BZOJ4002 [JLOI2015] meaningful string

It is said that these two games add up as long as 170 = = And this is the simplest topic qaq

See $ (\frac {b + \sqrt {d}} {2}) ^n$, the first reaction is a conjugate radical $ (\frac {B-\sqrt {d}} {2}) ^n$

First there are $ (\frac {b + \sqrt {d}} {2}) ^n + (\frac {b-\sqrt {d}} {2}) ^n$ as integers

From high school textbook knowledge, the above is actually a three-item recursive sequence of the formula, and the recurrence of the sequence is very simple

$ $f [x] = b * f[x-1]-\frac{b^2-d} {4} * f[x-2]$$

where $f[0] = 2, f[1] = b$, this way direct matrix multiplication is good ~

See $ A = (\frac {b-\sqrt {d}} {2}) ^n \in [-1, 1]$

And then... And then found Bzoj on the wrong side of the Qaq, is actually "for 20% of data $b=1,d=5$"

So $ A > 0$ when and only if the $d \not= b^2$ and $n$ is even, this time to reduce $f[n]$ $1$, otherwise do not reduce

1 /**************************************************************2 problem:40023 User:rausen4 language:c++5 result:accepted6 time:48 Ms7 memory:1272 KB8 ****************************************************************/9  Ten#include <cstdio> One#include <iostream> A#include <cstring> -#include <algorithm> -   the using namespacestd; -typedef unsignedLong Longll; - Constll mod =7528443412579576937ull; -   +Template <classT>T Sqr (t x) { -     returnX *x; + } A   atTemplate <classT>T Mul (t X, t y) { -     StaticT Res; -     if(X <y) Swap (x, y); -res =0; -      while(y) { -         if(Y &1) Res = (res + x)%MoD; inx = (x <<1)% mod, y >>=1; -     } to     returnRes; + } -   the ll B, D, N; *   $ structMat {Panax Notoginsengll x[3][3]; -       theInlinevoidClear () { +memset (x,0,sizeof(x)); A     } theInlinevoidOne () { +memset (x,0,sizeof(x)); -x[1][1] = x[2][2] =1; $     } $InlinevoidPre () { -          This-Clear (); -x[1][1] =0, x[1][2] = (D-SQR (b)) >>2, x[2][1] =1, x[2][2] =b; the     } -      WuyiInline ll*operator[] (inti) { the         returnX[i]; -     } Wu       -Inline matoperator* (ConstMat &p)Const { About         StaticMat Res; $         Static intI, J, K; -          for(Res.clear (), i =1; I <=2; ++i) -              for(j =1; J <=2; ++j) -                  for(k =1; K <=2; ++k) ARES[I][J] = (Res[i][j] + mul (x[i][k], p.x[k][j]))%MoD; +         returnRes; the     } -Inline mat&operator*= (ConstMat &p) { $         return* This= * This*p; the     } the } A; the   theInline Mat Pow (ConstMat &p, ll y) { -     StaticMat X, res; inRes.one (), x =p; the      while(y) { the         if(Y &1) Res *=x; Aboutx *= x, y >>=1; the     } the     returnRes; the } +   - intMain () { theCIN >> B >> D >>N;Bayi A.pre (); theA =Pow (A, n); thecout << ((a[1][1] <<1)% mod + mul (b, a[2][1])-(d! = Sqr (b) &&! (N &1))% mod + MoD)% mod <<Endl; -     return 0; -}

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BZOJ4002 [JLOI2015] meaningful string