poj 1006 Biorhythms

daBiorhythms

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 160650		Accepted: 52401

Description

Some people believe that there are three cycles in a person's life that start the day he or she is born. These three cycles are the physical, emotional, and intellectual 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 a cycle, 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 cycles generally occur at different times. We would like to determine when a triple peak occurs (the peaks of all three cycles occur in the same day) for any person. For each cycle, you will be given the number of days from the beginning of 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 the beginning of the current year. You task is to determine the number of days from the given date to the next triple peak. The given date is not counted. For example, if the given date is 10 and the next triple peak occurs on day 12, the answer is 2, not 3. If a triple peak occurs on the given date, you should give the number of days to the next occurrence of a triple peak.

Input

You will be given a number of cases. The input for each case consists of one line of four integers p, e, i, and d. The values p, e, and i are the number of days from the beginning of the current year at which the physical, emotional, and intellectual cycles peak, respectively. The value d is the given date and may be 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 given date. The end of input is indicated by a line in which p = e = i = d = -1.

Output

For each test case, print the case number followed by a message indicating the number of days 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.

生物节律

描述

有些人相信一个人的生命有三个周期，从他或她出生的那一天开始。这三个周期分别是身体周期、情绪周期和智力周期，它们的周期分别为23天、28天和33天。在一个周期的每个周期中都有一个峰。在一个周期的顶峰，一个人在相应的领域(身体的、情感的或精神的)表现最好。例如，如果是精神曲线，思维过程会更敏锐，注意力也会更容易集中。

由于三个周期有不同的周期，三个周期的峰值一般出现在不同的时间。我们想要确定何时出现三重峰(所有三个周期的峰发生在同一天)。对于每个周期，你会得到从年初开始的天数，其中一个峰值(不一定是第一个)出现。你还会得到一个日期，表示从今年开始的天数。您的任务是确定从给定日期到下一个三峰的天数。给定的日期不计算在内。例如，如果给定日期是10，而下一个三重峰出现在第12天，那么答案是2，而不是3。如果一个三重峰出现在给定的日期，你应该给出下一次三重峰出现的天数。

输入

你会遇到很多情况。每种情况的输入由一行4个整数p、e、i和d组成。p、e和i的值分别是从今年年初开始物理、情感和智力周期达到峰值的天数。值d是给定的日期，可以小于p、e或i中的任何一个。所有的值都是非负的，最多365，你可以假设一个三重峰值将在给定日期的21252天内出现。输入的结束由一行表示，其中p = e = i = d = -1。

输出

对于每个测试用例，以如下形式打印用例号，后面跟着指示到下一个三峰的天数的消息:

案例1:下一个三重高峰发生在1234天。

即使答案是1，也要用复数形式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.


题意：
　　人自出生起就有体力，情感和智力三个生理周期，分别为23，28和33天。
一个周期内有一天为峰值，在这一天，人在对应的方面（体力，情感或智力）表现
最好。通常这三个周期的峰值不会是同一天。现在给出三个日期，分别对应于体力
，情感，智力出现峰值的日期。然后再给出一个起始日期，要求从这一天开始，算
出最少再过多少天后三个峰值同时出现。
思路：
　　这道题需要用到中国剩余定理，中国剩余定理，也称孙子定理。这里有一个经
典问题：
《孙子算经》中的题目：有物不知其数，三个一数余二，五个一数余三，七个一数又余二，问该物总数几何？
　　意思就是有一个数除以3余2，除以5余3，除以7余2，问这个数是多少。
　　而孙子定理（中国剩余定理）就是求解这个问题的方法。
　　再看这道题，你要求多少天之后，出现三重峰，即要求的天数da要求加上开始
的天数d除以三个生理周期23，28，33都是整除。我们将da+d看成一个数n，即
n%k1=0，n%k2=0，n%k3=0。那么我们只要把n求出来，就能求出da（d已知）。

代码：
#include
int main()
{
    int p,e,i,d,Case=1;
    while(scanf("%d %d %d %d",&p,&e,&i,&d)!=EOF)
    {
        if(p==-1 && e==-1 && i==-1 && d==-1)
            break;
        int da = (5544*p+14421*e+1288*i-d+21252)%21252;
        if(da==0)
            printf("Case %d: the next triple peak occurs in 21252 days.\n",Case++);
        else
            printf("Case %d: the next triple peak occurs in %d days.\n",Case++,da);
    }
    return 0;
}