POJ 1006-Biorhythms Biorhythms Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 114815 Accepted: 35991 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 East Central North America 1999
这一题考的是中学数学，稍微分析一下：假设最终结果为rs，则距离第一天rs+d=M，也就是说在第M天，三种周期同时达到高潮，又因为三种周期某次高潮的时间为第p、e、i天，周期分别为23、28、33，所以可得M-p、M-e、M-i分别为23、28、33的倍数。又因为题干中有如下两句话：
If a triple peak occurs on the given date, you should give the number of days to the next occurrence of a triple peak. and you may assume that a triple peak will occur within 21252 days of the given date.所以M的取值范围为[d+1,d+21252]，最后就是用穷举法来一个一个试了。具体代码如下： [cpp] #include<iostream> #include<string> using namespace std; int main() { int p,e,i,d; int case_num=1; while(cin>>p>>e>>i>>d&&p!=-1&&e!=-1&&i!=-1&&d!=-1) { for(int rs=d+1;rs<=21252+d;rs++) { if(((rs-p)%23==0)&&((rs-e)%28==0)&&((rs-i)%33==0)) { cout<<"Case "<<case_num<<": the next triple peak occurs in "<<rs-d<<" days."<<endl; break; } } case_num++; } return 0; } [/cpp] 提交结果AC，用时797MS，内存216K，这里还有几种优化的方法，可以参考。]]>