---
id: 5900f48b1000cf542c50ff9e
challengeType: 5
title: 'Problem 287: Quadtree encoding (a simple compression algorithm)'
---

## Description
<section id='description'>
The quadtree encoding allows us to describe a 2N×2N  black and white image as a sequence of bits (0 and 1). Those sequences are to be read from left to right like this:
the first bit deals with the complete 2N×2N region;
"0" denotes a split:
the current 2n×2n region is divided into 4 sub-regions of dimension 2n-1×2n-1,
the next bits contains the description of the top left, top right, bottom left and bottom right sub-regions - in that order;
"10" indicates that the current region contains only black pixels;
"11" indicates that the current region contains only white pixels.Consider the following 4×4 image (colored marks denote places where a split can occur):

This image can be described by several sequences, for example :
"001010101001011111011010101010", of length 30, or
"0100101111101110", of length 16, which is the minimal sequence for this image.

For a positive integer N, define DN as the 2N×2N image with the following coloring scheme:
the pixel with coordinates x = 0, y = 0 corresponds to the bottom left pixel,
if (x - 2N-1)2 + (y - 2N-1)2 ≤ 22N-2 then the pixel is black,
otherwise the pixel is white.What is the length of the minimal sequence describing D24 ?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler287()</code> should return 313135496.
    testString: assert.strictEqual(euler287(), 313135496, '<code>euler287()</code> should return 313135496.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler287() {
  // Good luck!
  return true;
}

euler287();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>