续上之前第1章的问题，今天把这个问题扩展一下，情况稍微复杂点。
扩展在哪里呢？之前是，两个箱子如果分在一单，那么计算这一单的型号总数的时候，是直接把两箱各自的型号数相加就行了，而现在，如果两个箱子里面，有包含相同型号的，分到同一单的话，可以把型号合并，箱子间去重后的型号总数，才是这个单的型号总数。
这里有一个型号合并的概念，举个例子解释一下：
箱1有下面10个型号
[1] => (
[0] => 55766e89a05caba74e09e05f3cada80e
[1] => 77b5c09b6d5e1d3323ad0b7ff352aeaa
[2] => b0a3e7babe36a55cb2f13336577a96fd
[3] => 46e902f68228c599a3c09f11e8a11dce
[4] => 43f9e4663d50b618f6c658f1be53b113
[5] => d690a3f429eec0c41f11ad325d98e299
[6] => d9804f1ed77995d5689566795836e8cf
[7] => 288becbe90890e297c905ef8195e2897
[8] => 75777ef58fa286b124c51a17fa141aea
[9] => a473d5d14febc5e9f721257dcd664d5d
)
箱2有下面7个型号
[2] => (
[0] => 87415b41b663fbb5d78629d303bf53d0
[1] => 59d99b563381a33cfaa5c4ebaf8025a1
[2] => d690a3f429eec0c41f11ad325d98e299
[3] => 9a85df0bf0badae7fbfcca5d70165de4
[4] => 77b5c09b6d5e1d3323ad0b7ff352aeaa
[5] => 5ffe4ee06c146d9f419cc5b14181accb
[6] => 288becbe90890e297c905ef8195e2897
)
可以看到两个箱子里面，d690a3f429eec0c41f11ad325d98e299，77b5c09b6d5e1d3323ad0b7ff352aeaa，288becbe90890e297c905ef8195e2897，这三个型号两箱都有，所以合在一起的时候，型号总数 = 10 + 7 - 3 = 14，而不是简单相加的17。
明白这个概念后，就来看真正的问题：一批货，有多个箱子，每个箱子里面有不同的型号，现在要求把这批货分开成N个单，每单可以包含多个箱子，但是每个箱子只能属于1单，而且每单里面的【合并型号】总数不能大于50个，求怎么分法能达到最优解？ 跟第1章相比，只是【合并型号数】和【简单相加数】的区别，但是要考虑的点就要多得多了。
想象一下，如果一个箱子，刚好有50个型号，第二个箱子，有13个型号，而且第二个箱子里的13个型号，在第1个箱子里面都有，按照问题2的规则，两个箱是可以合成1单的，因为型号全部重复了。但是问题1的规则，只能分成2单，50个满了，13只能入第2单。
这还不止，还有更复杂的： 箱1 =》 45型号 箱2 =》 5型号 箱3 =》 10型号 后面更多箱省略。。。。
箱1箱2重复2型号，箱1箱3重复5型号。按照问题1：箱1箱2加一起50，完美凑1单。但是按照问题2：箱1箱2算48，箱1箱3算50，明显1和3合更好。 而且后面如果还有很多箱，例如箱4有8型号，都在1,3里面有包含，那么1,3,4是可以合1单的。总之，【合并型号】总数不超50个就可以了。
想到这里，大部分人都会想到用数组array_merge，再array_unique去重然后count算总数就行，但是如何组最优解还是一个大问题。30跟15合掉10，是优于30跟20合掉5的。
我呢，解题算法是写出来了，能运行得出结果无错误。但是实话说，是没有实现到最优解的。先送上代码（PHP版）吧，解法思路在代码注释里面有写。
/***** AutoDistributeDec.php *****/
<?php
/**
* Class AutoDistributeDec
* 箱子间合并型号分单类
*/
class AutoDistributeDec
{
// $boxProsnoNum 箱子内型号数
public $boxProsnoNum = [];
// $boxMergeProsnoNum 箱子内合并型号数
public $boxMergeProsnoNum = [];
// $boxMergeProsnoMd5 箱子内合并型号MD5索引
public $boxMergeProsnoMd5 = [];
// $keyBoxs 排序后箱子顺序索引号
public $keyBoxs = [];
// $decToBox 分好后单对应箱子的索引
public $decToBox = [];
// $decToProsnoMd5 分好后单对应型号MD5索引 - 调试用
public $decToProsnoMd5 = [];
// $tmpMergeBox 分单过程中临时组装的数组，每分完一单重置
public $tmpMergeBox = [];
/**
* 组装合单之前的数据
*/
public function handleOrderDetail($customsDetailArr){
foreach ($customsDetailArr as $value){
$tmp['box_num'] = $value['box_num'];
$tmp['prosno_md5'] = $value['prosno_md5'];
$this->boxProsnoNum[$tmp['box_num']] = empty($this->boxProsnoNum[$tmp['box_num']]) ? 1 : ++$this->boxProsnoNum[$tmp['box_num']];
$this->boxMergeProsnoNum[$tmp['box_num']][$tmp['prosno_md5']] = 1;
}
foreach ($this->boxMergeProsnoNum as $k3 => $v3){
$this->boxMergeProsnoNum[$k3] = count($v3);
foreach ($v3 as $k4 => $v4) {
$this->boxMergeProsnoMd5[$k3][] = $k4;
}
}
arsort($this->boxProsnoNum);
