線性期望（BUPT2015校賽.F）

將整體期望分成部分期望來做。

F. network?

時間限制?3000 ms?內存限制?65536 KB

題目描述

A social network is a social structure made up of a set of social actors (such?as individuals or organizations) and a set of the relationships between these?actors. In simple cases, we may represent people as nodes in a graph, and if two?people are friends, then an edge occurs between two nodes.

There are many interesting properties in a social network. Recently, we are researching on the ?SocialButterfly. A social butterfly should satisfy?the following conditions:

? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?A simple social network,where C knows everyone but D knows just C.

Now we have already had several networks in our database, but since the data?only contain nodes and edges, we don't know whether a node represents a male or?a female. We are interested, that if there are equal probabilities for a node to?be male and female (each with?1/2?probability).A?node is a social butterfly if and only if this node is a?female?and connects with?at?least?K?males.What will be the expectation?of number of?social?butterflies?in the network?

?

輸入格式

The number of test cases?T(T≤104)?will occur in the first line of?input.

For each test case:

The first line contains the number of nodes?N(1≤N≤30)and the?parameter?K (0 <= K <?N))

Then an?N×Nmatrix?G?followed, where?Gij=1?denotes?j?as?a friend of?i, otherwise?Gij=0. Here, it's always satisfied that?Gii=0and?Gij=Gji?for all?1≤i,j≤N.

輸出格式

For each test case, output the expectation of number of social butterflies in 3?decimals.

?

?

##Hint

In the first sample, there are totally 4 cases: {Female, Female}, {Female,
Male},{Male, Female} and?{Male, Male}, whose number of social butterflies
are respectively 0, 1, 1, 0. Hence, the expectation should be

?

E=14×0+14×1+14×1+14×0=12

?

輸入樣例

2
2 1
0 1
1 0
3 1
0 1 1
1 0 1
1 1 0

輸出樣例

0.500
1.125

//
//  main.cpp
//  160323.F
//
//  Created by 陳加壽 on 16/3/25.
//  Copyright ? 2016年 chenhuan001. All rights reserved.
//

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <math.h>
using namespace std;
#define N 31int mat[N][N];
double C[N][N];int main() {C[0][0]=1;for(int i=1;i<=30;i++){C[i][0]=1;for(int j=1;j<=i;j++){C[i][j] = C[i-1][j-1]+C[i-1][j];}}int T;cin>>T;while(T--){int n,k;scanf("%d%d",&n,&k);for(int i=0;i<n;i++)for(int j=0;j<n;j++)scanf("%d",&mat[i][j]);double ans=0;for(int i=0;i<n;i++){int cnt=0;for(int j=0;j<n;j++){cnt+=mat[i][j];}double tmp=0;for(int j=k;j<=cnt;j++)tmp += C[cnt][j];tmp = tmp/pow(2.0,cnt);tmp *= 0.5;ans += tmp;}printf("%.3lf\n",ans);}return 0;
}

?

?