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HomeBackend DevelopmentPHP Tutorialphp实现猴子选大王问题算法实例_php技巧

本文实例讲述了php实现猴子选大王问题算法。分享给大家供大家参考。具体分析如下:

一、问题:

n只猴子围坐成一个圈,按顺时针方向从1到n编号。
然后从1号猴子开始沿顺时针方向从1开始报数,报到m的猴子出局,再从刚出局猴子的下一个位置重新开始报数,
如此重复,直至剩下一个猴子,它就是大王。

设计并编写程序,实现如下功能:
(1)   要求由用户输入开始时的猴子数$n、报数的最后一个数$m。
(2)   给出当选猴王的初始编号。

二、解决方法:

/**
 * @param int $n 开始时的猴子数量
 * @param int $m 报道的最后一个数
 *(报到这个数的猴子被淘汰,然后下一个猴子重新从①开始报数) 
 * @return int 猴子的初始编号 
 */
function monkeySelectKing($n,$m)
{
 //猴子的初始数量不能小于2
 if ($n<2)
 {
 return false;
 }
 
 $arr=range(1,$n);
 //将猴子分到一个数组里, 数组的值对应猴子的初始编号
 $unsetNum=0;
 //定义一个变量,记录猴子的报数
 
 for ($i = 2; $i <=$n*$m ; $i++)
 //总的循环次数不知道怎么计算,
 {
 //不过因为循环中设置了return,所以$m*$len效率还可以
 foreach ($arr as $k => $v)
 {
  $unsetNum++; //每到一个猴子, 猴子报数+1
 
 //当猴子的报数等于淘汰的数字时:淘汰猴子(删除数组元素)
 //报数归0(下一个猴子从1开始数)
  if ($unsetNum==$m) 
  {
//  echo "<pre class="brush:php;toolbar:false">";//打开注释,可以看到具体的淘汰过程
//  print_r($arr);
  unset($arr[$k]);
 //淘汰猴子  
  $unsetNum=0;
 //报数归零
  if (count($arr)==1)
 //判断数组的长度, 如果只剩一个猴子, 返回它的值
  {
   return reset($arr);
  }
  }
 }
 }
}
 
var_dump(monkeySelectKing(6, 3));

补充改进算法(该算法更加简洁明了!):

function yuesefu($n,$m) { 
  $r=0; 
  for($i=2; $i<=$n; $i++) {

      $r=($r+$m)%$i; 
  }
  return $r+1; 
} 
print_r(yuesefu(3,3));

希望本文所述对大家的php程序算法设计有所帮助。

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