arsort($this->boxMergeProsnoNum);
}
/**
* 合并型号组单
* 允许不同箱子中包含同型号的项合并，这样每单的总项可以大于50项，但是每一个单的总去重合并型号数不大于50个
* 同时，每一个箱子只能属于一个单，但是一个单可以包含多个箱子。
*
* 组单原理：
* 把箱子号按照箱内合并型号数顺序排列，取第1个箱，然后取倒数最后1个补，2个箱去重合并后，判断够不够50，够就跳出
* 不够取倒数第2个继续补，继续合并去重，直到够50为止，就组合一单。
* 循环去掉首尾取出的，从剩下的里面继续重复上面的操作。直到剩余数组为空，或者剩余数无法组装够50为止退出。
*
* 优化点
* 动态规划，第一次首尾合并后如果不足50，则不应该取倒数第二个箱取合，而是应该从剩下可组合选项中，循环尝试合并，得出可能的最优合并项
* 最优合并项定义：array_intersect($a1,$a2) 求出两个数组交集的个数最多，且真正合并后不超过50的那项，如果交集个数相等则取总项数大的
*/
public function getBestSplit(){
$this->keyBoxs = array_keys($this->boxMergeProsnoNum); // 数组实现链表
$this->decToBox = [];
$allIndex = 0; // 合同单索引
while(count($this->keyBoxs) > 0) {
$headIndex = 0; // 准备每份新单前的首尾指针
$tailIndex = count($this->keyBoxs)-2;
$t = 0;
$this->tmpMergeBox = []; // 重置临时数组
list($total, $t) = $this->getTwoBoxMerge($allIndex, $headIndex, $tailIndex, $t);
while ($total < 50) {
if ($t > 0) { // 合并后少于50且为有效数据 把尾指针的箱号加入到当前单数组
$this->decToBox[$allIndex][] = $this->keyBoxs[$tailIndex];
array_pop($this->keyBoxs); // 弹出尾指针
$tailIndex = $tailIndex - 1; // 尾指针向前+1
}
$t = $t + 1;
list($total, $t) = $this->getTwoBoxMerge($allIndex, $headIndex, $tailIndex, $t);
if(count($this->keyBoxs) == 0){ // 没有剩余箱，退出当前单判断
break;
}
}
if ($total == 50) { // 加入一个项后 合并数刚好等于50，注意不能把上面while<50改为<=50，不然会无限死循环
if ($t > 0) {
$this->decToBox[$allIndex][] = $this->keyBoxs[$tailIndex]; // 把尾指针的箱号加入到当前单数组
array_pop($this->keyBoxs); // 弹出尾指针
$tailIndex = $tailIndex - 1; // 尾指针向前+1
}
}
$allIndex = $allIndex + 1; // 合同单索引+1
}
// 判断去除单内有0箱子的情况
foreach ($this->decToBox as $k1 => $v1){
if(count($v1) == 0){
unset($this->decToBox[$k1]);
}
if(count($v1) == 1 && ($v1[0] == "" || $v1[0] == 0)){
unset($this->decToBox[$k1]);
}
}
/***
// 组装每单内含有合并型号md5值的数组，用于开发调试用，实际并不需要
foreach ($this->decToBox as $k3 => $v3){
$this->decToProsnoMd5[$k3] = [];
foreach ($v3 as $v4){
$this->decToProsnoMd5[$k3] = array_unique(array_merge($this->decToProsnoMd5[$k3],$this->boxMergeProsnoMd5[$v4]));
}
}
print_r($this->decToProsnoMd5); die;
***/
return $this->decToBox;
}
/**
* 判断两个箱子是否能合成一个单，合完后去重型号总数是多少
*/
public function getTwoBoxMerge($allIndex, $headIndex, $tailIndex, $t){
if($t == 0){
$this->tmpMergeBox = $this->boxMergeProsnoMd5[$this->keyBoxs[0]]; // 把首指针的箱号加入临时合并数组
$this->decToBox[$allIndex][] = $this->keyBoxs[$headIndex]; // 把首指针的箱号加入到当前单数组
array_shift($this->keyBoxs); // 弹出当前首指针
return [count($this->boxMergeProsnoMd5[$this->keyBoxs[0]]), 0];
}
$t = end($this->keyBoxs); // 把t置大，标为非首项
$hBox = $this->keyBoxs[$headIndex]; // 首箱号
$tBox = $this->keyBoxs[$tailIndex]; // 尾箱号
if($hBox == $tBox){ // 首尾箱号相同，证明只剩下最后一箱
if(is_array($this->boxMergeProsnoMd5[$tBox])){
$this->tmpMergeBox = array_unique(array_merge($this->tmpMergeBox, $this->boxMergeProsnoMd5[$tBox]));
}
if(count($this->tmpMergeBox) > 50){ // 大于50,让这个箱单独成一单
$this->decToBox[$allIndex+1][] = $hBox;
