What day is that day? ZOJ - 3785 数学

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).

<h4< style="background-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; box-shadow: none; font-family: &quot;Merriweather&quot;,serif; font-size: 18px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" dd=""> Output

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

<h4< style="background-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; box-shadow: none; font-family: &quot;Merriweather&quot;,serif; font-size: 18px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" dd=""> Sample Input

2
1
2

<h4< style="background-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; box-shadow: none; font-family: &quot;Merriweather&quot;,serif; font-size: 18px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" dd=""> Sample Output

Sunday
Thursday

<h4< style="background-color: transparent; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; box-shadow: none; font-family: &quot;Merriweather&quot;,serif; font-size: 18px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" dd=""> Hint

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

题意就是快速求 1 ¹ + 2 ² + 3 ³ + ... + N ^N 对7取余的余数

思路见dalao coldfresh——https://blog.csdn.net/Coldfresh/article/details/80094497

import java.io.BufferedInputStream;
import java.util.Scanner;

public class Main {
	static int fun(int a,int b) {
		int ans = 1;
		while(b!=0) {
			if(b%2==1)ans=(ans*a)%7;
			a=(a*a)%7;
			b>>=1;
		}
		//System.out.println(ans);
		return (int)(ans%7);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedInputStream(System.in));
		int n;
		n = sc.nextInt();
		String[] week = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday","Saturday"};
		while(n--!=0) {
			int t = sc.nextInt();
			int lim;
			if(t>6)lim = 6;
			else lim = t;
			int ans=0;
			for(int i=1;i<=lim;i++) {
				int base = t/7;
				int items = (t-i+7)/7;//项数 t-i防止小于0 直接加7 符合对应大小关系
				if(i==1) {
					ans = (ans + 1*items)%7;
				}
				else {
					int q = fun(i,7);//q的大小
					int ny = fun(q+6,5);//逆元 防止变成负数
					int now = (((fun(i,i)*(fun(q,items)+6))%7)*ny)%7;// a1*(q^n-1)*ny  防止变成负数导致计算错误：fun-1->fun-1+7
					ans = (ans+now)%7;
				}
			}
			System.out.println(week[(int) ((ans+6)%7)]);
		}
	}
}