UVa11582 - Colossal Fibonacci Numbers!

Problem F: Colossal Fibonacci Numbers!

The i'th Fibonacci number f (i) is recursively defined in the following way:f (0) = 0 and f (1) = 1f (i+2) = f (i+1) + f (i) for every i ≥ 0Your task is to compute some values of this sequence.Input begins with an integer t ≤ 10,000, the number of test cases. Each test case consists of three integersa,b,n where 0 ≤ a,b < 264 (a and b will not bothbe zero) and 1 ≤ n ≤ 1000.For each test case, output a single line containing the remainder of f (ab) upon division by n.

Sample input

3
1 1 2
2 3 1000
18446744073709551615 18446744073709551615 1000

Sample output

1
21
250

利用斐波那契循环的性质！

#include <iostream>#include <cstdio>#include <cstring>#include <vector>#include <string>#include <algorithm>#include <queue>using namespace std;unsigned long long m,n;int MOD;vector<int> fib[1001];void init(){for(int i = 2; i <= 1000; i++){int mod = i;int a = 0,b = 1,c = (a+b)%mod;fib[i].push_back(a);fib[i].push_back(b);fib[i].push_back(1%mod);while(!(b==0&&c==1)){a = b;b = c;c = (a+b)%mod;fib[i].push_back(c);}fib[i].pop_back();fib[i].pop_back();//cout<<fib[i].size()<<" "<<i<<endl;}}int main(){int ncase;cin >> ncase;init();while(ncase--){cin >> n >> m >> MOD;if(MOD == 1){cout<<0<<endl;continue;}int a = 0,b = 1,c = (a+b)%MOD;unsigned long long  mm = fib[MOD].size(),ans = 1;while(m){if(m&1)ans = ((n%mm)*(ans%mm))%mm;n = ((n%mm)*(n%mm))%mm;m >>= 1;}//cout<<<<endl;cout<<fib[MOD][ans]<<endl;}return 0;}

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