Algorithm：老钟表匠和表差问题

今天碰到一个比较有趣的问题：
从前有一位老钟表匠，为一个教堂装一只大钟。他年老眼花，把长短针装配错了，短针走的速度反而是长针的12倍。
装配的时候是上午6点，他把短针指在“6”上，长针指在“12”上。老钟表匠装好就回家去了。
人们看这钟一会儿7点，过了不一会儿就8点了，都很奇怪，立刻去找老钟表匠。
等老钟表匠赶到，已经是下午7点多钟。他掏出怀表来一对，钟准确无误，疑心人们有意捉弄他，一生气就回去了。
这钟还是8点、9点地跑，人们再去找钟表匠。老钟表匠第二天早晨8点多赶来用表一对，仍旧准确无误。
请你想一想，老钟表匠第一次对表的时候是7点几分？第二次对表又是8点几分？
A. 35 42
B. 26 35
C. 38 44
D. 05 10

解决这个问题的代码：

<?
class clock{
    const TIME_SCALE = 60;
    const DAY_SCALE = 12;
    private $correct_time_hour;
    private $correct_time_min;
    private $clock_time_hour;
    private $clock_time_min;
    private $clock_time;
    private $am_or_pm;

    public function __construct(){
        $this->correct_time_hour = 6;
        $this->correct_time_min = 0;
        $this->clock_time_hour = 0;
        $this->clock_time_min = 30;
        $this->clock_time_display_hour = null;
        $this->clock_time_display_min = null;
        $this->am_or_pm = 1;
    }
    public function main(){
        do {
            $this->correct_time_min = $this->correct_time_min + 1;
            if ($this->correct_time_min >= 60){
                $this->correct_time_min = $this->correct_time_min - 60;
                $this->correct_time_hour++;
                if ($this->correct_time_hour >= 12){
                    $this->correct_time_hour = $this->correct_time_hour - 12;
                    $this->am_or_pm++;
                }
            }
            $this->clock_time_hour = $this->clock_time_hour + 1;
            if ($this->clock_time_hour >= 60){
                $this->clock_time_hour = $this->clock_time_hour - 60;
            }
            if ( $this->clock_time_hour % 12 === 0 ){
                $this->clock_time_min++;
                if ($this->clock_time_min >= 60){
                    $this->clock_time_min = $this->clock_time_min - 60;
                }
            }
            $clock_time = $this->getClockTime();
            if ($this->isFirstDayPmSeven()){
                printf("First day 7 PM time : %s:%s\n", $this->correct_time_hour, $this->correct_time_min);
            }
            if ($this->isSecondDayAmEight()){
                printf("Second day 8 AM time : %s:%s\n", $this->correct_time_hour, $this->correct_time_min);
                break;
            }
            if ($this->isTimeCorrect()){
                printf("Time correct when : %s:%s\n", $this->correct_time_hour, $this->correct_time_min);
            }
            if ($this->dayNo() > 2){
                echo 'error : has bug' . "\n";
                break;
            }
        } while (true);
        return true;
    }
    private function isFirstDayPmSeven(){
        if (($this->dayNo() === 1) && $this->isPM()
            && ($this->correct_time_hour === 7) && ($this->clock_time_display_hour === 7)
            && ($this->correct_time_min === $this->clock_time_display_min)){
            return true;
        }
        return false;
    }
    private function isSecondDayAmEight(){
        if (($this->dayNo() === 2) && $this->isAM()
            && ($this->correct_time_hour === 8) && ($this->clock_time_display_hour === 8)
            && ($this->correct_time_min === $this->clock_time_display_min)){
            return true;
        }
        return false;
    }
    private function isTimeCorrect(){
        if (($this->correct_time_hour === $this->clock_time_display_hour)
            && ($this->correct_time_min === $this->clock_time_display_min)){
            return true;
        }
        return false;
    }
    private function dayNo(){
        return intval(ceil($this->am_or_pm / 2));
    }
    private function isPM(){
        return (($this->am_or_pm % 2) === 0) ? true : false;
    }
    private function isAM(){
        return (($this->am_or_pm % 2) === 1) ? true : false;
    }
    private function getClockTime(){
        $this->clock_time_display_hour = intval(floor($this->clock_time_hour / 5));
        $this->clock_time_display_min = $this->clock_time_min;
    }
    private function outputTime($hour, $min){
        printf('%s:%s', $hour, $min);
    }
}//class

$objClock = new clock();
$objClock->main();

执行输出：
Time correct when : 6:32
Time correct when : 7:38
Time correct when : 8:43
Time correct when : 9:49
Time correct when : 10:54
Time correct when : 11:59
Time correct when : 0:0
Time correct when : 1:5
Time correct when : 2:10
Time correct when : 3:16
Time correct when : 4:21
Time correct when : 5:27
Time correct when : 6:32
First day 7 PM time : 7:38
Time correct when : 7:38
Time correct when : 8:43
Time correct when : 9:49
Time correct when : 10:54
Time correct when : 11:59
Time correct when : 0:0
Time correct when : 1:5
Time correct when : 2:10
Time correct when : 3:16
Time correct when : 4:21
Time correct when : 5:27
Time correct when : 6:32
Time correct when : 7:38
Second day 8 AM time : 8:43

红色字体部分是问题的答案，会发现答案和选项存在误差，选项中的答案是44，而输出的是43。
这是由于代码中对于 分钟采用的是向下取整的处理方式，如果按照四舍五入的方式，可以得到和选项一致的答案。

输出中还打印出了表的展示的时间和实际的时间一致的时间点，可以发现每过1小时，5分钟或6分钟（精度的原因，实际上是具有规律的相同值），
表的展示的时间和实际的时间一致就会发生一次。