2326: [HNOI2011] Math Homework

2326: [HNOI2011] Math homeworkDescription

Don't say anything acty.

Exercises

Linear recursion is easy to write, F[i]=f[i-1]*10+i (mod)

But when n is large, you need to use matrix multiplication.

We have enough to build the matrix

10^i 0 0 f[i-1] f[i]

1 1 0 * i-1 = i

1 1 1) 1 1

#include <stdio.h>#include<iostream>#include<string.h>using namespacestd;#definell Long Longinti;ll n,m,s,a[4][4],b[4][4],c[4][4];voidMul (LL a[4][4],ll b[4][4],ll ans[4][4]){    inti,j,k; Memset (c,0,sizeof(c));  for(i=1; i<=3; i++)      for(j=1; j<=3; j + +)       for(k=1; k<=3; k++) C[i][j]= (c[i][j]+ (a[i][k]%m) * (b[k][j]%m))%m;  for(i=1; i<=3; i++)      for(j=1; j<=3; j + +) Ans[i][j]=c[i][j];}voidSolve (ll x,ll y) {y=y-x/Ten+1; memset (b,0,sizeof(b)); b[1][1]=x; b[2][1]=b[3][1]=b[2][2]=b[3][2]=b[3][3]=1;  while(y) {if(y&1) Mul (a,b,a);        Mul (B,B,B); Y>>=1; }}intMain () {CIN>>n>>m;  for(i=1; i<=3; i++) A[i][i]=1; S=Ten;  while(n>=s) {Solve (S,s-1); S*=Ten;    } solve (S,n); cout<<a[3][1]; return 0;}

2326: [HNOI2011] Math Homework