72 lines
1.4 KiB
Markdown
72 lines
1.4 KiB
Markdown
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---
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id: 5900f48d1000cf542c50ffa0
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challengeType: 5
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title: 'Problem 289: Eulerian Cycles'
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forumTopicId: 301940
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---
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## Description
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<section id='description'>
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Let C(x,y) be a circle passing through the points (x, y), (x, y+1), (x+1, y) and (x+1, y+1).
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For positive integers m and n, let E(m,n) be a configuration which consists of the m·n circles:
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{ C(x,y): 0 ≤ x < m, 0 ≤ y < n, x and y are integers }
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An Eulerian cycle on E(m,n) is a closed path that passes through each arc exactly once.
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Many such paths are possible on E(m,n), but we are only interested in those which are not self-crossing:
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A non-crossing path just touches itself at lattice points, but it never crosses itself.
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The image below shows E(3,3) and an example of an Eulerian non-crossing path.
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Let L(m,n) be the number of Eulerian non-crossing paths on E(m,n).
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For example, L(1,2) = 2, L(2,2) = 37 and L(3,3) = 104290.
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Find L(6,10) mod 1010.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler289()</code> should return 6567944538.
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testString: assert.strictEqual(euler289(), 6567944538);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler289() {
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return true;
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}
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euler289();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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