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Scout YYF I
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 1 0.5 2 2 0.5 2 4 Sample Output 0.5000000 0.2500000 Source |
#include<stdio.h>
#include<algorithm>
#include<string.h>
using namespace std;
double p;
int pos[17];
struct Matrax
{
double m[2][2];
}a,per,tmp;
void init()//建立矩阵
{
a.m[0][0]=p;a.m[0][1]=1-p;
a.m[1][0]=1;a.m[1][1]=0;
per.m[0][0]=1;per.m[0][1]=0;
per.m[1][0]=0;per.m[1][1]=1;
}
Matrax multi(Matrax a,Matrax b)//矩阵相乘
{
Matrax c;
for(int i=0;i<2;i++)
for(int j=0;j<2;j++)
{
c.m[i][j]=0;
for(int k=0;k<2;k++)
c.m[i][j]+=a.m[i][k]*b.m[k][j];
}
return c;
}
Matrax power(int k)//矩阵快速幂
{
Matrax pp=a,ans=per;
while(k)
{
if(k&1){ans=multi(ans,pp);k--;}
else {k>>=1;pp=multi(pp,pp);}
}
return ans;
}
int main()
{
int n;
while(scanf("%d%lf",&n,&p)!=EOF)
{
bool no=false;
double ans=1;
memset(pos,0,sizeof(pos));
for(int i=1;i<=n;i++)
scanf("%d",&pos[i]);
sort(pos+1,pos+n+1);
for(int i=1;i<=n;i++)
if(pos[i]==1||pos[i]==pos[i-1]){no=true;break;}
if(no){printf("%.7lf\n",0);continue;}
init();
tmp=power(pos[1]-1);//求从1到第一个雷的概率
ans*=(1-tmp.m[0][0]);//求不到第一个雷的概率
for(int i=2;i<=n;i++)
{
if(pos[i]==pos[i-1])continue;
tmp=power(pos[i]-pos[i-1]-1);//求从第i-1个雷后面一步到第i个雷的概率
ans*=(1-tmp.m[0][0]);//不到第i个雷的概率
}
printf("%.7lf\n",ans);
}
return 0;
}POJ 3744 Scout YYF I 矩阵快速幂优化--概率dp
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原文地址：http://blog.csdn.net/crescent__moon/article/details/43268895
