- 当排列组合数或者幂很大时可以利用对数计算,之后再用exp还原,保证一定的精度。
- 数学期望是每一个可能的值和相应的概率的乘积和,没有可能值可以设。
- 仔细读题,吃完最后一个糖果后不知道是否已经吃完,所以需要再选一次。
- %f用来输入float,输出float double.
- %lf 用来输入double,输出long double.
题目链接:https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=825&problem=4514&mosmsg=Submission+received+with+ID+17971092
#include<cstdio>
#include<iostream>
#include<sstream>
#include<cstdlib>
#include<cmath>
#include<cctype>
#include<string>
#include<cstring>
#include<algorithm>
#include<stack>
#include<queue>
#include<set>
#include<map>
#include<ctime>
#include<vector>
#include<fstream>
#include<list>
using namespace std;
#define ms(s) memset(s,sizeof(s))
typedef unsigned long long ULL;
typedef long long LL;
const int INF = 0x3fffffff;
const int maxn = 400010;
long double logF[maxn];
void make_logF(){
logF[0] = 0;
for(int i = 1; i <= maxn; ++i)
logF[i] = logF[i-1]+log(i);
}
long double getC(int n,int r){
return logF[n] - logF[n-r] - logF[r];
}
int main(){
freopen("F:\\input.txt","r",stdin);
// freopen("F:\\output.txt","w",stdout);
// ios::sync_with_stdio(false);
int n;
double p;
double ans;
long double t1,t2,c;
int cas = 1;
make_logF();
while(~scanf("%d%lf",&n,&p)){
ans = 0;
for(int i = 0; i <= n; ++i){
c = getC(2*n-i,n);
t1 = c + (n+1)*log(p)+(n-i)*log(1-p);
t2 = c + (n+1)*log(1-p)+(n-i)*log(p);
ans += i*(exp(t1)+exp(t2));
}
printf("Case %d: %.6f\n",cas,ans);
cas++;
}
return 0;
}