}else{ // 小于等于50,凑一单
$this->decToBox[$allIndex][] = $hBox;
}
$this->keyBoxs = []; // 退出整个大循环
return [999, $t];
}
if(count($this->tmpMergeBox) == 0) {
$this->tmpMergeBox = array_unique(array_merge($this->boxMergeProsnoMd5[$hBox], $this->boxMergeProsnoMd5[$tBox]));
}else{
// 把现有临时数组和尾箱组成新的临时数组
$this->tmpMergeBox = array_unique(array_merge($this->tmpMergeBox, $this->boxMergeProsnoMd5[$tBox]));
}
return [count($this->tmpMergeBox), $t];
}
}
/***** demo.php *****/
<?php
include 'AutoDistributeDec.php';
$testDataStr = '[{"box_num":"1","prosno_md5":"55766e89a05caba74e09e05f3cada80e"},{"box_num":"1","prosno_md5":"77b5c09b6d5e1d3323ad0b7ff352aeaa"},{"box_num":"1","prosno_md5":"b0a3e7babe36a55cb2f13336577a96fd"},{"box_num":"1","prosno_md5":"46e902f68228c599a3c09f11e8a11dce"},{"box_num":"1","prosno_md5":"43f9e4663d50b618f6c658f1be53b113"},{"box_num":"1","prosno_md5":"d690a3f429eec0c41f11ad325d98e299"},{"box_num":"1","prosno_md5":"d9804f1ed77995d5689566795836e8cf"},{"box_num":"1","prosno_md5":"d9804f1ed77995d5689566795836e8cf"},{"box_num":"1","prosno_md5":"d690a3f429eec0c41f11ad325d98e299"},{"box_num":"1","prosno_md5":"d690a3f429eec0c41f11ad325d98e299"},{"box_num":"1","prosno_md5":"d690a3f429eec0c41f11ad325d98e299"},{"box_num":"1","prosno_md5":"d690a3f429eec0c41f11ad325d98e299"},{"box_num":"1","prosno_md5":"77b5c09b6d5e1d3323ad0b7ff352aeaa"},{"box_num":"1","prosno_md5":"288becbe90890e297c905ef8195e2897"},{"box_num":"1","prosno_md5":"75777ef58fa286b124c51a17fa141aea"},{"box_num":"1","prosno_md5":"a473d5d14febc5e9f721257dcd664d5d"},{"box_num":"1","prosno_md5":"bbb80c56253abc8d29ed0932ee28803b"},{"box_num":"1","prosno_md5":"a473d5d14febc5e9f721257dcd664d5d"},{"box_num":"1","prosno_md5":"288becbe90890e297c905ef8195e2897"},{"box_num":"1","prosno_md5":"6a0d77b6117be7ae467f901a524cbe5e"},{"box_num":"1","prosno_md5":"6a0d77b6117be7ae467f901a524cbe5e"},{"box_num":"1","prosno_md5":"6a0d77b6117be7ae467f901a524cbe5e"},{"box_num":"1","prosno_md5":"77a3de3b5cc3b50ab96beac63ba6d992"},{"box_num":"1","prosno_md5":"7a1bfb3f4aebb6f6c01750089f785f3c"},{"box_num":"1","prosno_md5":"89dccb2b7ae54dc9daa6fffc63618d2f"},{"box_num":"1","prosno_md5":"0d5f3e546451d4849861111e486657bd"},{"box_num":"1","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"1","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"1","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"1","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"1","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"2","prosno_md5":"b9b887b6d81825540b584e503350246b"},{"box_num":"3","prosno_md5":"87415b41b663fbb5d78629d303bf53d0"},{"box_num":"3","prosno_md5":"87415b41b663fbb5d78629d303bf53d0"},{"box_num":"3","prosno_md5":"59d99b563381a33cfaa5c4ebaf8025a1"},{"box_num":"3","prosno_md5":"776d4c82e30f90484d6f57f7375901b6"},{"box_num":