uva 11021 Tribles 【概率】

Description
Tribbles
Input: Standard Input
Output: Standard Output
GRAVITATION, n.
“The tendency of all bodies to approach one another with a strength
proportion to the quantity of matter they contain – the quantity of
matter they contain being ascertained by the strength of their tendency
to approach one another. This is a lovely and edifying illustration of
how science, having made A the proof of B, makes B the proof of A.”
Ambrose Bierce
You have a population of kTribbles. This particular species of Tribbles live for exactly one day and then die. Just before death, a single Tribble has the probability Pi of giving birth to i more Tribbles. What is the probability that after m generations, every Tribble will be dead?
Input
The first line of input gives the number of cases, N. N test cases follow. Each one starts with a line containing n (1<= n<=1000) , k (0<= k<=1000) and m (0<= m<=1000) . The next n lines will give the probabilities P0, P1, …,Pn-1.
Output
For each test case, output one line containing “Case #x:” followed by the answer, correct up to an absolute or relative error of 10-6.
Sample Input
Sample Output
4
3 1 1
0.33
0.34
0.33
3 1 2
0.33
0.34
0.33
3 1 2
0.5
0.0
0.5
4 2 2
0.5
0.0
0.0
0.5
Case #1: 0.3300000
Case #2: 0.4781370
Case #3: 0.6250000
Case #4: 0.3164062

要求计算第m天k个生物全部死亡的概率，f[i]表示第i天全部死亡；

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <ctype.h>
#include <time.h>
#include <queue>

using namespace std;

const int MAXN = 1010;
double p[MAXN], f[MAXN];
int n, k, m;
int cases = 1;

int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d%d",&n,&k,&m);
        for (int i = 0; i < n; i++)
            scanf("%lf",&p[i]);
        f[0] = 0; f[1] = p[0];//f[i]表示第i天全部死亡的概率；
        for (int i = 2; i <= m; i++)
        {
            f[i] = 0;
            for (int j = 0; j < n; j++)
            {
                f[i] += p[j] * pow(f[i-1],j);//j个全部死亡，乘法原理
            }
        }
        printf("Case #%d: %.7lf\n",cases++,pow(f[m],k));
    }
    return 0;
}