POJ3744----Scout YYF I

/*************************************************************************
    > File Name: POJ3744.cpp
    > Author: ALex
    > Mail: 405045132@qq.com 
    > Created Time: 2014年12月24日 星期三 21时20分51秒
 ************************************************************************/

#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

int pos[15];

struct martix
{
	double mat[2][2];
};

martix multiply(martix a, martix b)
{
	martix c;
	c.mat[0][0] = c.mat[0][1] = c.mat[1][0] = c.mat[1][1] = 0;
	for (int i = 0; i < 2; ++i)
	{
		for (int j = 0; j < 2; ++j)
		{
			for (int k = 0; k < 2; ++k)
			{
				c.mat[i][j] += a.mat[i][k] * b.mat[k][j];
			}
		}
	}
	return c;
}

martix fast_pow(martix a, int b)
{
	martix c;
	c.mat[0][0] = 1;
	c.mat[0][1] = c.mat[1][0] = 0;
	c.mat[1][1] = 1;
	while (b)
	{
		if (b & 1)
		{
			c = multiply(c, a);
		}
		a = multiply(a, a);
		b >>= 1;
	}
	return c;
}

int main()
{
	int n;
	double p;
	while (~scanf("%d%lf", &n, &p))
	{
		for (int i = 1; i <= n; ++i)
		{
			scanf("%d", &pos[i]);
		}
		double ans = 1;
		sort (pos + 1, pos + n + 1);
		martix x;
		x.mat[0][0] = p;
		x.mat[0][1] = 1 - p;
		x.mat[1][0] = 1;
		x.mat[1][1] = 0;
		martix tmp;
		tmp = fast_pow(x, pos[1] - 1);
		ans *= (1 - tmp.mat[0][0]);
		for (int i = 2; i <= n; ++i)
		{
			if (pos[i] == pos[i - 1])
			{
				continue;
			}
			tmp = fast_pow(x, pos[i] - pos[i - 1] - 1);
			ans *= (1 - tmp.mat[0][0]);
		}
		printf("%.7f\n", ans);
	}
	return 0;
}