PHP method sample code for calculating permutations and combinations

Permutation and combination are the most basic concepts of combinatorics. The so-called arrangement means to sort a specified number of elements from a given number of elements. Combination refers to taking out only a specified number of elements from a given number of elements, regardless of sorting. The central problem of permutations and combinations is to study the total number of possible situations for permutations and combinations of given requirements. Permutation and combination are closely related to classical probability theory.

The mathematical problem to be solved in this article using PHP is to calculate the combination of C(a,1) * C(b, 1) * ... * C(n, 1), where C(n, 1 ) represents randomly selecting an element from n elements

A few days ago, due to business needs, I wrote a piece of code to calculate permutations and combinations. Today I sorted it out for future use

The code is as follows:

<?php
/**
 * 要解决的数学问题    ：算出C(a,1) * C(b, 1) * ... * C(n, 1)的组合情况，其中C(n, 1)代表从n个元素里任意取一个元素
 *
 * 要解决的实际问题样例：某年级有m个班级，每个班的人数不同，现在要从每个班里抽选一个人组成一个小组，
 *                       由该小组来代表该年级参加学校的某次活动，请给出所有可能的组合
 */
/* ################################### 开始计算 ################################### */
/**
 * 需要进行排列组合的
数组
 *
 * 数组说明：该数组是一个
二维数组
，第一维
索引
代表班级编号，第二维索引代表学生编号
 */
$CombinList = array(1 => array("Student10", "Student11"),
                    2 => array("Student20", "Student21", "Student22"),
                    3 => array("Student30"),
                    4 => array("Student40", "Student41", "Student42", "Student43"));
/* 计算C(a,1) * C(b, 1) * ... * C(n, 1)的值 */
$CombineCount = 1;
foreach
($CombinList as $Key => $Value)
{
    $CombineCount *= count($Value);
}
$RepeatTime = $CombineCount;
foreach($CombinList as $ClassNo => $StudentList)
{
    // $StudentList中的元素在拆分成组合后纵向出现的最大重复次数
    $RepeatTime = $RepeatTime / count($StudentList);
    $Start
Position
 = 1;
    // 开始对每个班级的学生进行
循环
    foreach($StudentList as $Student)
    {
        $TempStartPosition = $StartPosition;
        $SpaceCount = $CombineCount / count($StudentList) / $RepeatTime;
        for($J = 1; $J <= $SpaceCount; $J ++)
        {
            for($I = 0; $I < $RepeatTime; $I ++)
            {
               $Result[$TempStartPosition + $I][$ClassNo] = $Student;
            }
            $TempStartPosition += $RepeatTime * count($StudentList);
        }
        $StartPosition += $RepeatTime;
    }
}
/* 打印结果 */
echo "<pre class="brush:php;toolbar:false">";
print_r($Result);
?>

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