POJ 3744 Scout YYF I （概率dp+矩阵优化）-优快云博客

本文链接：https://blog.youkuaiyun.com/u014737310/article/details/44358069

本博客讨论了在存在雷区的长路上，玩家YYF如何通过计算概率安全到达终点的问题。通过输入雷区数量和行走概率，计算不踩到雷的概率。此任务涉及到动态规划和概率论的应用。

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Scout YYF I

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 5504		Accepted: 1522

Description

YYF is a couragous scout. Now he is on a dangerous mission which is to penetrate into the enemy's base. After overcoming a series difficulties, YYF is now at the start of enemy's famous "mine road". This is a very long road, on which there are numbers of mines. At first, YYF is at step one. For each step after that, YYF will walk one step with a probability of p, or jump two step with a probality of 1- p. Here is the task, given the place of each mine, please calculate the probality that YYF can go through the "mine road" safely.

Input

The input contains many test cases ended with EOF.
Each test case contains two lines.
The First line of each test case is N (1 ≤ N ≤ 10) and p (0.25 ≤ p ≤ 0.75) seperated by a single blank, standing for the number of mines and the probability to walk one step.
The Second line of each test case is N integer standing for the place of N mines. Each integer is in the range of [1, 100000000].

Output

For each test case, output the probabilty in a single line with the precision to 7 digits after the decimal point.

Sample Input

Sample Output

0.5000000
0.2500000

Source

POJ Monthly Contest - 2009.08.23, Simon

题意：当前点是 1 ，有n个放置的雷，求不踩雷的概率通过

思路: 参照 kuangbin 大神博客 http://www.cnblogs.com/kuangbin/archive/2012/10/02/2710586.html

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<stack>
#include<vector>
#include<set>
#include<map>


#define L(x) (x<<1)
#define R(x) (x<<1|1)
#define MID(x,y) ((x+y)>>1)

#define eps 1e-8
typedef __int64 ll;

#define fre(i,a,b)  for(i = a; i <b; i++)
#define free(i,b,a) for(i = b; i >= a;i--)
#define mem(t, v)   memset ((t) , v, sizeof(t))
#define ssf(n)      scanf("%s", n)
#define sf(n)       scanf("%d", &n)
#define sff(a,b)    scanf("%d %d", &a, &b)
#define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c)
#define pf          printf
#define bug         pf("Hi\n")

using namespace std;

#define INF 0x3f3f3f3f
#define N 15

int a[N];
int n;
double p;

struct mat{
   double A[3][3];
   mat(){ mem(A,0); }

   mat operator * (mat b)
   {
      mat c;
      int i,j,k;

   	  fre(i,0,3)
   	   fre(j,0,3)
   	   {
            fre(k,0,3)
   	   	     c.A[i][j]+=A[i][k]*b.A[k][j];
   	   }

   	   return c;
   }

}s;

mat pow_mul(mat s,int n)
{
     mat ans;
     int i,j;

     fre(i,0,3)
     	ans.A[i][i]=1;

    while(n)
	{
		if(n&1) ans=ans*s;
		s=s*s;
		n>>=1;
	}

	return ans;
}

int main()
{
	int i,j;

	while(~scanf("%d%lf",&n,&p))
	{
		fre(i,0,n)
		 sf(a[i]);

		 double ans=1;

		 s.A[0][0]=p;
		 s.A[0][1]=1-p;
		 s.A[1][0]=1;
		 s.A[1][1]=0;

		 mat temp;

		 sort(a,a+n);

		 temp=pow_mul(s,a[0]-1);   //计算走到这一个点的概率

		 ans*=(1-temp.A[0][0]);

		 fre(i,1,n)
		 {
		 	 if(a[i]==a[i-1]) continue;
		 	 temp=pow_mul(s,a[i]-a[i-1]-1);
		 	 ans*=(1-temp.A[0][0]);
		 }

       pf("%.7f\n",ans);
	}
    return 0;
}