PHP algorithm for generating random red envelopes

1. Background introduction

A while ago, the company's business had a need to generate red envelopes, which are divided into fixed red envelopes and random red envelopes. There is nothing much to say about fixed red envelopes, and random red envelopes require a minimum value. , and the maximum value, there must be at least one maximum value, there can be no minimum value, but any red envelope cannot be less than the minimum value.
I have never done this before and was a little confused, so I went to Baidu and found that all the red envelope algorithms I could find had various bugs. They would either calculate negative values ​​or exceed the maximum value, so Decided to make a set myself.

## 2. Basic ideas

In terms of random number generation, I learned from this The thoughts of a blogger@The miserable uncle:

Original text: For example, if you want to distribute 1 red envelope to N people, it is actually equivalent to getting N percentage data The condition is that the sum of these N percentages = 100/100. The average of these N percentages is 1/N. And these N percentage data conform to a normal distribution (most values ​​are closer to the mean).
Interpretation: For example, if I have 1,000 yuan and send out 50 red envelopes, I will first randomly select 50 numbers, and then calculate the average value of these 50 numbers, $avg, using $avg/(1/N ), you get a base $mixrand, and then divide the 50 randomly generated numbers by $mixrand to get the percentage of each number relative to the base $randVal, and then multiply $randVal by 1,000 yuan to get each The specific amount of the red envelope.

Still not sure what’s going on? It doesn’t matter, let’s code together!

##3. Talk is cheap, show me your code!

Red envelope generation core Algorithm:

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);
        }
    }
}

Details to consider:

The following code is used to control specific business logic, and set aside fixed maximum and minimum red envelope amounts according to specific needs;

When calling splitReward($total, $num,$max - 0.01, $min); in the code, the maximum value I passed in was reduced by 0.01, which ensures that the maximum value of the red envelope generated is absolute. Will not exceed the maximum value we set.

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;
    }
}

4. Pull it out for a walk

Basic code:

Set various initial values

Performance test:
 Because of the memory_limit limit, I only measured the average of 5 times, and the results were all around 1.6s. 
for($i=0; $i<5; $i++) {
    $time_start = microtime_float();
    $reward_arr = $create_reward->random_red($total, $num, $max, $min);
    $time_end = microtime_float();
    $time[] = $time_end - $time_start;
}
echo array_sum($time)/5;
function microtime_float()
{
    list($usec, $sec) = explode(" ", microtime());
    return ((float)$usec + (float)$sec);
}
Running results:





##Data check:
Detect whether there are negative values, whether there is a maximum value, how many maximum values ​​there are, and whether there is a value smaller than the minimum value; 
$reward_arr = $create_reward->random_red($total, $num, $max, $min);
sort($reward_arr);//正序，最小的在前面
$sum = 0;
$min_count = 0;
$max_count = 0;
foreach($reward_arr as $i => $val) {
    if ($i<3) {
        echo "
第".($i+1)."个红包，金额为：".$val."
";  
    } 
    if ($val == $max) {
          $max_count++;
    }
    if ($val < $min) {
        $min_count++;
    }
    $val = $val*100;
    $sum += $val;
}
//检测钱是否全部发完
echo '
已生成红包总金额为：'.($sum/100).';总个数为：'.count($reward_arr).'
';
//检测有没有小于0的值
echo "
最大值:".($val/100).',共有'.$max_count.'个最大值，共有'.$min_count.'个值比最小值小';
Run results: 

 



##Normal distribution chart:
Note that when publishing the chart, do not give too many red envelopes, otherwise the page will render If it doesn’t come out, it will collapse



##
$reward_arr = $create_reward->random_red($total, $num, $max, $min);
$show = array();
rsort($reward_arr);
//为了更直观的显示正态分布效果,需要将数组重新排序
foreach($reward_arr as $k=>$value)
{
    $t=$k%2;
    if(!$t) $show[]=$value;;
    else array_unshift($show,$value);
}
echo "设定最大值为:".$max.',最小值为:'.$min.'
';
echo "";
foreach($show as $val)
{
    #线条长度计算
    $width=intval($num*$val*300/$total);
    echo "";
}
echo "
红包金额
图示
 {$val} 
";

Run result:





 PS: A friend asked me if the data I generated has been verified mathematically to see if it conforms to the standard normal distribution, because my mathematics No, I really haven’t thought about this. I just looked like him and assumed he was. 
 Since I have encountered this problem, I must solve it, so I used php
built-in function
 to calculate it. The calculated result is relatively close to the normal distribution when the amount of data is small. But when the amount of data increases, it cannot be viewed. I don’t quite understand this. If you are interested, you can find out the reason. 
 Four functions of php: stats_standard_deviation (standard deviation), stats_variance (variance), stats_kurtosis (kurtosis), stats_skew (skewness) 
 Using the above functions requires 
 installation stats extension＠Download Address
5. In the end
At this point, I have finished writing the red envelope. I don’t know if I can get a 50 yuan salary increase, but it should be able to solve the urgent need. 




##Oh yes, I also left this code to package and download







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