Hdu 4686 ARC of Dream (Matrix fast power multiplication)

problem Description

 is a curve defined by following function:

where== ai-1*ax+== bi-1*bx+ is 1,007?

Input

 Case 7  as  is10182x109.

Output

 Case 1,007,and so on.

Sample Input

1 1 2 3 4 5 6 2 1 2 3 4 5 6 3 1 2 3 4 5 6

Sample Output

4 134 1902

Author Zejun Wu (Watashi)

Source multi-university Training Contest 9

because: a[i]*b[i]= (a[i-1]*ax+ay) * (B[i-1]*bx+by)

= (A[i-1]*b[i-1]*ax*bx+a[i-1]*ax*by+b[i-1]*bx*ay+ay*by)

Construct The matrix:

| 1 0 0 0 0 |

| Ax*by AX 0 Ax*by 0 |

{AoD (n-1), a[i-1],b[i-1],a[i-1]*b[i-1],1}* |      Bx*ay 0 BX Bx*ay 0 | ={aod (n), a[i],b[i],a[i]*b[i],1}

| AX*BX 0 0 AX*BX 0 |

| Ay*by AY by Ay*by 1 |

Also note:

if (n==0) {//This judging condition is very important, it will not be timed out
printf ("0\n");
Continue
}

1 #pragmaComment (linker, "/stack:1024000000,1024000000")2#include <iostream>3#include <cstdio>4#include <cstring>5#include <cmath>6#include <math.h>7#include <algorithm>8#include <queue>9#include <Set>Ten#include <bitset> One#include <map> A#include <vector> -#include <stdlib.h> -#include <stack> the using namespacestd; - #definePI ACOs (-1.0) - #defineMax (a) (a) > (b)? (a): (b) - #defineMin (a) (a) < (b)? (a): (b) + #definell Long Long - #defineEPS 1e-10 + #defineMOD 1000000007 A #defineN 1000000 at #defineINF 1e12 - ll N; - ll A0,ax,ay,b0,bx,by; - structmatrix{ -ll mp[5][5]; - }; in Matrix Mul (Matrix A,matrix b) { - Matrix Res; to     for(LL i=0;i<5; i++){ +        for(LL j=0;j<5; j + +){ -res.mp[i][j]=0; the           for(LL k=0;k<5; k++){ *Res.mp[i][j]= (res.mp[i][j]+ (a.mp[i][k]*b.mp[k][j])%mod+mod)%MOD; $          }Panax Notoginseng       } -    } the    returnRes; + } A Matrix fastm (Matrix A,ll b) { the Matrix Res; +memset (RES.MP,0,sizeof(RES.MP)); -     for(LL i=0;i<5; i++){ $res.mp[i][i]=1; $    } -     while(b) { -       if(b&1){ theres=Mul (res,a); -       }WuyiA=Mul (a,a); theb>>=1; -    } Wu    returnRes; - } About intMain () $ { -     while(SCANF ("%i64d", &n) = =1){ -scanf"%i64d%i64d%i64d%i64d%i64d%i64d",&a0,&ax,&ay,&b0,&bx,&by ); -        A       if(n==0){//This condition of judgment is very important and will not be timed out. +printf"0\n"); the          Continue; -       } $        the        thell a0=A0; thell b0=B0; the  - Matrix tmp; inmemset (TMP.MP,0,sizeof(TMP.MP)); thetmp.mp[0][0]=1%MOD; thetmp.mp[1][0]=ax*by%MOD; Abouttmp.mp[1][1]=ax%MOD; thetmp.mp[1][3]=ax*by%MOD; thetmp.mp[2][0]=bx*ay%MOD; thetmp.mp[2][2]=bx%MOD; +tmp.mp[2][3]=bx*ay%MOD; -tmp.mp[3][0]=ax*bx%MOD; thetmp.mp[3][3]=ax*bx%MOD;Bayitmp.mp[4][0]=ay*by%MOD; thetmp.mp[4][1]=ay%MOD; thetmp.mp[4][2]=by%MOD; -tmp.mp[4][3]=ay*by%MOD; -tmp.mp[4][4]=1%MOD; the  theMatrix cnt=fastm (tmp,n-1); the  the Matrix G; -memset (G.MP,0,sizeof(G.MP)); theg.mp[0][0]=a0*b0%MOD; theg.mp[0][1]=a0%MOD; theg.mp[0][2]=b0%MOD;94g.mp[0][3]=a0*b0%MOD; theg.mp[0][4]=1%MOD; theMatrix ans=Mul (g,cnt); theprintf"%i64d\n", ans.mp[0][0]);98    } About     return 0; -}

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Hdu 4686 ARC of Dream (Matrix fast power multiplication)