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poj 1006:Biorhythms(水题,经典题,中国剩余定理)

Biorhythms
Time Limit: 1000MS   Memory Limit: 10000K
Total Submissions: 110991   Accepted: 34541

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.

Source

  
  水题,中国剩余定理,经典题
  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)。
  这样直接套用中国剩余定理的解法即可。
  详细的过程就不写了,可以猛戳右方链接,说的很详细:POJ1006-Biorhythms
  对中国剩余定理还不是很懂的可以见百度百科的介绍,写的不错:中国剩余定理 - 百度百科
  代码
 1 #include <iostream>
 2 
 3 using namespace std;
 4 int main()
 5 {
 6     int p,e,i,d,Case=1;
 7     while(cin>>p>>e>>i>>d){
 8         if(p==-1 && e==-1 && i==-1 && d==-1) break;
 9         int da = (5544*p+14421*e+1288*i-d+21252)%21252;
10         if(da==0)
11             cout<<"Case "<<Case++<<": the next triple peak occurs in 21252 days."<<endl;
12         else
13             cout<<"Case "<<Case++<<": the next triple peak occurs in "
14             <<da<<" days."<<endl;
15     }
16     return 0;
17 }

 

Freecode : www.cnblogs.com/yym2013

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