PHP排列组合算法
排列：从M个数字中选择N个数字，数字可以重复
组合：从M个数字中选择N个数字，数字不能重复
<?php
// 阶乘
function factorial($n)
{
return array_product(range(1, $n));
}
// 计算排列个数
function A($n, $m)
{
return factorial($n)/factorial($n-$m);
}
// 计算组合个数
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 ======
$arr = array(1,2,3,4,5);//可用数字
$arr_len=count($arr);
$maxlength=3; //选择几位
$r = A($arr_len, $maxlength);
echo "排列 P({$arr_len}, {$maxlength})={$r}<br>";
$r = arrangement($arr, $maxlength);
foreach($r as $v)
{
echo join('',$v).' ';
}
echo '<hr>';
$r = C($arr_len, $maxlength);
echo "组合 C({$arr_len}, {$maxlength})={$r}<br>";
$r = combination($arr, $maxlength);
foreach($r as $v)
{
echo join('',$v).' ';
}
排列 P(5, 3)=60
123 124 125 132 134 135 142 143 145 152 153 154 213 214 215 231 234 235 241 243 245 251 253 254 312 314 315 321 324 325 341 342 345 351 352 354 412 413 415 421 423 425 431 432 435 451 452 453 512 513 514 521 523 524 531 532 534 541 542 543
组合 C(5, 3)=10
123 124 125 134 135 145 234 235 245 345
原文转自：https://blog.csdn.net/song5198038_1/article/details/50188739
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