71 lines
1.4 KiB
Markdown
71 lines
1.4 KiB
Markdown
|
---
|
|||
|
|
id: 5900f4e81000cf542c50fffb
|
|||
|
|
challengeType: 5
|
|||
|
|
title: 'Problem 380: Amazing Mazes!'
|
|||
|
forumTopicId: 302044
|
|||
|
|
---
|
|||
|
|
|
|||
|
|
## Description
|
|||
|
|
<section id='description'>
|
|||
|
|
An m×n maze is an m×n rectangular grid with walls placed between grid cells such that there is exactly one path from the top-left square to any other square. The following are examples of a 9×12 maze and a 15×20 maze:
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
Let C(m,n) be the number of distinct m×n mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.
|
|||
|
|
|
|||
|
|
|
|||
|
|
It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415, and C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant digits).
|
|||
|
|
Find C(100,500) and write your answer in scientific notation rounded to 5 significant digits.
|
|||
|
|
|
|||
|
|
|
|||
|
|
When giving your answer, use a lowercase e to separate mantissa and exponent.
|
|||
|
|
E.g. if the answer is 1234567891011 then the answer format would be 1.2346e12.
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Instructions
|
|||
|
|
<section id='instructions'>
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Tests
|
|||
|
|
<section id='tests'>
|
|||
|
|
|
|||
|
|
```yml
|
|||
|
|
tests:
|
|||
|
|
- text: <code>euler380()</code> should return Infinity.
|
|||
|
|
testString: assert.strictEqual(euler380(), Infinity);
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Challenge Seed
|
|||
|
|
<section id='challengeSeed'>
|
|||
|
|
|
|||
|
|
<div id='js-seed'>
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
function euler380() {
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
euler380();
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
## Solution
|
|||
|
|
<section id='solution'>
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
// solution required
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</section>
|