hdu 4465 Candy （快速排列組合 ）

Candy

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2115 Accepted Submission(s): 910
Special Judge

Problem Description LazyChild is a lazy child who likes candy very much. Despite being very young, he has two large candy boxes, each contains n candies initially. Everyday he chooses one box and open it. He chooses the first box with probability p and the second box with probability (1 - p). For the chosen box, if there are still candies in it, he eats one of them; otherwise, he will be sad and then open the other box.
He has been eating one candy a day for several days. But one day, when opening a box, he finds no candy left. Before opening the other box, he wants to know the expected number of candies left in the other box. Can you help him?
Input There are several test cases.
For each test case, there is a single line containing an integer n (1 ≤ n ≤ 2 × 10⁵) and a real number p (0 ≤ p ≤ 1, with 6 digits after the decimal).
Input is terminated by EOF.
Output For each test case, output one line “Case X: Y” where X is the test case number (starting from 1) and Y is a real number indicating the desired answer.
Any answer with an absolute error less than or equal to 10^-4 would be accepted.
Sample Input

10 0.400000
100 0.500000
124 0.432650
325 0.325100
532 0.487520
2276 0.720000

Sample Output

Case 1: 3.528175
Case 2: 10.326044
Case 3: 28.861945
Case 4: 167.965476
Case 5: 32.601816
Case 6: 1390.500000

從兩個箱子裡取糖果，直到發現某一個箱子裡的糖果已經取完，求另一個箱子裡剩余糖果的期望。

因為取完的箱子選擇了N+1次，故為p^(n+1)，精度問題可以取對數處理。

#include
#include
#include
#include
#include
using namespace std;
#define LL __int64
#define N 400005
const LL mod=1000000007;
double f[N];
double logc(int m,int n)  //快速排列組合函數C（n,m）=exp(lggc(n,m));
{
    return f[m]-f[n]-f[m-n];
}
int main()
{
    double p,q;
    int n,i,k,cnt=1;
    f[0]=0;
    for(i=1;i