zoj3785 What day is that day?

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What day is that day?

Time Limit: 2 Seconds Memory Limit: 65536 KB

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

Sample Output

SundayThursday

Hint

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

Author: ZHOU, Yuchen

Source: The 11th Zhejiang Provincial Collegiate Programming Contest

解析：循环节。

预备知识：(a*b) % x=( (a%x) * (b%x) ) %x。

那么根据上方的公式就可以将1+2^2+....+n^n化简：

1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 + 0

1 + 2^2*2^7 + 3^3*3^7 + 4^4*4^7 + 5^5*5^7 + 6^6*6^7 + 0

。。。。。。

以 2 为例，（2^7）%7=2，那么上述第二列向下的数对 7 取模后，依次就为：4 1 2 4 1 2 。。。

出现循环节：4 1 2

我们可以发现他们的和恰好就为 7 ，那么就得到上述第二列向下依次求和，再对 7 取模后为： 4 5 0 4 5 0 。。。。

出现循环节：4 5 0

对其余各列依次查找循环节后，就可以再将上式化简为：

1 + 4 + 6 + 4 + 3 + 1 + 0

2 + 5 + 3 + 6 + 4 + 0 + 0

3 + 0 + 1 + 0 + 2

4 2 6

5 5 5

6 0 0

好了，基本思路就这样，代码见下方：

#include<cstdio>using namespace std;int a[7][10]={0,0,0,0,0,0,0,0,0,0,              0,1,2,3,4,5,6,0,0,7,              0,4,5,0,0,0,0,0,0,3,              0,6,3,1,2,5,0,0,0,6,              0,4,6,0,0,0,0,0,0,3,              0,3,4,2,6,5,0,0,0,6,       0,1,0,0,0,0,0,0,0,2};char s[10][10]={"Saturday",                "Sunday",                "Monday",                "Tuesday",                "Wednesday",                "Thursday",                "Friday"};void work(){  int n,i,j,k,ans=0;  scanf("%d",&n);  k=n/7,j=n%7;  for(i=1;i<=j;i++)ans+=a[i][(k+1)%a[i][9]];  if(k>0)for(i=j+1;i<=6;i++)ans+=a[i][k%a[i][9]];  printf("%s\n",s[ans%7]);}int main(){  freopen("1.in","r",stdin);  int t,i,j,k;  while(scanf("%d",&t)!=EOF)    for(i=1;i<=t;i++)work();  return 0;}

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