PHP实现微信红包分包算法源码（抛物线的模型）

```
<?php

/*
 *Author:Kermit
 *Time:2015-8-26
 *Note:红包生成随机算法
 */

header("Content-type:text/html;charset=utf-8");
date_default_timezone_set('PRC');

#红包生成的算法程序
class reward
{
     public $rewardMoney;        #红包金额、单位元
     public $rewardNum;                  #红包数量
     public $scatter;            #分散度值1-10000
     public $rewardArray;        #红包结果集
     
     #初始化红包类
     public function __construct()
     {
            $this->rewardArray=array();
     }
     
     #执行红包生成算法
     public function splitReward($rewardMoney,$rewardNum,$scatter=100)
     {
             #传入红包金额和数量
             $this->rewardMoney=$rewardMoney;
            $this->rewardNum=$rewardNum;
            $this->scatter=$scatter;
            $this->realscatter=$this->scatter/100;
            
            /*
             *前言：今天我突然这样一想，比如要把1个红包分给N个人，实际上就是相当于要得到N个百分比数据
             *     条件是这N个百分比之和=100/100。这N个百分比的平均值是1/N。
             *     并且这N个百分比数据符合一种正态分布（多数值比较靠近平均值）
             *观点：微信红包里很多0.01的红包，我觉得这是微信程序里的人为控制，目的是为了防止总红包数超过总额，先分了几个0.01的红包。
             *     不然不管是以随机概率还是正态分布都很难会出现非常多的0.01元红包。
             */
            
            #我的思路：正如上面说的，比如：1个红包发给5个人，我要得出5个小数，它们的和是1，他们的平均值是1/5
            #计算出发出红包的平均概率值、精确到小数4位。即上面的1/N值。
            $avgRand=round(1/$this->rewardNum,4);
             
            #红包的向平均数集中的分布正像数学上的抛物线。抛物线y=ax2，|a|越大则抛物线的开口就越小，|a|越小则抛物线的开口就越大,a>0时开口向上，我们这都是正数，就以a>0来考虑吧。
            #程序里的$scatter值即为上方的a，此值除以100，当做100为基准，
            #通过开方(数学里的抛物线模型，开方可缩小变化值)得出一个小数字较多（小数字多即小红包多）的随机分布,据此生成随机数
            $randArr=array();
            while(count($randArr)<$rewardNum)
            {
                    $t=round(sqrt(mt_rand(1,10000)/$this->realscatter));
                    $randArr[]=$t;
            }
            
            #计算当前生成的随机数的平均值，保留4位小数
            $randAll=round(array_sum($randArr)/count($randArr),4);
            
            #为将生成的随机数的平均值变成我们要的1/N，计算一下生成的每个随机数都需要除以的值。我们可以在最后一个红包进行单独处理，所以此处可约等于处理。
            $mixrand=round($randAll/$avgRand,4);
            
            #对每一个随机数进行处理，并剩以总金额数来得出这个红包的金额。
            $rewardArr=array();
            foreach($randArr as $key=>$randVal)
            {
                    $randVal=round($randVal/$mixrand,4);
                    $rewardArr[]=round($this->rewardMoney*$randVal,2);
            }
            
            #对比红包总数的差异、修正最后一个大红包
            sort($rewardArr);
            $rewardAll=array_sum($rewardArr);
            $rewardArr[$this->rewardNum-1]=$this->rewardMoney-($rewardAll-$rewardArr[$this->rewardNum-1]);
            rsort($rewardArr);

#对红包进行排序一下以方便在前台图示展示
            foreach($rewardArr as $k=>$value)
            {
                    $t=$k%2;
                    if($t) array_push($this->rewardArray,$value);
                    else array_unshift($this->rewardArray,$value);
            }
            $rewardArr=NULL;
            return $this->rewardArray;
     }
    
}

$money=1000;    #总共要发的红包数;
$people=50;        #总共要发的人数
$scatter=100;    #分散度
$reward=new reward();
$rewardArr=$reward->splitReward($money,$people,$scatter);
echo "发放红包个数：{$people}，红包总金额{$money}元。下方所有红包总额之和：".array_sum($reward->rewardArray).'元。下方用图展示红包的分布';
echo '<hr>';
echo "<table style='font-size:12px;width:600px;border:1px solid #ccc;text-align:left;'><tr><td>红包金额</td><td>图示</td></tr>";
foreach($rewardArr as $val)
{
    #线条长度计算
    $width=intval($people*$val*300/$money);
    echo "<tr><td>{$val}</td><td width='500px;text-align:left;'><hr style='width:{$width}px;height:3px;border:none;border-top:3px double red;margin:0 auto 0 0px;'></td></tr>";    
}
echo "</table>";
?>
```
测试结果[10块分5个包]：
```
["0.13","2.66","3.05","3.04","1.12"]
["0.68","2.19","2.93","2.69","1.51"]
["1.12","1.89","2.7","2.65","1.64"]
["0.44","2.5","2.98","2.65","1.43"]
["0.94","1.6","3.07","2.95","1.44"]
["1.28","2.26","2.45","2.41","1.6"]
["0.37","2.3","2.7","2.6","2.03"]
["1.38","2.03","2.37","2.36","1.86"]
["1.39","1.77","2.68","2.49","1.67"]
["0.53","2.22","3.13","2.22","1.9"]
["1.16","2.04","2.6","2.4","1.8"]
["1.37","2.01","2.91","2.16","1.55"]
["1.27","2.09","2.45","2.2","1.99"]
["0.74","2.06","2.66","2.61","1.93"]
["0.86","1.84","3.35","2.5","1.45"]
["0.18","2.16","2.98","2.59","2.09"]
["0.75","2.19","2.61","2.52","1.93"]
["0.86","2.46","2.65","2.55","1.48"]
["1.02","1.62","3.16","2.99","1.21"]
["0.86","2.14","2.96","2.45","1.59"]
```

PHP实现微信红包分包算法源码（抛物线的模型）

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