Successive approximation of unkown value - php

Question

I have a url with a page system.
For instance https://myURL?p=50
But I want a script to find the last page available, for instance, let's say p=187
I have a function checkEmpty() that tells me whether the page is empty or not.
So for instance:
$myUrl = new URL(50); //https://myURL?p=50
$myUrl->checkEmpty();
//This evaluates to false -> the page exists
$myUrl = new URL(188); //https://myURL?p=188
$myUrl->checkEmpty();
//This evaluates to true -> the page does NOT exist
$myUrl = new URL(187); //https://myURL?p=187
$myUrl->checkEmpty();
//This evaluates to false -> the page exists
I did a naive algorithm, that you might guess it, performs too much requests.
My question is:
What would be the algorithm to find the last page with the minimal amount of requests?
EDIT
As requested by people in the comment here is the checkEmpty() implementation
<?php
public function checkEmpty() : bool
{
$criteria = "Aucun contenu disponible";
if(strstr( $this->replace_carriage_return(" ", $this->getHtml()), $criteria) !== false)
{
return true;
}
else
{
return false;
}
}

Answer 1

Since the upper bound is not known, exponentially increase the page no by 2 starting from 1. The moment you hit a non-existent page, you can do a binary search from previous existing page + 1 till this new upper bound where the page doesn't exist.
This way, you can get your answer in O(log(n)) attempts asymptotically where n is the no. of existing pages here as the sample space.
<?php
$lowerBound = 1;
$upperBound = 1;
while(true){
$myUrl = new URL($upperBound);
if($myUrl->checkEmpty()){
break;
}
$lowerBound = $upperBound + 1;
$upperBound <<= 1;
}
$ans = $lowerBound;
while($lowerBound <= $upperBound){
$mid = $lowerBound + (($upperBound - $lowerBound) >> 1);
$myUrl = new URL($mid);
if($myUrl->checkEmpty()){
$upperBound = $mid - 1;
}else{
$lowerBound = $mid + 1;
$ans = $lowerBound;
}
}
echo $ans;