Feat: add new Markdown parser (#39800)
and change all the challenges to new `md` format.
This commit is contained in:
Oliver Eyton-Williams
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commit
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@ -1,24 +1,25 @@
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---
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title: Closest-pair problem
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id: 5951a53863c8a34f02bf1bdc
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title: Closest-pair problem
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challengeType: 5
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forumTopicId: 302232
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---
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## Description
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<section id='description'>
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Provide a function to find the closest two points among a set of given points in two dimensions, i.e. to solve the <a href="https://en.wikipedia.org/wiki/Closest pair of points problem" title="wp: Closest pair of points problem" target="blank">Closest pair of points problem</a> in the <i>planar</i> case.
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The straightforward solution is a O(n<sup>2</sup>) algorithm (which we can call <i>brute-force algorithm</i>); the pseudo-code (using indexes) could be simply:
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<pre>
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<strong>bruteForceClosestPair</strong> of P(1), P(2), ... P(N)
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<strong>if</strong> N < 2 <strong>then</strong>
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# --description--
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Provide a function to find the closest two points among a set of given points in two dimensions, i.e. to solve the [Closest pair of points problem](<https://en.wikipedia.org/wiki/Closest pair of points problem> "wp: Closest pair of points problem") in the *planar* case.
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The straightforward solution is a O(n<sup>2</sup>) algorithm (which we can call *brute-force algorithm*); the pseudo-code (using indexes) could be simply:
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<pre><strong>bruteForceClosestPair</strong> of P(1), P(2), ... P(N)
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<strong>if</strong> N < 2 <strong>then</strong>
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<strong>return</strong> ∞
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<strong>else</strong>
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minDistance ← |P(1) - P(2)|
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minPoints ← { P(1), P(2) }
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<strong>foreach</strong> i ∈ [1, N-1]
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<strong>foreach</strong> j ∈ [i+1, N]
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<strong>if</strong> |P(i) - P(j)| < minDistance <strong>then</strong>
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<strong>if</strong> |P(i) - P(j)| < minDistance <strong>then</strong>
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minDistance ← |P(i) - P(j)|
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minPoints ← { P(i), P(j) }
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<strong>endif</strong>
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@ -27,9 +28,10 @@ The straightforward solution is a O(n<sup>2</sup>) algorithm (which we can call
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<strong>return</strong> minDistance, minPoints
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<strong>endif</strong>
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</pre>
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A better algorithm is based on the recursive divide and conquer approach, as explained also at <a href="https://en.wikipedia.org/wiki/Closest pair of points problem#Planar_case" title="wp: Closest pair of points problem#Planar_case" target="_blank">Wikipedia's Closest pair of points problem</a>, which is <code>O(nlog(n))</code> a pseudo-code could be:
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<pre>
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<strong>closestPair</strong> of (xP, yP)
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A better algorithm is based on the recursive divide and conquer approach, as explained also at [Wikipedia's Closest pair of points problem](<https://en.wikipedia.org/wiki/Closest pair of points problem#Planar_case> "wp: Closest pair of points problem#Planar_case"), which is `O(nlog(n))` a pseudo-code could be:
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<pre><strong>closestPair</strong> of (xP, yP)
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where xP is P(1) .. P(N) sorted by x coordinate, and
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yP is P(1) .. P(N) sorted by y coordinate (ascending order)
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<strong>if</strong> N ≤ 3 <strong>then</strong>
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@ -39,20 +41,20 @@ A better algorithm is based on the recursive divide and conquer approach, as exp
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xR ← points of xP from ⌈N/2⌉+1 to N
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xm ← xP(⌈N/2⌉)<sub>x</sub>
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yL ← { p ∈ yP : p<sub>x</sub> ≤ xm }
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yR ← { p ∈ yP : p<sub>x</sub> > xm }
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yR ← { p ∈ yP : p<sub>x</sub> > xm }
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(dL, pairL) ← closestPair of (xL, yL)
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(dR, pairR) ← closestPair of (xR, yR)
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(dmin, pairMin) ← (dR, pairR)
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<strong>if</strong> dL < dR <strong>then</strong>
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<strong>if</strong> dL < dR <strong>then</strong>
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(dmin, pairMin) ← (dL, pairL)
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<strong>endif</strong>
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yS ← { p ∈ yP : |xm - p<sub>x</sub>| < dmin }
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yS ← { p ∈ yP : |xm - p<sub>x</sub>| < dmin }
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nS ← number of points in yS
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(closest, closestPair) ← (dmin, pairMin)
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<strong>for</strong> i <strong>from</strong> 1 <strong>to</strong> nS - 1
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k ← i + 1
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<strong>while</strong> k ≤ nS <strong>and</strong> yS(k)<sub>y</sub> - yS(i)<sub>y</sub> < dmin
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<strong>if</strong> |yS(k) - yS(i)| < closest <strong>then</strong>
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<strong>while</strong> k ≤ nS <strong>and</strong> yS(k)<sub>y</sub> - yS(i)<sub>y</sub> < dmin
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<strong>if</strong> |yS(k) - yS(i)| < closest <strong>then</strong>
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(closest, closestPair) ← (|yS(k) - yS(i)|, {yS(k), yS(i)})
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<strong>endif</strong>
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k ← k + 1
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@ -61,82 +63,72 @@ A better algorithm is based on the recursive divide and conquer approach, as exp
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<strong>return</strong> closest, closestPair
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<strong>endif</strong>
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</pre>
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For the input, expect the argument to be an array of objects (points) with <code>x</code> and <code>y</code> members set to numbers. For the output, return an object containing the key:value pairs for <code>distance</code> and <code>pair</code> (the pair of two closest points).
