55 lines
1.7 KiB
Markdown
55 lines
1.7 KiB
Markdown
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---
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id: 5900f48b1000cf542c50ff9e
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title: 'Problem 287: Quadtree encoding (a simple compression algorithm)'
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challengeType: 5
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forumTopicId: 301938
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dashedName: problem-287-quadtree-encoding-a-simple-compression-algorithm
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---
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# --description--
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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:
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the first bit deals with the complete 2N×2N region;
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"0" denotes a split:
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the current 2n×2n region is divided into 4 sub-regions of dimension 2n-1×2n-1,
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the next bits contains the description of the top left, top right, bottom left and bottom right sub-regions - in that order;
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"10" indicates that the current region contains only black pixels;
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"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):
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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.
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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 ?
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# --hints--
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`euler287()` should return 313135496.
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```js
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assert.strictEqual(euler287(), 313135496);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler287() {
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return true;
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}
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euler287();
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```
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# --solutions--
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```js
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// solution required
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```
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