Solving Algorithm (Josephus permutation) in PHP - php

Question

Suppose 100 people line up in a circle. Counting from person 1 to person 14, remove person from the circle. Following the count order, counting again and remove the 14th person. Repeat. Who is the last person standing?
I've tried everything to solve this and it seems to not be working with dead loops.
<?php
//init array
$array = array();
for ($i = 0; $i < 100; $i++) { $array[] = $i; }
//start from 0
$pos = 0;
while (count_not_null($array) > 1) {
//reset count
$count = 0;
while (true) {
//ignore NULL for count, that position is already removed
if ($array[$pos] !== NULL) {
$count++;
if($count == 14) { break; }
}
$pos++;
//go back to beginning, we cant go over 0-99, for 100 elements
if ($pos > 99) { $pos = 0; }
}
echo "set index {$pos} to NULL!" ."<br>";
$array[$pos] = NULL;
if (count_not_null($array) === 1) { break; }
}
echo "<pre>";
print_r($array);
echo "</pre>";
//counting not null elements
function count_not_null($array) {
$count = 0;
for ($i = 0; $i < count($array); $i++) {
if ($array[$i] !== NULL) { $count++; }
}
return $count;
}
?>

Answer 1

For solving this with as little code as possible and quickest you could do like this:
function josephus($n,$k){
if($n ==1)
return 1;
else
return (josephus($n-1,$k)+$k-1) % $n+1;
}
echo josephus(100,14);
Here we are using an recursive statement instead, as what you are trying to solve can be defined by this mathematical statement f(n,k) = (f(n-1,k) + k) % n
For reading more about this mathematical formula you can see it here on the wiki page.

Answer 2

The problem is this while loop
while ($count < 14) {
if ($array[$pos] != NULL) {
$count++;
}
$pos++;
if ($pos > 99) { $pos = 0; }
}
Because you increment $pos even if count is 14 you will end with incorrect values and loop forever. Replace it with this:
while (true) {
if ($array[$pos] != NULL) {
$count++;
if($count == 14) {break;}
}
$pos++;
if ($pos > 99) { $pos = 0; }
}
Also comparing 0 to NULL won't give you the expected results as mentioned by #Barmar, so you can either change the NULL comparison, or start counting from 1
NOTE: This would be way faster if you didn't loop through array every time :D consider using a variable to count the remaining items

Answer 3

Anyone who stumbles across this again, here is a slightly quicker one:
function josephus($n){
$toBin = decbin($n); // to binary
$toBack = substr($toBin,1) . "1"; // remove first bit and add to end
return bindec($toBack); // back to value
}
Based on this solution.