[POJ 3774] Scout YYF I

A line segment, the starting point is 1, there are some points can not go, each time the probability of p to go to the right 1 steps, or the probability of (1-P) 2 steps to the right.

The probability of going through the whole line safely

First, if 1 can not walk the dog belt, if there are 2 consecutive points can not walk the dog belt

For all points can go, dp[i] represents the probability of walking to I, dp[i]=dp[i-1]*p+dp[i-1]* (p-2)

The matrix {{p,1-p},{1,0}} can be constructed, and the DP is optimized by the matrix fast Power

Segment by points that cannot be walked

1#include <cstdio>2#include <algorithm>3 using namespacestd;4 inta[ the];5 structmatrix{6     Doublea[2][2];7     voidClear () {a[0][0]=a[1][1]=1, a[0][1]=a[1][0]=0; }8Matrixoperator*(Matrix t) {9 Matrix sum;Ten          for(intI=0;i<2; i++) One              for(intj=0;j<2; j + +){ Asum.a[i][j]=0; -                  for(intk=0;k<2; k++) -sum.a[i][j]+=a[i][k]*T.a[k][j]; the             } -         returnsum; -     } - }; + DoubleQP (Matrix BS,intx) { - Matrix sum; sum.clear (); +      while(x) { A         if(x&1) sum=sum*BS; atbs=bs*bs,x>>=1; -     } -     returnsum.a[0][0]; - } - intMain () { -     intNDoublep; in      while(SCANF ("%d", &n)! =EOF) { -scanf"%LF",&p); to          for(intI=1; i<=n;i++) +scanf"%d",&a[i]); -Sort (A +1, A +1+n); the         BOOLflag=a[1]==1?true:false; *          for(intI=2; i<=n;i++) $             if(a[i]==a[i-1]+1) flag=true;Panax Notoginseng         Doubleans; -         if(a[1]==1) flag=true; the         if(flag) ans=0; +         Else{ A Matrix F; thef.a[0][0]=p,f.a[0][1]=1-p; +f.a[1][0]=1, f.a[1][1]=0; -ans=1;intlst=0; $              for(intI=1; i<=n;i++){ $Ans*= (1-p) *QP (f,a[i]-lst-2); -lst=A[i]; -             } the         } -printf"%.7f\n", ans);//Wuyi     } the     return 0; -}

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[POJ 3774] Scout YYF I