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<strong>References and further readings:</strong>
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For the input, expect the argument to be an array of objects (points) with `x` and `y` members set to numbers. For the output, return an object containing the key:value pairs for `distance` and `pair` (the pair of two closest points).
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**References and further readings:**
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<ul>
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<li><a href="https://en.wikipedia.org/wiki/Closest pair of points problem" title="wp: Closest pair of points problem" target="_blank">Closest pair of points problem</a></li>
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<li><a href="https://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html" target="_blank">Closest Pair (McGill)</a></li>
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<li><a href="https://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf" target="_blank">Closest Pair (UCSB)</a></li>
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<li><a href="https://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf" target="_blank">Closest pair (WUStL)</a></li>
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<li><a href='https://en.wikipedia.org/wiki/Closest pair of points problem' title='wp: Closest pair of points problem' target='_blank'>Closest pair of points problem</a></li>
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<li><a href='https://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html' target='_blank'>Closest Pair (McGill)</a></li>
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<li><a href='https://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf' target='_blank'>Closest Pair (UCSB)</a></li>
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<li><a href='https://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf' target='_blank'>Closest pair (WUStL)</a></li>
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</ul>
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</section>
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## Instructions
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<section id='instructions'>
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# --hints--
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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>getClosestPair</code> should be a function.
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testString: assert(typeof getClosestPair === 'function');
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- text: Distance should be the following.
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testString: assert.equal(getClosestPair(points1).distance, answer1.distance);
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- text: Points should be the following.
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testString: assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points1))).pair, answer1.pair);
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- text: Distance should be the following.
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testString: assert.equal(getClosestPair(points2).distance, answer2.distance);
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- text: Points should be the following.
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testString: assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points2))).pair, answer2.pair);
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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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`getClosestPair` should be a function.
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```js
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const Point = function(x, y) {
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this.x = x;
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this.y = y;
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};
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Point.prototype.getX = function() {
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return this.x;
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};
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Point.prototype.getY = function() {
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return this.y;
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};
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function getClosestPair(pointsArr) {
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return true;
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}
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assert(typeof getClosestPair === 'function');
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```
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</div>
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Distance should be the following.
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```js
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assert.equal(getClosestPair(points1).distance, answer1.distance);
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```
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### After Test
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<div id='js-teardown'>
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Points should be the following.
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```js
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assert.deepEqual(
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JSON.parse(JSON.stringify(getClosestPair(points1))).pair,
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answer1.pair
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);
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```
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Distance should be the following.
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```js
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assert.equal(getClosestPair(points2).distance, answer2.distance);
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```
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Points should be the following.
