【解題】Clock Hands

ACM Volume V 579 - Clock Hands


The Problem

The medieval interest in mechanical contrivances is well illustrated by the development of the mechanical clock, the oldest of which is driven by weights and controlled by a verge, an oscillating arm engaging with a gear wheel. It dates back to 1386.

Clocks driven by springs had appeared by the mid-15th century, making it possible to con- struct more compact mechanisms and preparing the way for the portable clock.

English spring-driven pendulum clocks were first commonly kept on a small wall bracket and later on a shelf. Many bracket clocks contained a drawer to hold the winding key. The earliest bracket clocks, made for a period after 1660, were of architectural design, with pillars at the sides and a pediment on top.

In 17th- and 18th-century France, the table clock became an object of monumental design, the best examples of which are minor works of sculpture.

The longcase clocks (also called grandfather clocks) are tall pendulum clock enclosed in a wooden case that stands upon the floor and is typically from 6 to 7.5 feet (1.8 to 2.3 m) in height. Later, the name ``grandfather clock'' became popular after the popular song "My Grandfather's Clock," written in 1876 by Henry Clay Work.


One of the first atomic clocks was an ammonia-controlled clock. It was built in 1949 at the National Bureau of Standards, Washington, D.C.; in this clock the frequency did not vary by more than one part in 10⁸.

Nuclear clocks are built using two clocks. The aggregate of atoms that emit the gamma radiation of precise frequency may be called the emitter clock; the group of atoms that absorb this radiation is the absorber clock. One pair of these nuclear clocks can detect energy changes of one part in 10¹⁴ , being about 1,000 times more sensitive than the best atomic clock.

The cesium clock is the most accurate type of clock yet developed. This device makes use of transitions between the spin states of the cesium nucleus and produces a frequency which is so regular that it has been adopted for establishing the time standard.


The history of clocks is fascinating, but unrelated to this problem. In this problem, you are asked to find the angle between the minute hand and the hour hand on a regular analog clock. Assume that the second hand, if there were one, would be pointing straight up at the 12. Give all angles as the smallest positive angles. For example 9:00 is 90 degrees; not -90 or 270 degrees.


Input

The input is a list of times in the form H:M, each on their own line, with 1 ≦ H ≦ 12 and 00 ≦ M ≦ 59. The input is terminated with the time 0:00. Note that H may be represented with 1 or 2 digits (for 1-9 or 10-12, respectively); M is always represented with 2 digits (The input times are what you typically see on a digital clock).


Output

The output displays the smallest positive angle in degrees between the hands for each time. The answer should between 0 degrees and 180 degrees for all input times. Display each angle on a line by itself in the same order as the input. The output should be rounded to the nearest 1/1000, i.e., three places after the decimal point should be printed.


Sample Input

12:00
9:00
8:10
0:00


Sample Output

0.000
90.000
175.000


解題思考

　　這一題在判斷某時分針與時針角度的差。

　　首先是資料輸入方面，我嫌處理麻煩，就直接使用 scanf("%d:%d", &h, &m) 的方式抓取 hour 跟 minute 了。

　　接著在處理角度差的時候，我們需要將 hour 乘以 30、minute 乘以 6 來換算成角度。需要注意的是，當分針不是指向 00 的時候，還需要將時針加上些微的移動。

　　因為每個小時的角度差為 30 度，所以我們將 30 除以 60(每小時 60 分)，便可以得到：準點過後，每過一分鐘時針的移動為 0.5 度。整理一下，便可以得到角度差為 h * 30 + m * 0.5 - m * 6 = h * 30 - m * 5.5。

　　接著再將角度值做個調整，以符合題目要求的「非負數的最小角度」，就可以了。


參考解答(C++)

#include <iostream>
#include <iomanip>

using namespace std;

int main(void)
{
    // 設定顯示至小數點第三位
    cout << setiosflags(ios::fixed) << setprecision(3);

    while (1)
    {
        int h, m;
        scanf("%d:%d", &h, &m);

        if (!h && !m) { break; }

        // 分針每前進 1 度, 時針就前進 0.5 度
        double angle = (double)h * 30 - (double)m * 5.5;
        if (angle < 0)      { angle *= -1; }
        if (angle > 180)    { angle = 360 - angle; }

        cout << angle << endl;
    }

#ifndef ONLINE_JUDGE
    system("pause");
#endif
}