -1
  }
  return n - 1
}