The linked list solution and mathematical solution of Joseph Ring related problems (PHP)

The chain list solution and mathematical solution of Joseph Ring problem (PHP)

Joseph Ring Question

A group of monkeys in a circle, according to 1,2,...,n sequentially numbered. Then, starting from the 1th, Count to M., Kick It Out of the loop, start counting from behind it, Count to M., and Kick It out ... and so on, until the last monkey is left, the monkey is called the King. Requires programming to simulate this process, enter M, N, and output the number of the last king.

Chain List Solution

function king($n,$m){    $monky = range(1,$n);    $i = 0;    while(count($monky)>1){        $i+=1;        $head = array_shift($monky);        if($i%$m!=0){            array_push($monky,$head);        }    }    return $monky[0];}echo king(10,3);

Mathematical Solutions

• X ' = 2 3 4 5 0
• x = 0 1 2 3 4

• X ' = (x+m)%n

  function king2($n,$m){    $r = 0;    for($i=2;$i<=$n;$i++){        $r = ($r+$m)%$i;    }    return $r+1;}echo king2(10,3);

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

