Colossal Fibonacci Numbers! UVA - 11582（快速幂）

Problem Description

The i’th Fibonacci number f(i) is recursively defined in the following way:

•$f(0)=0$and $f(1)=1$
•$f(i+2)=f(i+1)+f(i)$ for every $i\ge 0$
Your task is to compute some values of this sequence

Input

Input begins with an integer $t\le 10,000$, the number of test cases.

Each test case consists of three integers $a,b,n$ where $0\le a,b<2^{64}$ ($a$ and $b$ will not both be zero) and $1\le n\le 1000$.

Output

For each test case, output a single line containing the remainder of $ƒ(ab$) upon division by n.

Sample Input

3
1 1 2
2 3 1000
18446744073709551615 18446744073709551615 1000

Sample Output

1
21
250

题目大意：
　　　给出$a,b,n$,让你计算$f(a^b)\%n$,$f(n)=f(n-1)+f(n-2)$;因为是$\%n$所以余数最多$n\ast n$种，于是我们就可以用快速幂求出是在数列中是第几个数，然后代入$f[]$输出就可以了~
　　
代码如下：

#include<iostream>
#include<cstdio>
using namespace std;
#define ll unsigned long long
const int maxx=1100;
int f[maxx*maxx];
int pow(ll m,ll n,int k)
{
    int b=1;
    while(n>0)
    {
        if(n&1)//为奇数
        {
            b=(b*m)%k;
        }
        n=n>>1;
        m=(m*m)%k;
    }
    return b;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        ll a,b;
        int n,m;
        scanf("%llu%llu%d",&a,&b,&n);
        if(n==1||a==0)
            printf("0\n");
        else
        {
            f[0]=0;
            f[1]=1;
            m=n*n+10;
            int s;
            for(int i=2; i<=m; i++)
            {
                f[i]=(f[i-1]+f[i-2])%n;
                if(f[i]==f[1]&&f[i-1]==f[0])
                {
                    s=i-1;
                    break;
                }
            }
            int k=pow(a%s,b,s);
            printf("%d\n",f[k]);
        }
    }
    return 0;
}

实践是检验真理的唯一标准