1.7 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f48b1000cf542c50ff9e | Problem 287: Quadtree encoding (a simple compression algorithm) | 5 | 301938 | problem-287-quadtree-encoding-a-simple-compression-algorithm |
--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 ?
--hints--
euler287()
should return 313135496.
assert.strictEqual(euler287(), 313135496);
--seed--
--seed-contents--
function euler287() {
return true;
}
euler287();
--solutions--
// solution required