PHP random number WeChat randomly generates red envelope amount algorithm PHP version

Recently I was studying the function of sending red envelopes, so I wrote a red envelope generation algorithm.

The requirements of the red envelope generation algorithm
Generate all red envelopes in advance or randomly generate a red envelope with a request
Simply put, it is to decompose a large integer m (directly into units, such as 1 yuan or 100) into n A process of small integers, the range of small integers is [min, max]
The simplest idea is to guarantee the bottom first, each small red envelope is guaranteed to have min, and then each request randomly generates a range from 0 to (max-min). The integer plus min is the amount of the red envelope.
Although this algorithm is simple, it has a drawback: the final red envelope may be min. In other words, the final red envelope may be 0.01 yuan. Another way is to generate all red envelopes in advance, which is easier to control. What I choose is to generate all red envelopes in advance.

Ideal red envelope generation algorithm

The ideal red envelope generation result is that there are more red envelopes near the average value. The number of big red envelopes and small red envelopes is relatively small.
You can imagine that the distribution of the number of generated red envelopes is a bit like a normal distribution.

So how to achieve this requirement of having more values ​​near the average line?

We need to find a way. Algorithm can improve the probability near the average value. Then use a method of "expansion" and "shrinkage" to achieve this effect.
First square, then generate a random number within the square range, and then take the square root, then the probability will not be the same. It’s average again.
Specific algorithm: (The total amount of money, total number of people, maximum and minimum values ​​set must be reasonable)
Php code

/** 
 * 求一个数的平方 
 * @param $n 
 */ 
function sqr($n){ 
  return $n*$n; 
} 
 
/** 
* 生产min和max之间的随机数，但是概率不是平均的，从min到max方向概率逐渐加大。 
* 先平方，然后产生一个平方值范围内的随机数，再开方，这样就产生了一种“膨胀”再“收缩”的效果。 
*/  
function xRandom($bonus_min,$bonus_max){ 
  $sqr = intval(sqr($bonus_max-$bonus_min)); 
  $rand_num = rand(0, ($sqr-1)); 
  return intval(sqrt($rand_num)); 
} 
 
 
 /** 
 *  
 * @param $bonus_total 红包总额 
 * @param $bonus_count 红包个数 
 * @param $bonus_max 每个小红包的最大额 
 * @param $bonus_min 每个小红包的最小额 
 * @return 存放生成的每个小红包的值的一维数组 
 */  
function getBonus($bonus_total, $bonus_count, $bonus_max, $bonus_min) {  
  $result = array();  
 
  $average = $bonus_total / $bonus_count;  
 
  $a = $average - $bonus_min;  
  $b = $bonus_max - $bonus_min;  
 
  //  
  //这样的随机数的概率实际改变了，产生大数的可能性要比产生小数的概率要小。  
  //这样就实现了大部分红包的值在平均数附近。大红包和小红包比较少。  
  $range1 = sqr($average - $bonus_min);  
  $range2 = sqr($bonus_max - $average);  
 
  for ($i = 0; $i 平均值，则产生小红包  
    //当随机数 $average) {  
      // 在平均线上减钱  
      $temp = $bonus_min + xRandom($bonus_min, $average);  
      $result[$i] = $temp;  
      $bonus_total -= $temp;  
    } else {  
      // 在平均线上加钱  
      $temp = $bonus_max - xRandom($average, $bonus_max);  
      $result[$i] = $temp;  
      $bonus_total -= $temp;  
    }  
  }  
  // 如果还有余钱，则尝试加到小红包里，如果加不进去，则尝试下一个。  
  while ($bonus_total > 0) {  
    for ($i = 0; $i  0 && $result[$i]  $bonus_min) {  
        $result[$i]--;  
        $bonus_total++;  
      }  
    }  
  }  
  return $result;  
} 
$bonus_total = 200; 
$bonus_count = 100; 
$bonus_max = 10;//此算法要求设置的最大值要大于平均值 
$bonus_min = 1; 
$result_bonus = getBonus($bonus_total, $bonus_count, $bonus_max, $bonus_min); 
$total_money = 0; 
$arr = array(); 
foreach ($result_bonus as $key => $value) { 
  $total_money += $value; 
  if(isset($arr[$value])){ 
    $arr[$value] += 1; 
  }else{ 
    $arr[$value] = 1; 
  } 
   
} 
//输出总钱数，查看是否与设置的总数相同 
echo $total_money; 
//输出所有随机红包值 
var_dump($result_bonus); 
//统计每个钱数的红包数量，检查是否接近正态分布 
ksort($arr); 
var_dump($arr);

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