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CleverCode recently received a request to write a fixed red envelope + random red envelope algorithm.
1 Fixed red envelope means that the amount of each red envelope is the same. You can send as many fixed red envelopes as there are.
2 The demand for random red envelopes is. For example, if the total amount of red envelopes is 5 yuan, 10 red envelopes need to be sent. The random range is 0.01 to 0.99; 5 yuan must be paid out, and the amount needs to have a normal distribution with a certain trend. (0.99 can be specified arbitrarily, or it can be avg * 2 - 0.01; for example, avg = 5 / 10 = 0.5; (avg * 2 - 0.01 = 0.99))
If it is a fixed red envelope, the algorithm is a straight line. t is the fixed amount of red envelope. As shown in the picture.
f(x) = t;（1 <= x <= num）
If we Use the random function rand. rand(0.01,0.99); then 10 random times, if the worst case scenario is the amount is 0.99, the total amount is 9.9 yuan. It will be more than 5 yuan. Amounts will also not be normally distributed. Finally, I thought about using mathematical functions as a random red envelope generator. Parabolas and trigonometric functions can be used. Finally, the isosceles trigonometric linear function was selected.
1 Algorithm principle
If the total amount of red envelopes to be issued is totalMoney, the number of red envelopes is num, and the amount range is [min,max], the linear equation is as shown in the figure .
Coordinates of three points:
（x1,y1） = (1,min) (x2,y2) = (num/2,max) (x3,y3) = (num,min)
Determined linear equation:
$y = 1.0 * ($x - $x1) / ($x2 - $x1) * ($y2 - $y1) + $y1 ; （x1 <= x <= x2） $y = 1.0 * ($x - $x2) / ($x3 - $x2) * ($y3 - $y2) + $y2; （x2 <= x <= x3）
Revised data:
y (Total) = y1 + y2 + y3 +... ynum;
y (Total) may be > totalMoney, indicating that the generated amount is too much and the data needs to be revised, then start from (y1, y2, y3. ....ynum) These are reduced by 0.01 each time. Until y(total) = totalMoney.
y (together) may be < totalMoney, indicating that the generated amount is less and the data needs to be revised, then add 0.01 each time from (y1, y2, y3...ynum). Until y(total) = totalMoney.
2 Algorithm Principle Example
If the total amount of red envelopes to be issued is 11470, the number of red envelopes is 7400, and the amount range is [0.01,3.09] , the linear equation is shown in the figure.
num = $num;
$self->rangeStart = $rangeStart;
$self->rangeEnd = $rangEnd;
$self->totalMoney = $totalMoney;
$self->builderStrategy = $builderStrategy;
$self->randFormatType = $randFormatType;
return $self;
}/*}}}*/
}/*}}}*/
//红包生成器接口
interface IBuilderStrategy
{/*{{{*/
//创建红包
public function create();
//设置配置
public function setOption(OptionDTO $option);
//是否可以生成红包
public function isCanBuilder();
//生成红包函数
public function fx($x);
}/*}}}*/
//固定等额红包策略
class EqualPackageStrategy implements IBuilderStrategy
{/*{{{*/
//单个红包金额
public $oneMoney;
//数量
public $num;
public function construct($option = null)
{
if($option instanceof OptionDTO)
{
$this->setOption($option);
}
}
public function setOption(OptionDTO $option)
{
$this->oneMoney = $option->rangeStart;
$this->num = $option->num;
}
public function create()
{/*{{{*/
$data = array();
if(false == $this->isCanBuilder())
{
return $data;
}
$data = array();
if(false == is_int($this->num) || $this->num <= 0)
