zoj3785 What day is that day?

It's Saturday today, what day is it after 11 + 22 + 33 + ... + NN 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 + ... + NN 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。

 

 1 /*
 2  * Author:  Joshua
 3  * Created Time:  2014/5/17 13:18:55
 4  * File Name: j.cpp
 5  */
 6 #include<cstdio>
 7 #include<iostream>
 8 #include<cstring>
 9 #include<cstdlib>
10 #include<cmath>
11 #include<algorithm>
12 #include<string>
13 #include<map>
14 #include<set>
15 #include<vector>
16 #include<queue>
17 #include<stack>
18 #include<ctime>
19 #include<utility>
20 #define M0(x) memset(x, 0, sizeof(x))
21 #define MP make_pair
22 #define Fi first
23 #define Se second
24 #define rep(i, a, b) for (int i = (a); i <= (b); ++i)
25 #define red(i, a, b) for (int i = (a); i >= (b); --i)
26 #define PB push_back
27 #define Inf 0x3fffffff
28 #define eps 1e-8
29 typedef long long LL;
30 using namespace std;
31 
32 string ans[7]={"Saturday","Sunday","Monday","Tuesday","Wednesday","Thursday","Friday"};
33 
34 void solve()
35 {
36     int n,m,t=0,temp;
37     scanf("%d",&n);
38     m=n/42;
39     t=(t+m*6)%7;
40     for (int i=1;i<=n%42;i++)
41     {
42       temp=1;
43       for (int j=1;j<=i;j++)
44         temp=(temp*i)%7;
45         t=(t+temp)%7;
46     }
47     cout<<ans[t]<<endl;
48 }
49 int main()
50 {
51     int tt;
52     scanf("%d",&tt);
53     while (tt)
54     {
55         tt--;
56         solve();
57     }
58     return 0;
59 }

 

许久没写了，代码太丑，大家凑合着看。。。

 

posted @ 2014-05-18 14:12  一个大叔  阅读(416)  评论(0)  编辑  收藏  举报