zoj3785 What day is that day?

It's Saturday today, what day is it after 1¹ + 2² + 3³ + ... + N^N days?

Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

There is only one line containing one integer N (1 <= N <= 1000000000).

Output

For each test case, output one string indicating the day of week.

Sample Input

2
1
2

Sample Output

Sunday
Thursday

Hint

A week consists of Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.

 

题目大意：今天是星期六，输入n，问1¹ + 2² + 3³ + ... + N^N 天后是星期几？

思路：因为n是10亿，解法必定是数学方法或者找规律。注意到7是素数，所以可以使用费马小定理进行简化。即当p是素数是，a^(p-1) mod p=1，简化后发现每42个数就会出现一个循环，得数mod7=6。所以求解过程就是先求出n由几个42组成，对于42取余的剩下的部分就可以直接模拟做了。

 

/*
 * Author:  Joshua
 * Created Time:  2014/5/17 13:18:55
 * File Name: j.cpp
 */
#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<string>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<stack>
#include<ctime>
#include<utility>
#define M0(x) memset(x, 0, sizeof(x))
#define MP make_pair
#define Fi first
#define Se second
#define rep(i, a, b) for (int i = (a); i <= (b); ++i)
#define red(i, a, b) for (int i = (a); i >= (b); --i)
#define PB push_back
#define Inf 0x3fffffff
#define eps 1e-8
typedef long long LL;
using namespace std;

string ans[7]={"Saturday","Sunday","Monday","Tuesday","Wednesday","Thursday","Friday"};

void solve()
{
    int n,m,t=0,temp;
    scanf("%d",&n);
    m=n/42;
    t=(t+m*6)%7;
    for (int i=1;i<=n%42;i++)
    {
      temp=1;
      for (int j=1;j<=i;j++)
        temp=(temp*i)%7;
        t=(t+temp)%7;
    }
    cout<<ans[t]<<endl;
}
int main()
{
    int tt;
    scanf("%d",&tt);
    while (tt)
    {
        tt--;
        solve();
    }
    return 0;
}

 

许久没写了，代码太丑，大家凑合着看。。。