{
return $data;
}
for($i = 1;$i <= $this->num;$i++)
{
$data[$i] = $this->fx($i);
}
return $data;
}/*}}}*/
/**
* 等额红包的方程是一条直线
*
* @param mixed $x
* @access public
* @return void
*/
public function fx($x)
{/*{{{*/
return $this->oneMoney;
}/*}}}*/
/**
* 是否能固定红包
*
* @access public
* @return void
*/
public function isCanBuilder()
{/*{{{*/
if(false == is_int($this->num) || $this->num <= 0)
{
return false;
}
if(false == is_numeric($this->oneMoney) || $this->oneMoney <= 0)
{
return false;
}
//单个红包小于1分
if($this->oneMoney < 0.01)
{
return false;
}
return true;
}/*}}}*/
}/*}}}*/
//随机红包策略(三角形)
class RandTrianglePackageStrategy implements IBuilderStrategy
{/*{{{*/
//总额
public $totalMoney;
//红包数量
public $num;
//随机红包最小值
public $minMoney;
//随机红包最大值
public $maxMoney;
//修数据方式：NO_LEFT: 红包总额 = 预算总额；CAN_LEFT: 红包总额 <= 预算总额
public $formatType;
//预算剩余金额
public $leftMoney;
public function construct($option = null)
{/*{{{*/
if($option instanceof OptionDTO)
{
$this->setOption($option);
}
}/*}}}*/
public function setOption(OptionDTO $option)
{/*{{{*/
$this->totalMoney = $option->totalMoney;
$this->num = $option->num;
$this->formatType = $option->randFormatType;
$this->minMoney = $option->rangeStart;
$this->maxMoney = $option->rangeEnd;
$this->leftMoney = $this->totalMoney;
}/*}}}*/
/**
* 创建随机红包
*
* @access public
* @return void
*/
public function create()
{/*{{{*/
$data = array();
if(false == $this->isCanBuilder())
{
return $data;
}
$leftMoney = $this->leftMoney;
for($i = 1;$i <= $this->num;$i++)
{
$data[$i] = $this->fx($i);
$leftMoney = $leftMoney - $data[$i];
}
//修数据
list($okLeftMoney,$okData) = $this->format($leftMoney,$data);
//随机排序
shuffle($okData);
$this->leftMoney = $okLeftMoney;
return $okData;
}/*}}}*/
/**
* 是否能够发随机红包
*
* @access public
* @return void
*/
public function isCanBuilder()
{/*{{{*/
if(false == is_int($this->num) || $this->num <= 0)
{
return false;
}
if(false == is_numeric($this->totalMoney) || $this->totalMoney <= 0)
{
return false;
}
//均值
$avgMoney = $this->totalMoney / 1.0 / $this->num;
//均值小于最小值
if($avgMoney < $this->minMoney )
{
return false;
}
return true;
}/*}}}*/
/**
* 获取剩余金额
*
* @access public
* @return void
*/
public function getLeftMoney()
{/*{{{*/
return $this->leftMoney;
}/*}}}*/
/**
* 随机红包生成函数。三角函数。[(1,0.01),($num/2,$avgMoney),($num,0.01)]
*
* @param mixed $x,1 <= $x <= $this->num;
* @access public
* @return void
*/
public function fx($x)
{/*{{{*/
if(false == $this->isCanBuilder())
{
return 0;
}
if($x < 1 || $x > $this->num)
{
return 0;
}
$x1 = 1;
$y1 = $this->minMoney;
//我的峰值
$y2 = $this->maxMoney;
//中间点
$x2 = ceil($this->num / 1.0 / 2);
//最后点
$x3 = $this->num;
$y3 = $this->minMoney;
//当x1,x2,x3都是1的时候(竖线)
if($x1 == $x2 && $x2 == $x3)
{
return $y2;
}
// '/_\'三角形状的线性方程
//'/'部分
if($x1 != $x2 && $x >= $x1 && $x <= $x2)
{
$y = 1.0 * ($x - $x1) / ($x2 - $x1) * ($y2 - $y1) + $y1;
return number_format($y, 2, '.', '');
}
//'\'形状
if($x2 != $x3 && $x >= $x2 && $x <= $x3)
{
$y = 1.0 * ($x - $x2) / ($x3 - $x2) * ($y3 - $y2) + $y2;
return number_format($y, 2, '.', '');
}
return 0;
}/*}}}*/
/**
* 格式化修红包数据
*
* @param mixed $leftMoney
* @param array $data
* @access public
* @return void
*/
private function format($leftMoney,array $data)
{/*{{{*/
//不能发随机红包
if(false == $this->isCanBuilder())
{
return array($leftMoney,$data);
}
//红包剩余是0
if(0 == $leftMoney)
{
return array($leftMoney,$data);
}
//数组为空
if(count($data) < 1)
