A1167 Summit (25分)

散列

1. 原文

A summit (峰会) is a meeting of heads of state or government. Arranging the rest areas for the summit is not a simple job. The ideal arrangement of one area is to invite those heads so that everyone is a direct friend of everyone.

Now given a set of tentative arrangements, your job is to tell the organizers whether or not each area is all set.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N (≤ 200), the number of heads in the summit, and M, the number of friendship relations. Then M lines follow, each gives a pair of indices of the heads who are friends to each other. The heads are indexed from 1 to N.

Then there is another positive integer K (≤ 100), and K lines of tentative arrangement of rest areas follow, each first gives a positive number L (≤ N), then followed by a sequence of L distinct indices of the heads. All the numbers in a line are separated by a space.

Output Specification:

For each of the K areas, print in a line your advice in the following format:

if in this area everyone is a direct friend of everyone, and no friend is missing (that is, no one else is a direct friend of everyone in this area), print Area X is OK…

if in this area everyone is a direct friend of everyone, yet there are some other heads who may also be invited without breaking the ideal arrangement, print Area X may invite more people, such as H. where H is the smallest index of the head who may be invited.

if in this area the arrangement is not an ideal one, then print Area X needs help. so the host can provide some special service to help the heads get to know each other.

Here X is the index of an area, starting from 1 to K.

Sample Input:

8 10
5 6
7 8
6 4
3 6
4 5
2 3
8 2
2 7
5 3
3 4
6
4 5 4 3 6
3 2 8 7
2 2 3
1 1
2 4 6
3 3 2 1

Sample Output:

Area 1 is OK.
Area 2 is OK.
Area 3 is OK.
Area 4 is OK.
Area 5 may invite more people, such as 3.
Area 6 needs help.

2. 解析思路

8个峰会代表人，10个好友组

安排的圆桌会议中

• 如果所有人都是直接好友，并且加一个代表人a，a跟圆桌内的所有人并不是直接好友，则当前圆桌是完美的
• 可以加一个a，跟圆桌内的所有人都是直接好友，该圆桌可以增加人数
• 圆桌内并不是好友，需要调整

用 fre[a*maxn+b]=1 代表a和b是好友

3. 代码

#include<cstdio>
#include<vector>
#include<set>
#include<map>
#include<algorithm>
using namespace std;
const int maxn = 210;
map<int,int> fre;
int arr[110]={};
bool visit[110]={};
int main(){
	int n,m;
	scanf("%d%d",&n,&m);
	for (int i = 0; i < m; ++i)
	{
		int a,b;
		scanf("%d%d",&a,&b);
		fre[a*maxn+b]=1;
		fre[b*maxn+a]=1;
	}
	int k;
	scanf("%d",&k);
	for (int i = 1; i <= k; ++i)
	{
		int l;
		scanf("%d",&l);
		fill(visit,visit+maxn,false);
		for(int j = 0; j < l; j++){

			scanf("%d",&arr[j]);
			visit[arr[j]]=true;
		}
		int flag = 0;
		for (int j = 0; j < l; j++)
		{
			for (int k = j+1; k < l; ++k)
			{
				if (fre[arr[j]*maxn+arr[k]]==0)
				{
					flag = 1;
					break;
				}
			}
		}
		if (flag == 1)
		{
			printf("Area %d needs help.\n",i);
			continue;
		}
		int cnt = 0;
		int index = 1<<30;
		for (int j = 1; j <= n; ++j)
		{
			int morepe = 0;
			if (visit[j]==false)
			{
				for (int k = 0; k < l; ++k)
				{
					if(fre[j*maxn+arr[k]]==0){
						morepe = 1;
						break;
					}
				}
				if (morepe==0)
				{
					if (j<index)
					{
						index = j;
					}
					cnt++;
				}
			}
		}

		if (flag == 0)
		{
			if(cnt == 0){
				printf("Area %d is OK.\n",i);
		 	}
		 	else{
		 		printf("Area %d may invite more people, such as %d.\n",i,index);
		 	}
		}
	}
	
	return 0;
}