计算两个整数的最大公约数算法

1. [PHP]代码

<?php
//计时，返回秒
function  microtime_float ()
{
    list( $usec ,  $sec ) =  explode ( " " ,  microtime ());
    return ((float) $usec  + (float) $sec );
}

//////////////////////////////////////////
//欧几里得算法
function ojld($m, $n) {
    if($m ==0 && $n == 0) {
        return false;
    }
    if($n == 0) {
        return $m;
    }
    while($n != 0){
        $r = $m % $n;
        $m = $n;
        $n = $r;
    }
    return $m;
}

//////////////////////////////////////////
//基于最大公约数的定义
function baseDefine($m, $n) {
    if($m ==0 && $n == 0) {
        return false;
    }
    $min = min($m, $n);
    while($min >= 1) {
        if($m % $min == 0){
            if($n % $min ==0) {
                return $min;
            }
        }
        $min -= 1;
    }
    return $min;
}

////////////////////////////////////////////
//中学数学里面的计算方法
function baseSchool($m, $n) {
    $mp = getList($m); //小于$m的全部质数
    $np = getList($n); //小于$n的全部质数
    $mz = array();  //保存$m的质因数
    $nz = array();  //保存$n的质因数
    $mt = $m;
    $nt = $n;

    //m所有质因数
    //遍历m的全部质数，当能够被m整除时，继续下一次整除，知道不能被整除再取下一个能够被m整除
    //的质数，一直到所有出现的质数的乘积等于m时停止
    foreach($mp as $v) {
        while($mt % $v == 0) {
            $mz[] = $v;
            $mt = $mt / $v;
        }
        $c = 1;
        foreach($mz as $v) {
            $c *= $v;
            if($c == $m){
                break 2;
            }
        }
    }

    //n所有质因数
    foreach($np as $v) {
        while($nt % $v == 0) {
            $nz[] = $v;
            $nt = $nt / $v;
        }
        $c = 1;
        foreach($nz as $v) {
            $c *= $v;
            if($c == $n){
                break 2;
            }
        }
    }

    //公因数
    $jj = array_intersect($mz, $nz); //取交集
    $gys = array();

    //取出在俩数中出现次数最少的因数，去除多余的。
    $c = 1; //记录数字出现的次数
    $p = 0; //记录上一次出现的数字
    sort($jj);
    foreach($jj as $key => $v) {
        if($v == $p) {
            $c++;
        }
        elseif($p != 0) {
            $c = 1;
        }
        $p = $v;
        $mk = array_keys($mz, $v);
        $nk = array_keys($nz, $v);
        $k = ( count($mk) > count($nk) ) ? count($nk) : count($mk);
        if($c > $k) {
            unset($jj[$key]);
        }
    }

    $count = 1;
    foreach($jj as $value) {
        $count *= $value;
    }
    return $count;
}

//求给定大于等于2的整数的连续质数序列
//埃拉托色尼筛选法
function getList($num) {
    $a = array();
    $a = array();
    for($i = 2; $i <= $num; $i++) {
        $a[$i] = $i;
    }
    for( $i = 2; $i <= floor( sqrt($num) ); $i++ ) {
        if($a[$i] != 0) {
            $j = $i * $i;
            while($j <= $num) {
                $a[$j] = 0;
                $j = $j + $i;
            }
        }
    }

    $p = 0;
    for($i = 2; $i <= $num; $i++) {
        if($a[$i] != 0) {
            $L[$p] = $a[$i];
            $p++;
        }
    }
    return $L;
}

/////////////////////////////////////
//test
$time_start  =  microtime_float ();
//echo ojld(60, 24);       //0.0000450611 seconds
//echo baseDefine(60, 24); //0.0000557899 seconds
echo baseSchool(60, 24);   //0.0003471375 seconds
$time_end  =  microtime_float ();
$time  =  $time_end  -  $time_start ;
echo '<br>' . sprintf('%1.10f', $time) . 'seconds';