poj 1006 Biorhythms

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#中国剩余定理 #POJ

Biorhythms

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 97218		Accepted: 29897

Description

Somepeople believe that there are three cycles in a person's life that start theday he or she is born. These three cycles are the physical, emotional, andintellectual cycles, and they have periods of lengths 23, 28, and 33 days,respectively. There is one peak in each period of a cycle. At the peak of acycle, a person performs at his or her best in the corresponding field(physical, emotional or mental). For example, if it is the mental curve,thought processes will be sharper and concentration will be easier.
Since the three cycles have different periods, the peaks of the three cyclesgenerally occur at different times. We would like to determine when a triplepeak occurs (the peaks of all three cycles occur in the same day) for anyperson. For each cycle, you will be given the number of days from the beginningof the current year at which one of its peaks (not necessarily the first)occurs. You will also be given a date expressed as the number of days from thebeginning of the current year. You task is to determine the number of days fromthe given date to the next triple peak. The given date is not counted. Forexample, if the given date is 10 and the next triple peak occurs on day 12, theanswer is 2, not 3. If a triple peak occurs on the given date, you should givethe number of days to the next occurrence of a triple peak.

Input

You willbe given a number of cases. The input for each case consists of one line offour integers p, e, i, and d. The values p, e, and i are the number of daysfrom the beginning of the current year at which the physical, emotional, andintellectual cycles peak, respectively. The value d is the given date and maybe smaller than any of p, e, or i. All values are non-negative and at most 365,and you may assume that a triple peak will occur within 21252 days of the givendate. The end of input is indicated by a line in which p = e = i = d = -1.

Output

For eachtest case, print the case number followed by a message indicating the number ofdays to the next triple peak, in the form:

Case 1: the next triple peak occurs in 1234 days.

Use the plural form ``days'' even if the answer is 1.

Sample Input

0 0 0 0

0 0 0 100

5 20 34 325

4 5 6 7

283 102 23 320

203 301 203 40

-1 -1 -1 -1

Sample Output

Case 1: the next triple peak occurs in 21252 days.

Case 2: the next triple peak occurs in 21152 days.

Case 3: the next triple peak occurs in 19575 days.

Case 4: the next triple peak occurs in 16994 days.

Case 5: the next triple peak occurs in 8910 days.

Case 6: the next triple peak occurs in 10789 days.

Source

East Central North America 1999

生理周期

Time Limit: 1000MS	Memory Limit: 10000K
Total Submissions: 103004	Accepted: 31796

Description

人生来就有三个生理周期，分别为体力、感情和智力周期，它们的周期长度为23天、28天和33天。每一个周期中有一天是高峰。在高峰这天，人会在相应的方面表现出色。例如，智力周期的高峰，人会思维敏捷，精力容易高度集中。因为三个周期的周长不同，所以通常三个周期的高峰不会落在同一天。对于每个人，我们想知道何时三个高峰落在同一天。对于每个周期，我们会给出从当前年份的第一天开始，到出现高峰的天数（不一定是第一次高峰出现的时间）。你的任务是给定一个从当年第一天开始数的天数，输出从给定时间开始（不包括给定时间）下一次三个高峰落在同一天的时间（距给定时间的天数）。例如：给定时间为10，下次出现三个高峰同天的时间是12，则输出2（注意这里不是3）。

Input

输入四个整数：p, e, i和d。 p, e, i分别表示体力、情感和智力高峰出现的时间（时间从当年的第一天开始计算）。d 是给定的时间，可能小于p, e, 或 i。所有给定时间是非负的并且小于365, 所求的时间小于等于21252。

当p = e = i= d = -1时，输入数据结束。

Output

从给定时间起，下一次三个高峰同天的时间（距离给定时间的天数）。

采用以下格式：
Case 1: the next triple peak occurs in 1234 days.

注意：即使结果是1天，也使用复数形式“days”。

Sample Input

0 0 0 0

0 0 0 100

5 20 34 325

4 5 6 7

283 102 23 320

203 301 203 40

-1 -1 -1 -1

Sample Output

Case 1: the next triple peak occurs in 21252 days.

Case 2: the next triple peak occurs in 21152 days.

Case 3: the next triple peak occurs in 19575 days.

Case 4: the next triple peak occurs in 16994 days.

Case 5: the next triple peak occurs in 8910 days.

Case 6: the next triple peak occurs in 10789 days.

Source

East Central North America 1999

Translator

北京大学程序设计实习2007, XieDi

中国剩余定理，根据算法导论，这里只要求出ci就能用一个算式来求出结果

所以先求ci是

使33×28×a被23除余1，用33×28×8=5544；
使23×33×b被28除余1，用23×33×19=14421；
使23×28×c被33除余1，用23×28×2=1288。

然后用算式：n=（5544×p+14421×e+1288×i-d）%21252

之后由于结果不能为负，所以要加上一个21252

n=（5544×p+14421×e+1288×i-d+21252）%21252

而后当结果为0的时候，应该默认为21252，于是此题代码很水。

#include <stdio.h>

int main(void)
{
	int p, e, i, d, k = 1;
	int s;
	while(scanf("%d%d%d%d", &p, &e, &i, &d) && (p > -1 && e > -1 && i > -1 && d > -1))
	{
	    s = (p*5544+e*14421+i*1288-d+21252) % 21252;
	    if (!s) s = 21252;
		printf("Case %d: the next triple peak occurs in %d days.\n", k++, s);
	}
}