{
return array($leftMoney,$data);
}
//如果是可以有剩余，并且$leftMoney > 0
if('Can_Left' == $this->formatType
&& $leftMoney > 0)
{
return array($leftMoney,$data);
}
//我的峰值
$myMax = $this->maxMoney;
// 如果还有余钱，则尝试加到小红包里，如果加不进去，则尝试下一个。
while($leftMoney > 0)
{
$found = 0;
foreach($data as $key => $val)
{
//减少循环优化
if($leftMoney <= 0)
{
break;
}
//预判
$afterLeftMoney = (double)$leftMoney - 0.01;
$afterVal = (double)$val + 0.01;
if( $afterLeftMoney >= 0 && $afterVal <= $myMax)
{
$found = 1;
$data[$key] = number_format($afterVal,2,'.','');
$leftMoney = $afterLeftMoney;
//精度
$leftMoney = number_format($leftMoney,2,'.','');
}
}
//如果没有可以加的红包，需要结束,否则死循环
if($found == 0)
{
break;
}
}
//如果$leftMoney < 0 ,说明生成的红包超过预算了，需要减少部分红包金额
while($leftMoney < 0)
{
$found = 0;
foreach($data as $key => $val)
{
if($leftMoney >= 0)
{
break;
}
//预判
$afterLeftMoney = (double)$leftMoney + 0.01;
$afterVal = (double)$val - 0.01;
if( $afterLeftMoney <= 0 && $afterVal >= $this->minMoney)
{
$found = 1;
$data[$key] = number_format($afterVal,2,'.','');
$leftMoney = $afterLeftMoney;
$leftMoney = number_format($leftMoney,2,'.','');
}
}
//如果一个减少的红包都没有的话，需要结束，否则死循环
if($found == 0)
{
break;
}
}
return array($leftMoney,$data);
}/*}}}*/
}/*}}}*/
//维护策略的环境类
class RedPackageBuilder
{/*{{{*/
// 实例
protected static $_instance = null;
/**
* Singleton instance（获取自己的实例）
*
* @return MemcacheOperate
*/
public static function getInstance()
{ /*{{{*/
if (null === self::$_instance)
{
self::$_instance = new self();
}
return self::$_instance;
} /*}}}*/
/**
* 获取策略【使用反射】
*
* @param string $type 类型
* @return void
*/
public function getBuilderStrategy($type)
{ /*{{{*/
$class = $type.'PackageStrategy';
if(class_exists($class))
{
return new $class();
}
else
{
throw new Exception("{$class} 类不存在！");
}
} /*}}}*/
public function getRedPackageByDTO(OptionDTO $optionDTO)
{/*{{{*/
//获取策略
$builderStrategy = $this->getBuilderStrategy($optionDTO->builderStrategy);
//设置参数
$builderStrategy->setOption($optionDTO);
return $builderStrategy->create();
}/*}}}*/
}/*}}}*/
class Client
{/*{{{*/
public static function main($argv)
{
//固定红包
$dto = OptionDTO::create(1000,10,100,100,'Equal');
$data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto);
//print_r($data);
//随机红包[修数据]
$dto = OptionDTO::create(5,10,0.01,0.99,'RandTriangle');
$data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto);
print_r($data);
//随机红包[不修数据]
$dto = OptionDTO::create(5,10,0.01,0.99,'RandTriangle','Can_Left');
$data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto);
//print_r($data);
}
}/*}}}*/
Client::main($argv);1 Fixed red envelope
//固定红包 $dto = OptionDTO::create(1000,10,100,100,'Equal'); $data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto); print_r($data);
2 Random red envelope (data modification)
The random sorting function of PHP is used here, shuffle($okData), so the result you see is not linear, this result is more random.
//随机红包[修数据] $dto = OptionDTO::create(5,10,0.01,0.99,'RandTriangle'); $data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto); print_r($data);
3 Random red envelope (no data modification)
No data modification, the amount of 1 and num is the minimum Value 0.01.
//随机红包[不修数据] $dto = OptionDTO::create(5,10,0.01,0.99,'RandTriangle','Can_Left'); $data = RedPackageBuilder::getInstance()->getRedPackageByDTO($dto); print_r($data);
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