畅通工程，How Many Tables ACM第九天-图论

下面两题的方法是一样的都是并查集的应用；

并查集的重点就是找到祖先节点的过程。

重点在这里：int find(int x){ return p[x] == x ? x : p[x] = find( p[x]); }

不断地递归，递归到找到自己是自己的祖先为止。并且把它取接到那个祖先节点上；这样可以节省空间和时间。

How Many Tables

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 15414    Accepted Submission(s): 7560

Problem Description

Today is Ignatius' birthday. He invites a lot of friends. Now it's dinner time. Ignatius wants to know how many tables he needs at least. You have to notice that not all the friends know each other, and all the friends do not want to stay with strangers.

One important rule for this problem is that if I tell you A knows B, and B knows C, that means A, B, C know each other, so they can stay in one table.

For example: If I tell you A knows B, B knows C, and D knows E, so A, B, C can stay in one table, and D, E have to stay in the other one. So Ignatius needs 2 tables at least.

 

Input

The input starts with an integer T(1<=T<=25) which indicate the number of test cases. Then T test cases follow. Each test case starts with two integers N and M(1<=N,M<=1000). N indicates the number of friends, the friends are marked from 1 to N. Then M lines follow. Each line consists of two integers A and B(A!=B), that means friend A and friend B know each other. There will be a blank line between two cases.

 

Output

For each test case, just output how many tables Ignatius needs at least. Do NOT print any blanks.

 

Sample Input

2
5 3
1 2
2 3
4 5

5 1
2 5

 

Sample Output

2
4

 

Author

Ignatius.L

 

Source

杭电ACM省赛集训队选拔赛之热身赛

 

Recommend

Eddy

 

#include <cstdio>
#define maxn 1005
using namespace std;
int p[maxn];
int a[maxn];
int b[maxn];
int find(int x){
	return	p[x] == x? x : p[x] = find(p[x]);
}
int main(){
	int t;
	scanf("%d",&t);
	while(t--){
		int n,m;
		scanf("%d %d",&n,&m);
		for(int i = 1;i <= m;i++){
			scanf("%d %d",&a[i],&b[i]);
		}
		int ans = 0;
		for(int i = 1;i <= n;i++){
			p[i] = i;
		}
		for(int i = 0;i <= m;i++){
			int x = find(a[i]);
			int y = find(b[i]);
			if(x != y){
				ans++;
				p[x] = y;
			}
		}
		int answer = n - ans;
		printf("%d
",answer);
	}
	return	0;
}

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畅通工程

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 32971    Accepted Submission(s): 17391

Problem Description

某省调查城镇交通状况，得到现有城镇道路统计表，表中列出了每条道路直接连通的城镇。省政府“畅通工程”的目标是使全省任何两个城镇间都可以实现交通（但不一定有直接的道路相连，只要互相间接通过道路可达即可）。问最少还需要建设多少条道路？ 

 

Input

测试输入包含若干测试用例。每个测试用例的第1行给出两个正整数，分别是城镇数目N ( < 1000 )和道路数目M；随后的M行对应M条道路，每行给出一对正整数，分别是该条道路直接连通的两个城镇的编号。为简单起见，城镇从1到N编号。 
注意:两个城市之间可以有多条道路相通,也就是说
3 3
1 2
1 2
2 1
这种输入也是合法的
当N为0时，输入结束，该用例不被处理。 

 

Output

对每个测试用例，在1行里输出最少还需要建设的道路数目。 

 

Sample Input

4 2
1 3
4 3
3 3
1 2
1 3
2 3
5 2
1 2
3 5
999 0
0

 

Sample Output

1
0
2
998

Hint
Hint
 
Huge input, scanf is recommended.

 

Source

浙大计算机研究生复试上机考试-2005年

 

Recommend

JGShining

 

#include <cstdio>
#include <cstring>

using namespace std;
#define maxn 1005
int p[maxn];
int a[maxn];
int b[maxn];
int find(int x){
	return	p[x] == x? x : p[x] = find(p[x]);
}
int main(){
	int n,m;
	while(scanf("%d %d",&n,&m) && n){
		memset(p,0,sizeof(p));
		for(int i = 1;i <= m;i++){
			scanf("%d %d",&a[i],&b[i]);
		}
		int ans = 0;
		for(int i = 1;i <= n;i++){
			p[i] = i;
		}
		for(int i = 0;i <= m;i++){
			int x = find(a[i]);
			int y = find(b[i]);
			if(x != y){
				ans++;
				p[x] = y;
			}
		}
		int answer = n - 1 - ans;
		printf("%d
",answer);
	}
	return	0;
}