47fc3c6761
* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
60 lines
2.3 KiB
Markdown
60 lines
2.3 KiB
Markdown
---
|
||
id: 5900f48b1000cf542c50ff9e
|
||
title: 'Problem 287: Quadtree encoding (a simple compression algorithm)'
|
||
challengeType: 5
|
||
forumTopicId: 301938
|
||
dashedName: problem-287-quadtree-encoding-a-simple-compression-algorithm
|
||
---
|
||
|
||
# --description--
|
||
|
||
The quadtree encoding allows us to describe a $2^N×2^N$ 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 $2^N×2^N$ region;
|
||
- "0" denotes a split:
|
||
- the current $2^n×2^n$ region is divided into 4 sub-regions of dimension $2^{n - 1}×2^{n - 1}$,
|
||
- 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):
|
||
|
||
<img class="img-responsive center-block" alt="4x4 image with colored marks denoting place where split can occur" src="https://cdn.freecodecamp.org/curriculum/project-euler/quadtree-encoding-a-simple-compression-algorithm.gif" style="background-color: white; padding: 10px;">
|
||
|
||
This image can be described by several sequences, for example : "<strong><span style="color: red">0</span></strong><strong><span style="color: blue">0</span></strong>10101010<strong><span style="color: green">0</span></strong>1011111011<strong><span style="color: orange">0</span></strong>10101010", of length 30, or "<strong><span style="color: red">0</span></strong>10<strong><span style="color: green">0</span></strong>101111101110", of length 16, which is the minimal sequence for this image.
|
||
|
||
For a positive integer $N$, define $D_N$ as the $2^N×2^N$ image with the following coloring scheme:
|
||
|
||
- the pixel with coordinates $x = 0$, $y = 0$ corresponds to the bottom left pixel,
|
||
- if ${(x - 2^{N - 1})}^2 + {(y - 2^{N - 1})}^2 ≤ 2^{2N - 2}$ then the pixel is black,
|
||
- otherwise the pixel is white.
|
||
|
||
What is the length of the minimal sequence describing $D_{24}$?
|
||
|
||
# --hints--
|
||
|
||
`quadtreeEncoding()` should return `313135496`.
|
||
|
||
```js
|
||
assert.strictEqual(quadtreeEncoding(), 313135496);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function quadtreeEncoding() {
|
||
|
||
return true;
|
||
}
|
||
|
||
quadtreeEncoding();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|