2017 Multi-University Training Contest - Team 3 1008 RXD and math

本文介绍了一个复杂的数论计算问题,探讨了如何通过快速幂运算求解特定形式的数论表达式,并给出了一段实现该算法的C++代码示例。

RXD and math

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 261    Accepted Submission(s): 134


Problem Description
RXD is a good mathematician.
One day he wants to calculate:
i=1nkμ2(i)×nki

output the answer module 109+7.
1n,k1018
μ(n)=1(n=1)

μ(n)=(1)k(n=p1p2pk)

μ(n)=0(otherwise)

p1,p2,p3pk are different prime numbers
 

Input
There are several test cases, please keep reading until EOF.
There are exact 10000 cases.
For each test case, there are 2 numbers n,k.
 

Output
For each test case, output "Case #x: y", which means the test case number and the answer.
 

Sample Input
10 10
 

Sample Output
Case #1: 999999937
 
直接暴力打表,发现是n^k,快速幂直接水过
///AC代码
/* ***********************************************
┆  ┏┓   ┏┓ ┆
┆┏┛┻━━━┛┻┓ ┆
┆┃       ┃ ┆
┆┃   ━   ┃ ┆
┆┃ ┳┛ ┗┳ ┃ ┆
┆┃       ┃ ┆
┆┃   ┻   ┃ ┆
┆┗━┓ 马 ┏━┛ ┆
┆  ┃ 勒 ┃  ┆      
┆  ┃ 戈 ┗━━━┓ ┆
┆  ┃ 壁     ┣┓┆
┆  ┃ 的草泥马  ┏┛┆
┆  ┗┓┓┏━┳┓┏┛ ┆
┆   ┃┫┫ ┃┫┫ ┆
┆   ┗┻┛ ┗┻┛ ┆
************************************************ */
#include <iostream>
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <bitset>
#include <string>
#include <vector>
#include <iomanip>
#include <cstring>
#include <algorithm>
#include <functional>
#define PI acos(-1)
#define eps 1e-8
#define inf 0x3f3f3f3f
#define debug(x) cout<<"---"<<x<<"---"<<endl
typedef long long ll;
using namespace std;
const int mod = 1e9 + 7;

long long pow(long long a, long long n)
{
    long long text = 1;
    while (n)
    {
        if (n & 1)
        {
            text = (text % mod) * (a % mod) % mod;
        }
        a = (a % mod) * (a % mod) % mod;
        n >>= 1;
    }
    return text;
}
int main()
{
    long long n, k;
    int i = 1;
    while (~scanf("%lld%lld", &n, &k))
    {
        long long text = pow(n, k);
        printf("Case #%d: %lld\n", i++, text);
    }
    return 0;
}

/************************************************
┆  ┏┓   ┏┓ ┆
┆┏┛┻━━━┛┻┓ ┆
┆┃       ┃ ┆
┆┃   ━   ┃ ┆
┆┃ ┳┛ ┗┳ ┃ ┆
┆┃       ┃ ┆
┆┃   ┻   ┃ ┆
┆┗━┓    ┏━┛ ┆
┆  ┃    ┃  ┆      
┆  ┃    ┗━━━┓ ┆
┆  ┃  AC代马   ┣┓┆
┆  ┃           ┏┛┆
┆  ┗┓┓┏━┳┓┏┛ ┆
┆   ┃┫┫ ┃┫┫ ┆
┆   ┗┻┛ ┗┻┛ ┆
************************************************ */


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