Hihocode #1151: Domino cover Issue • Two

#1151: Domino cover issue • TwoTime Limit:10000mscase time Limit:1000msmemory LIMIT:256MB Description

Last week we studied the 2xN Domino problem, this week we might as well increase the difficulty, study the 3xN Domino problem?
So our question is: for the 3xN chessboard, how many different coverage methods are used to cover a 1x2 Domino?
First of all we can be sure that the odd length must not be covered, for even lengths, such as 2, 4, we have the following types of coverage:

Hint: 3xN Domino Overlay

input

Line 1th: an integer n. Represents the board length. 1≤n≤100,000,000

Output

Line 1th: An integer representing the number of coverage scenarios MOD 12357

Sample Input

62247088

Sample Output

4037


Solving problems: Making transfer equations

1#include <bits/stdc++.h>2 using namespacestd;3typedefLong LongLL;4 ConstLL mod =12357;5 structmatrix{6     intm[8][8];7 Matrix () {8 init ();9     }Ten     voidinit () { OneMemset (M,0,sizeofm); A     } -Matrixoperator*(ConstMatrix &RHS) { - Matrix ret; the          for(intK =0; K <8; ++k) -              for(inti =0; I <8; ++i) -                  for(intj =0; J <8; ++j) -RET.M[I][J] = (Ret.m[i][j] + m[i][k]*rhs.m[k][j])%MoD; +         returnret; -     } +     voidprint () { A          for(inti =0; I <8; ++i) { at              for(intj =0; J <8; ++j) -printf"%d", M[i][j]); -cout<<Endl; -         } -     } - }; in Matrix A, b; - voidQuickpow (LL index) { to      while(index) { +         if(index&1) A = A *b; -Index >>=1; theb = b*b; *     } $ }Panax Notoginseng BOOLtab[Ten][Ten]; - voidDfsintCurintSt) { the     if(cur >=3){ +         intSS =0; A          for(inti =2; I >=0; --i) { theSS <<=1; +SS |= tab[i][1]; -         } $b.m[st][ss]++; $         return; -     } -     if(!tab[cur][0]){ the         if(!tab[cur][1]){ -tab[cur][0] = tab[cur][1] =true;WuyiDFS (cur+1, ST); thetab[cur][0] = tab[cur][1] =false; -         } Wu         if(cur +1<3){ -             if(!tab[cur+1][0]){ Abouttab[cur+1][0] = tab[cur][0] =true; $DFS (cur+2, ST); -tab[cur+1][0] = tab[cur][0] =false; -             } -         } A}ElseDFS (cur +1, ST); + } the voidInitintSt) { -memset (tab,false,sizeoftab); $      for(inti =0, xst = st; I <3; ++i,xst >>=1) thetab[i][0] = xst&1; theDfs0, ST); the } the intMain () { -     intN; in      while(~SCANF ("%d",&N)) { the b.init (); the a.init (); About          for(inti =0; I <=7; ++i) init (i); thea.m[0][0] =1; the Quickpow (n); theprintf"%d\n", a.m[0][0]); +     } -     return 0; the}

View Code

Hihocode #1151: Domino Overlay problem • Two