ZOJ 3785 What day is that day? （找规律）

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本文介绍了一种通过数学计算预测从当前星期六开始，经过一定天数后是星期几的方法。利用预处理好的循环表及特定公式，可以快速得出答案。适用于算法竞赛中的日期计算问题。

1、http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3785

2、题目：

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

2
1
2

Sample Output

Sunday
Thursday

Hint

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

3、思路：

打表i的i次方%7后的值，就可以发现42一循环

然后用公式计算出结果

int ans=(n/42%7*(s[42]%7)%7+s[n%42]%7)%7;

最后输出

str[ans]

即可

4、AC代码：

#include<stdio.h>
int s[45];
char str[7][10]={"Saturday","Sunday","Monday","Tuesday","Wednesday","Thursday","Friday"};
int main()
{
    s[0]=0;
    for(int i=1;i<=44;i++)
    {
        int flag=i%7;
        int ans=1;
        for(int j=1;j<=i;j++)
            ans=(ans*flag)%7;
        s[i]=ans;
    }
    for(int i=1;i<=44;i++)
        {s[i]+=s[i-1];}
    int t;
    while(scanf("%d",&t)!=EOF)
    while(t--)
    {
        int n;
        scanf("%d",&n);
        int ans=(n/42%7*(s[42]%7)%7+s[n%42]%7)%7;
         printf("%s\n",str[ans]);
    }
}