"HDOJ5950" Recursive sequence (matrix multiplication, fast power)

Test instructions: f[1]=a,f[2]=b,f[i]=2f[i-2]+f[i-1]+i^4 (i>=3), multi-group inquiry f[n] 2147493647 modulo

N,a,b < 2^31

Idea: The focus is on the treatment of i^4

For the I transfer matrix, it is possible to record its 0,1,2,3,4 times

The power of I can be obtained by the power of I-1, and the last coefficient is the coefficient of two-term expansion.

Try a new moment multiplication template

1#include <cstdio>2#include <cstring>3#include <string>4#include <cmath>5#include <iostream>6#include <algorithm>7#include <map>8#include <Set>9#include <queue>Ten#include <vector> One using namespacestd; AtypedefLong Longll; -typedef unsignedint UINT; -typedef unsignedLong Longull; thetypedef pair<int,int>PII; -typedef vector<int>VI; - #defineFi first - #defineSe Second + #defineMP Make_pair - #defineN 2100000 + #defineMOD 2147493647 A #defineEPS 1e-8 at #definePi ACOs (-1) - Const intmaxn=Ten; -  - intRead () - {  -    intv=0, f=1; in    CharC=GetChar (); -     while(c< -|| $&LT;C) {if(c=='-') f=-1; C=GetChar ();} to     while( -<=c&&c<= $) v= (v<<3) +v+v+c- -, c=GetChar (); +    returnv*F; - } the  *  $ structMatrix//Matrix classPanax Notoginseng {    -     intn,m; the ll DATA[MAXN][MAXN]; + }; A  the matrix MA,MB; + ll A,b,c,d,p,n; -  $ Matrix Matrixmul (matrix A, matrix B) $ { - matrix re; -     if(a.m!=B.N) the     { -printf"error\n");Wuyi         returnre; the     } -memset (Re.data,0,sizeof(Re.data)); WuRE.N = A.N; RE.M =b.m; -      for(inti =1; I <= A.N; i++) About     { $          for(intj =1; J <= a.m.; J + +) -         { -             if(A.data[i][j] = =0)Continue; -              for(intK =1; K <= B.M; k++) A             { +Re.data[i][k] + = (a.data[i][j]% mod * b.data[j][k]% MoD)%MOD; theRE.DATA[I][K]%=MOD; -             } $         } the     } the     returnre; the } the  -Matrix Matrixpow (Matrix A,intb) in { the matrix re; the     if(a.n!=a.m.) About     { theprintf"error2\n"); the         returnre; the     } +re.n=re.m=A.N; -memset (Re.data,0,sizeof(Re.data)); the      for(intI=1; i<=re.n;i++) re.data[i][i]=1;Bayi      while(b) the     { the         if(b&1) re=Matrixmul (re,a); -A=Matrixmul (a,a); -b>>=1; the     } the     returnre; the } the  - voidInputmat (intNintM,matrix &a,ll *b) the { theA.N = n; a.m. =m; the      for(inti =1; I <= N; i++)94          for(intj =1; J <= M; J + +) theA.DATA[I][J] = * (b + (I-1) * m + (J-1)); the } the 98 voidinit () { Aboutll pt[1][7] = {B,a, -,8,4,2,1}; -Inputmat (1,7, ma,*PT);101ll pt2[7][7] = {1,1,0,0,0,0,0,102                     2,0,0,0,0,0,0,103                     1,0,1,0,0,0,0,104                     4,0,4,1,0,0,0, the                     6,0,6,3,1,0,0,106                     4,0,4,3,2,1,0,107                     1,0,1,1,1,1,1,};108Inputmat (7,7, mb,*pt2);109 } the 111 intMain () the {113     intCAs; thescanf"%d",&CAs); the      while(cas--) the     {117scanf"%i64d%i64d%i64d",&n,&a,&b); 118         intI=3;119a%=MOD; -b%=MOD;121         if(n = =1)122printf"%i64d\n", a);123         Else if(n = =2)124printf"%i64d\n", b); the         Else126         {127              - init ();129Ma=matrixmul (Ma,matrixpow (mb,n-2)); the         }131printf"%i64d\n", ma.data[1][1]); the     }133     return 0;134}

"HDOJ5950" Recursive sequence (matrix multiplication, fast power)