"3","prosno_md5":"9a85df0bf0badae7fbfcca5d70165de4"},{"box_num":"3","prosno_md5":"690e41db5122f94de87ff4ece724000d"},{"box_num":"3","prosno_md5":"5ffe4ee06c146d9f419cc5b14181accb"},{"box_num":"3","prosno_md5":"a31cd466b4d9598c030bb6608d84b802"},{"box_num":"3","prosno_md5":"4595441a6eb1eed82d721e690554bdf2"},{"box_num":"3","prosno_md5":"2bf1fe738538371ea8c56b090e0ea934"},{"box_num":"3","prosno_md5":"8faa5cc29938e2b1e1090eda9e21ebc2"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"545cda9ac049e8a6ca785370baa4c893"},{"box_num":"3","prosno_md5":"03475f4998fe0190da9be405521130cf"},{"box_num":"3","prosno_md5":"09f9c31a1db4c06a9e3eff7e93969fc7"},{"box_num":"3","prosno_md5":"9b07b091a5715e7de90e3907ae8e3db2"},{"box_num":"3","prosno_md5":"071326dbbfce4316f8c5a1aec778f17c"},{"box_num":"3","prosno_md5":"9fc2d0a7e6709dae36395d33325775d3"},{"box_num":"3","prosno_md5":"32d48d6dbd84ab334660dad4c68a8727"},{"box_num":"3","prosno_md5":"e6d2388dbd274cdee04a41763baf340f"},{"box_num":"3","prosno_md5":"2631cfec3f45489521473a8b13157752"},{"box_num":"3","prosno_md5":"d6d8db4d89d79859e2491c4a72efd8e8"},{"box_num":"3","prosno_md5":"747045556b1d2d9529a1250c66820126"},{"box_num":"3","prosno_md5":"5bab49670b5f668ef0ced066be7a590f"},{"box_num":"3","prosno_md5":"d583abc4bf0bde5a1106d414b5d83f98"},{"box_num":"3","prosno_md5":"abf7685103494b084e7082ac8172e6c1"},{"box_num":"3","prosno_md5":"bb882bb8c9dd4a0414fd03ccca6cf922"},{"box_num":"3","prosno_md5":"afeb209fcdfdb39048a3aca7df7db9a5"},{"box_num":"3","prosno_md5":"09b55bc6c98796209ba3c1a7cfe29334"},{"box_num":"3","prosno_md5":"eddf2e6eec3f9dbe7d3b102b0f85cdb4"},{"box_num":"3","prosno_md5":"c5e553f69ca524c3ebfd3bc1f5f1e187"},{"box_num":"3","prosno_md5":"492c8ae33cb48d78ffb4b81a5b08cc12"},{"box_num":"3","prosno_md5":"0d3e6267569a4a58484d7cc753142d2f"},{"box_num":"3","prosno_md5":"1081f7e8f9fff181433ee5094717d9a5"},{"box_num":"3","prosno_md5":"e5d104ff891540588c579909b5e27760"},{"box_num":"3","prosno_md5":"9aef046e53575c3678085ce9cf60a98e"},{"box_num":"3","prosno_md5":"c737eb08daf4686e5477fa66bcb0be1f"},{"box_num":"3","prosno_md5":"942ff5796e68c056f9362fb41f78a616"},{"box_num":"3","prosno_md5":"0d3e6267569a4a58484d7cc753142d2f"},{"box_num":"3","prosno_md5":"c047ce5f63391ba36afdf329a9191d5c"},{"box_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// 测试数据json字符串
$testDataArr = json_decode($testDataStr,true); // 把字符串转成数组
// print_r($testDataArr); die;
$AutoDistributeDec = new AutoDistributeDec();
$AutoDistributeDec->handleOrderDetail($testDataArr); // 组装合单之前的数据
$decToBox = $AutoDistributeDec->getBestSplit(); // 合并型号组单
print_r($decToBox); die;
demo.php内已经提供了1条测试数据。组单原理如代码注释，沿用问题1使用的首尾指针法。
至于最优解，需要动态规划，每一项都要循环查找与之匹配的[最优合并项]。思路是有的，但是码出来还是需要点时间，因为要考虑时间复杂度和空间复杂度的平衡，等解决了更新到下篇文章。
最后，原创不易，如果你觉得这篇文章对你有点用的话，麻烦你为本文点赞、评论或转发一下，作者需要一点正能量反馈，谢谢了。
