PHP排列组合算法

<?php

// 阶乘
function factorial($n) {
	return array_product(range(1, $n));
}

// 排列数
function A($n, $m) {
	return factorial($n)/factorial($n-$m);
}

// 组合数
function C($n, $m) {
	return A($n, $m)/factorial($m);
}

// 排列
function arrangement($a, $m) {
	$r = array();

	$n = count($a);
	if ($m <= 0 || $m > $n) {
		return $r;
	}

	for ($i=0; $i<$n; $i++) {
		$b = $a;
		$t = array_splice($b, $i, 1);
		if ($m == 1) {
			$r[] = $t;
		} else {
			$c = arrangement($b, $m-1);
			foreach ($c as $v) {
				$r[] = array_merge($t, $v);
			}
		}
	}

	return $r;
}

// 组合
function combination($a, $m) {
	$r = array();

	$n = count($a);
	if ($m <= 0 || $m > $n) {
		return $r;
	}

	for ($i=0; $i<$n; $i++) {
		$t = array($a[$i]);
		if ($m == 1) {
			$r[] = $t;
		} else {
			$b = array_slice($a, $i+1);
			$c = combination($b, $m-1);
			foreach ($c as $v) {
				$r[] = array_merge($t, $v);
			}
		}
	}

	return $r;
}


// ====== 测试 ======
$a = array("A", "B", "C", "D");

$r = arrangement($a, 2);
var_dump($r);

$r = A(4, 2);
echo $r."\n";

$r = combination($a, 2);
var_dump($r);

$r = C(4, 2);
echo $r."\n";