DZY Loves Chemistry 分类： CF 比赛 图论 2015-08-08 15:51 3人阅读 评论(0) 收藏

DZY Loves Chemistry
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

DZY loves chemistry, and he enjoys mixing chemicals.

DZY has n chemicals, and m pairs of them will react. He wants to pour these chemicals into a test tube, and he needs to pour them in one by one, in any order.

Let’s consider the danger of a test tube. Danger of an empty test tube is 1. And every time when DZY pours a chemical, if there are already one or more chemicals in the test tube that can react with it, the danger of the test tube will be multiplied by 2. Otherwise the danger remains as it is.

Find the maximum possible danger after pouring all the chemicals one by one in optimal order.
Input

The first line contains two space-separated integers n and m .

Each of the next m lines contains two space-separated integers xi and yi (1 ≤ xi < yi ≤ n). These integers mean that the chemical xi will react with the chemical yi. Each pair of chemicals will appear at most once in the input.

Consider all the chemicals numbered from 1 to n in some order.
Output

Print a single integer — the maximum possible danger.
Sample test(s)
Input

1 0

Output

1

Input

2 1
1 2

Output

2

Input

3 2
1 2
2 3

Output

4

Note

In the first sample, there’s only one way to pour, and the danger won’t increase.

In the second sample, no matter we pour the 1st chemical first, or pour the 2nd chemical first, the answer is always 2.

In the third sample, there are four ways to achieve the maximum possible danger: 2-1-3, 2-3-1, 1-2-3 and 3-2-1 (that is the numbers of the chemicals in order of pouring).
用并查集判断连通分量的个数

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <vector>
#include <string>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define eps 1e-9
#define LL long long
#define PI acos(-1.0)
#define INF 0x3f3f3f3f
#define CRR fclose(stdin)
#define CWW fclose(stdout)
#define RR freopen("input.txt","r",stdin)
#pragma comment(linker,"/STACK:102400000")
#define WW freopen("output.txt","w",stdout)

const int Max =  160000;
int pre[55];
int Find(int x)
{
    return pre[x]==x?x:pre[x]=Find(pre[x]);
}
void Link(int x,int y)
{
    int Fx=Find(x);
    int Fy=Find(y);
    if(Fx!=Fy)
    {
        pre[Fx]=Fy;
    }
}
int main()
{
    int u,v;
    int n,m;
    scanf("%d %d",&n,&m);
    for(int i=1;i<=n;i++)
    {
        pre[i]=i;
    }
    while(m--)
    {
        scanf("%d %d",&u,&v);
        Link(u,v);
    }
    LL sum=1;
    for(int i=1; i<=n; i++)
    {
        if(pre[i]!=i)
        sum*=2;
    }
    printf("%I64d\n",sum);

    return 0;
}

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