HDOJ 4549 M Fibonacci series ferma small theorem + rapid matrix power, hdoj4549

HDOJ 4549 M Fibonacci series ferma small theorem + rapid matrix power, hdoj4549

MF (I) = a ^ fib (I-1) * B ^ fib (I) (I> = 3)

Mod 1000000007 is a prime number. According to Fermat's small Theorem a ^ phi (p) = 1 (mod p) Here p is a prime number and a is smaller than p so a ^ (p-1) = 1 (mod p)

Therefore, a ^ k % p = a ^ (k % P-1) % p can be reduced for a large index.

Use the Matrix to quickly calculate the fib number.

M Fibonacci Series Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 65535/32768 K (Java/Others)
Total Submission (s): 1672 Accepted Submission (s): 482


Problem DescriptionM Fibonacci Series F [n] is an integer series. Its definition is as follows:

F [0] =
F [1] = B
F [n] = F [n-1] * F [N-2] (n> 1)

Can you find the value of F [n] For a, B, n?
The Input contains multiple groups of test data;
Each group of data occupies one row and contains three integers a, B, n (0 <= a, B, n <= 10 ^ 9)
Output outputs an integer F [n] for each group of test data. Since F [n] may be very large, you only need to Output the value after mod of F [n] To 1000000007, output a row of data in each group.
Sample Input

0 1 06 10 2

 
Sample Output

060

 
Source2013 Jinshan xishanju creative game program challenge-Preliminary Round (2)

/*************************************** * ******** Author: CKbossCreated Time:, Thursday, March 12, 2015 File Name: HDOJ4549.cpp *************************************** * ********/# include <iostream> # include <cstdio> # include <cstring> # include <algorithm> # include <string> # include <cmath> # include <cstdlib> # include <vector> # include <queue> # include <set> # include <map> using namespace std; typedef long int LL; const LL mod = limit 7ll; const LL md = limit 6ll; // getfibLL a, B, n; struct Matrix {Matrix (LL a = 0, LL B = 0, LL c = 0, LL d = 0) {m [0] [0] = a; m [0] [1] = B; m [1] [0] = c; m [1] [1] = d;} LL m [2] [2] ;}; Matrix MUI (Matrix &, matrix & B) {Matrix ret; ret. m [0] [0] = (. m [0] [0] * B. m [0] [0]) % md + (. m [0] [1] * B. m [1] [0]) % md; ret. m [0] [1] = (. m [0] [0] * B. m [0] [1]) % md + (. m [0] [1] * B. m [1] [1]) % md; ret. m [1] [0] = (. m [1] [0] * B. m [0] [0]) % md + (. m [1] [1] * B. m [1] [0]) % md; ret. m [1] [1] = (. m [1] [0] * B. m [0] [1]) % md + (. m [1] [1] * B. m [1] [1]) % md; return ret;} Matrix QUICKPOW (LL m) {Matrix E (,); Matrix, 1, 0); while (m) {if (m & 1LL) E = MUI (E, A); A = MUI (A, A); m/= 2LL ;} return E;} void showMat (Matrix M) {cout <endl; for (int I = 0; I <2; I ++) {for (int j = 0; j <2; j ++) cout <M. m [I] [j] <","; cout <endl ;}cout <endl ;}// get p_th fib numberLL getfib (LL p) {p --; Matrix M1 = QUICKPOW (p); return M1.m [0] [0];} LL QUICKPOW2 (LL a, LL x) {LL e = 1LL; while (x) {if (x & 1LL) e = (e * a) % mod; a = (a * a) % mod; x/= 2LL ;} return e;} LL solve () {if (n = 0) return a; else if (n = 1) return B; else if (n = 2) return (a * B) % mod; // fib coefficient of a-> fib (n-1) LL xa = getfib (n-1); LL partA = QUICKPOW2 (a, xa ); /// fib coefficient of B-> fib (I) LL xb = getfib (n); LL partB = QUICKPOW2 (B, xb); return (partA * partB) % mod;} int main () {// freopen ("in.txt", "r", stdin); // freopen ("out.txt", "w", stdout ); while (cin> a> B> n) cout <solve () <endl; return 0 ;}