Poj 3744 Scout yyf I probability dp + Matrix Multiplication

Poj 3744 Scout yyf I probability dp + Matrix Multiplication

Analysis:

The dis (k, v1, v2) function calculates the probability of reaching the current position as v1, the probability of one step prior to the current position as v2, the probability of arrival of the k step forward, and then accelerates the matrix.

Code:

 

//poj 3744//sep9#include 
 
  #include using namespace std;int pos[12];double p,mat[4][4];double ans[4][4];void mul1(){double c[4][4];c[0][1]=c[1][0]=c[0][0]=c[1][1]=0.0;for(int i=0;i<2;++i)for(int j=0;j<2;++j)for(int k=0;k<2;++k)c[i][j]+=ans[i][k]*mat[k][j];for(int i=0;i<2;++i)for(int j=0;j<2;++j)ans[i][j]=c[i][j];}void mul2(){double c[4][4];c[0][1]=c[1][0]=c[0][0]=c[1][1]=0.0;for(int i=0;i<2;++i)for(int j=0;j<2;++j)for(int k=0;k<2;++k)c[i][j]+=mat[i][k]*mat[k][j];for(int i=0;i<2;++i)for(int j=0;j<2;++j)mat[i][j]=c[i][j];}double dis(int len,double val,double val1){mat[1][0]=1.0;mat[0][1]=1-p;mat[0][0]=p;mat[1][1]=0;ans[1][0]=ans[0][1]=0;ans[0][0]=ans[1][1]=1.0;while(len){if(len&1) mul1();mul2();len>>=1;}return ans[0][0]*val+ans[0][1]*val1;}int main(){int n;while(scanf("%d%lf",&n,&p)==2){pos[0]=0;for(int i=1;i<=n;++i)scanf("%d",&pos[i]);sort(pos+1,pos+1+n);double ans=1,a1=1,a0=0;for(int i=1;i<=n;++i){if(pos[i]==pos[i-1]) continue;ans=ans-dis(pos[i]-pos[i-1]-1,a1,0);a1=ans;}printf("%.7lf\n",ans);}return 0;}