红包复杂算法

<?php
/*
 * 红包算法
 * */
class Redpaper
{
    public $rewardMoney;        #红包金额、单位元
    public $rewardNum;          #红包数量

    #执行红包生成算法
    public function splitReward($rewardMoney, $rewardNum, $max, $min)
    {
        #传入红包金额和数量，因为小数在计算过程中会出现很大误差，所以我们直接把金额放大100倍，后面的计算全部用整数进行
        $min = $min * 100;
        $max = $max * 100;
        #预留出一部分钱作为误差补偿，保证每个红包至少有一个最小值
        $this->rewardMoney = $rewardMoney * 100 - $rewardNum * $min;
        $this->rewardNum = $rewardNum;
        #计算出发出红包的平均概率值、精确到小数4位。
        $avgRand = 1 / $this->rewardNum;
        $randArr = array();
        #定义生成的数据总合sum
        $sum = 0;
        $t_count = 0;
        while ($t_count < $rewardNum) {
            #随机产出四个区间的额度
            $c = rand(1, 100);
            if ($c < 15) {
                $t = round(sqrt(mt_rand(1, 1500)));
            } else if ($c < 65) {
                $t = round(sqrt(mt_rand(1500, 6500)));
            } else if ($c < 95) {
                $t = round(sqrt(mt_rand(6500, 9500)));
            } else {
                $t = round(sqrt(mt_rand(9500, 10000)));
            }
            ++$t_count;
            $sum += $t;
            $randArr[] = $t;
        }

        #计算当前生成的随机数的平均值，保留4位小数
        $randAll = round($sum / $rewardNum, 4);

        #为将生成的随机数的平均值变成我们要的1/N，计算一下每个随机数要除以的总基数mixrand。此处可以约等处理，产生的误差后边会找齐
        #总基数 = 均值/平均概率
        $mixrand = round($randAll / $avgRand, 4);

        #对每一个随机数进行处理，并乘以总金额数来得出这个红包的金额。
        $rewardArr = array();
        foreach ($randArr as $key => $randVal) {
            #单个红包所占比例randVal
            $randVal = round($randVal / $mixrand, 4);
            #算出单个红包金额
            $single = floor($this->rewardMoney * $randVal);
            #小于最小值直接给最小值
            if ($single < $min) {
                $single += $min;
            }
            #大于最大值直接给最大值
            if ($single > $max) {
                $single = $max;
            }
            #将红包放入结果数组
            $rewardArr[] = $single;
        }

        #对比红包总数的差异、将差值放在第一个红包上
        $rewardAll = array_sum($rewardArr);
        $rewardArr[0] = $rewardMoney * 100 - ($rewardAll - $rewardArr[0]);#此处应使用真正的总金额rewardMoney，$rewardArr[0]可能小于0

        #第一个红包小于0时,做修正
        if ($rewardArr[0] < 0) {
            rsort($rewardArr);
            $this->add($rewardArr, $min);
        }

        rsort($rewardArr);
        #随机生成的最大值大于指定最大值
        if ($rewardArr[0] > $max) {
            #差额
            $diff = 0;
            foreach ($rewardArr as $k => &$v) {
                if ($v > $max) {
                    $diff += $v - $max;
                    $v = $max;
                } else {
                    break;
                }
            }
            $transfer = round($diff / ($this->rewardNum - $k + 1));
            $this->diff($diff, $rewardArr, $max, $min, $transfer, $k);
        }
        return $rewardArr;
    }

    #处理所有超过最大值的红包
    public function diff($diff, &$rewardArr, $max, $min, $transfer, $k)
    {
        #将多余的钱均摊给小于最大值的红包
        for ($i = $k; $i < $this->rewardNum; $i++) {
            #造随机值
            if ($transfer > $min * 20) {
                $aa = rand($min, $min * 20);
                if ($i % 2) {
                    $transfer += $aa;
                } else {
                    $transfer -= $aa;
                }
            }
            if ($rewardArr[$i] + $transfer > $max) continue;
            if ($diff - $transfer < 0) {
                $rewardArr[$i] += $diff;
                $diff = 0;
                break;
            }
            $rewardArr[$i] += $transfer;
            $diff -= $transfer;
        }
        if ($diff > 0) {
            $i++;
            $this->diff($diff, $rewardArr, $max, $min, $transfer, $k);
        }
    }

    #第一个红包小于0,从大红包上往下减
    public function add(&$rewardArr, $min)
    {
        foreach ($rewardArr as &$re) {
            $dev = floor($re / $min);
            if ($dev > 2) {
                $transfer = $min * floor($dev / 2);
                $re -= $transfer;
                $rewardArr[$this->rewardNum - 1] += $transfer;
            } elseif ($dev == 2) {
                $re -= $min;
                $rewardArr[$this->rewardNum - 1] += $min;
            } else {
                break;
            }
        }
        if ($rewardArr[$this->rewardNum - 1] > $min || $rewardArr[$this->rewardNum - 1] == $min) {
            return;
        } else {
            $this->add($rewardArr, $min);
        }
    }
 public    function random_red($total, $num, $max, $min)
    {
        #总共要发的红包金额，留出一个最大值;
        $total = $total - $max;
        $result_merge = $this->splitReward($total, $num, $max - 0.01, $min);
        sort($result_merge);
        $result_merge[1] = $result_merge[1] + $result_merge[0];
        $result_merge[0] = $max * 100;
        foreach ($result_merge as &$v) {
            $v = floor($v) / 100;
        }
        return $result_merge;
    }
}

<?php
header('content-type:text/html;charset=utf-8');
function dump($arr){
echo '<pre>'.print_r($arr,TRUE).'</pre>';
}
require_once('Redpaper.class.php');
$total = 10;//红包总金额
$num = 50;//分发个数
$max = 1;//最大金额
$min = 0.01;//最小金额
$a = new Redpaper();
$arr = $a->random_red($total, $num, $max, $min);
dump($arr);