1006 -- Biorhythms

Biorhythms

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 138926		Accepted: 44590

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.

好吧！题名就把我唬住了，没见过的单词啊。 没事，google一下。 

　　哈！ 还是不懂啥意思。 算了，直接看题目。

  题目说 ： 有些人认为啊，从人一出生开始，有三个周期就开始运转了，啥周期呢？身体、情感和智力周期。 它们的周期时长分别是23天,28天,33天。 然后呢，它们都会有一个顶峰嘛，在这个顶峰的时候，我们相对应的表现就会很牛逼。比如，如果是心理曲线,思考会更快，而且更容易集中。
  又因为呢，这三个周期的顶峰不一样，通常都会在不同的时间出现。 然后呢，我们现在想算一下，哪一天是三个顶峰同时出现（三buff齐加，上天了）。现在给出三个日期，分别对应于体力，情感，智力离今年第一天出现峰值的日期。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。

  解题： 我们假设这三个周期都是正弦波，画个图出来看看。
　
　

图画得非常丑啊！ 但是没关系，我们来看，要三buff齐开，就是要刚好三个顶峰凑在一起了。 假设我们已经知道了，三个顶峰将会在S天后出现，那么，S = N1 + T1*K1 = N2 + T2*K2=  N3 + T3*K3。 N是指单一顶峰出现的时间，T代表周期，K是正整数。

那我们现在有一种简单的做法，穷举！ 先试试。

import java.util.Scanner;

public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int T1 = 23;
int T2 = 28;
int T3 = 33;
int count = 0;
while(scanner.hasNext()){
count++;
int N1 = scanner.nextInt();
int N2 = scanner.nextInt();
int N3 = scanner.nextInt();
int C = scanner.nextInt();
if(N1 ==-1 && N2 ==-1 && N3 == -1 && C==-1){
return;
}
for(int i = 1 ; i <= 21252+C ;i++){
if((i-N1)%T1==0){

}else{
continue;
}

if((i-N2)%T2==0){

}else{
continue;
}
if((i-N3)%T3==0){

}else{
continue;
}
if(i-C<=0){
continue;
}

System.out.println("Case "+count+": the next triple peak occurs in "+(i-C)+" days.");
break;
}
}
}
}

　　OK！ 穷举的代码得出正确结果。 可是。。。。   超时了。 好~  不用这么拙劣的办法。我们先来看看，中国剩余定理！

　　看完之后我们再来解题， S = N1 + T1*K1 = N2 + T2*K2=  N3 + T3*K3

　　我们可以拆解成 ：

S%T1 = N1 ,

　　S%T2 = N2 ,

　　S%T3 = N3.

　　这样就可以用中国剩余定理了。