We have a network of computers and a list of bi-directional connections. Each of these connections allows a file transfer from one computer to another. Is it possible to send a file from any computer on the network to any other?
Input Specification:
Each input file contains one test case. For each test case, the first line contains N (2≤N≤104), the total number of computers in a network. Each computer in the network is then represented by a positive integer between 1 and N. Then in the following lines, the input is given in the format:
I c1 c2
where I
stands for inputting a connection between c1
and c2
; or
C c1 c2
where C
stands for checking if it is possible to transfer files between c1
and c2
; or
S
where S
stands for stopping this case.
Output Specification:
For each C
case, print in one line the word “yes” or “no” if it is possible or impossible to transfer files between c1
and c2
, respectively. At the end of each case, print in one line “The network is connected.” if there is a path between any pair of computers; or “There are k
components.” where k
is the number of connected components in this network.
Sample Input 1:
5
C 3 2
I 3 2
C 1 5
I 4 5
I 2 4
C 3 5
S
Sample Output 1:
no
no
yes
There are 2 components.
Sample Input 2:
5
C 3 2
I 3 2
C 1 5
I 4 5
I 2 4
C 3 5
I 1 3
C 1 5
S
Sample Output 2:
no
no
yes
yes
The network is connected.
这个题目就是很直接的并查集使用
#include <iostream>
#include <algorithm>
using namespace std;
/*static int n = []() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
return 0;
}();*/
class UnionFind {
private:
int* parent;
int count;
int* rank; // rank[i]表示以i为根集合的层数
public:
UnionFind(int count_) {
parent = new int[count_];
rank = new int[count_];
this->count = count_;
for (int i = 0; i < count_; i++) {
parent[i] = i;
rank[i] = 1;
}
}
~UnionFind() {
delete[] parent;
delete[] rank;
}
int find(int p) {
//assert(p >= 0 && p < count);
while (p != parent[p]) {
parent[p] = parent[parent[p]];
p = parent[p];
}
return p;
}
bool isConnected(int p, int q) {
return find(p) == find(q);
}
void unionElements(int p, int q) {
int pRoot = find(p);
int qRoot = find(q);
if (pRoot == qRoot)
return;
if (rank[pRoot] < rank[qRoot])
parent[pRoot] = qRoot;
else if (rank[qRoot] < rank[pRoot])
parent[qRoot] = pRoot;
else {
parent[pRoot] = qRoot;
rank[qRoot]++;
}
count--;
}
int size() {
return count;
}
};
int main()
{
int n, c1, c2;
char cmd;
cin >> n;
UnionFind Union = UnionFind(n+1);
while (true) {
cin >> cmd;
if (cmd == 'S') {
if (Union.size()-1 == 1)
cout << "The network is connected." << endl;
else if(Union.size()>2)
printf("There are %d components.", Union.size()-1);
break;
}
else if (cmd == 'C') {
cin >> c1 >> c2;
if (Union.isConnected(c1, c2))
cout << "yes" << endl;
else
cout << "no" << endl;
}
else if (cmd == 'I') {
cin >> c1 >> c2;
Union.unionElements(c1, c2);
}
}
}