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```js
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assert.deepEqual(
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JSON.parse(JSON.stringify(getClosestPair(points2))).pair,
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answer2.pair
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);
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```
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# --seed--
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## --after-user-code--
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```js
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const points1 = [
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new Point(0.748501, 4.09624),
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new Point(3.00302, 5.26164),
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new Point(3.61878, 9.52232),
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new Point(7.46911, 4.71611),
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new Point(5.7819, 2.69367),
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new Point(2.34709, 8.74782),
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new Point(2.87169, 5.97774),
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new Point(6.33101, 0.463131),
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new Point(7.46489, 4.6268),
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new Point(1.45428, 0.087596)
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new Point(0.748501, 4.09624),
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new Point(3.00302, 5.26164),
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new Point(3.61878, 9.52232),
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new Point(7.46911, 4.71611),
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new Point(5.7819, 2.69367),
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new Point(2.34709, 8.74782),
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new Point(2.87169, 5.97774),
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new Point(6.33101, 0.463131),
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new Point(7.46489, 4.6268),
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new Point(1.45428, 0.087596)
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];
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const points2 = [
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@ -229,13 +221,27 @@ const benchmarkPoints = [
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];
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```
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</div>
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## --seed-contents--
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</section>
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```js
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const Point = function(x, y) {
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this.x = x;
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this.y = y;
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};
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Point.prototype.getX = function() {
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return this.x;
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};
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Point.prototype.getY = function() {
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return this.y;
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};
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## Solution
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<section id='solution'>
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function getClosestPair(pointsArr) {
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return true;
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}
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```
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# --solutions--
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```js
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const Point = function(x, y) {
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@ -250,98 +256,98 @@ Point.prototype.getY = function() {
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};
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const mergeSort = function mergeSort(points, comp) {
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if(points.length < 2) return points;
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if(points.length < 2) return points;
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var n = points.length,
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i = 0,
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j = 0,
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leftN = Math.floor(n / 2),
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rightN = leftN;
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var n = points.length,
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i = 0,
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j = 0,
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leftN = Math.floor(n / 2),
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rightN = leftN;
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var leftPart = mergeSort( points.slice(0, leftN), comp),
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rightPart = mergeSort( points.slice(rightN), comp );
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var leftPart = mergeSort( points.slice(0, leftN), comp),
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rightPart = mergeSort( points.slice(rightN), comp );
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var sortedPart = [];
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var sortedPart = [];
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while((i < leftPart.length) && (j < rightPart.length)) {
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if(comp(leftPart[i], rightPart[j]) < 0) {
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sortedPart.push(leftPart[i]);
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i += 1;
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}
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else {
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sortedPart.push(rightPart[j]);
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j += 1;
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}
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}
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while(i < leftPart.length) {
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sortedPart.push(leftPart[i]);
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i += 1;
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}
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while(j < rightPart.length) {
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sortedPart.push(rightPart[j]);
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j += 1;
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}
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return sortedPart;
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while((i < leftPart.length) && (j < rightPart.length)) {
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if(comp(leftPart[i], rightPart[j]) < 0) {
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sortedPart.push(leftPart[i]);
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i += 1;
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}
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else {
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sortedPart.push(rightPart[j]);
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j += 1;
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}
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}
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while(i < leftPart.length) {
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sortedPart.push(leftPart[i]);
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i += 1;
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}
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while(j < rightPart.length) {
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sortedPart.push(rightPart[j]);
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j += 1;
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}
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return sortedPart;
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};
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const closestPair = function _closestPair(Px, Py) {
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if(Px.length < 2) return { distance: Infinity, pair: [ new Point(0, 0), new Point(0, 0) ] };
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if(Px.length < 3) {
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//find euclid distance
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var d = Math.sqrt( Math.pow(Math.abs(Px[1].x - Px[0].x), 2) + Math.pow(Math.abs(Px[1].y - Px[0].y), 2) );
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return {
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distance: d,
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pair: [ Px[0], Px[1] ]
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};
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}
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if(Px.length < 2) return { distance: Infinity, pair: [ new Point(0, 0), new Point(0, 0) ] };
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if(Px.length < 3) {
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//find euclid distance
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var d = Math.sqrt( Math.pow(Math.abs(Px[1].x - Px[0].x), 2) + Math.pow(Math.abs(Px[1].y - Px[0].y), 2) );
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return {
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distance: d,
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pair: [ Px[0], Px[1] ]
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};
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}
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var n = Px.length,
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leftN = Math.floor(n / 2),
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rightN = leftN;
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var n = Px.length,
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leftN = Math.floor(n / 2),
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rightN = leftN;
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var Xl = Px.slice(0, leftN),
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Xr = Px.slice(rightN),
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Xm = Xl[leftN - 1],
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Yl = [],
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Yr = [];
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//separate Py
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for(var i = 0; i < Py.length; i += 1) {
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if(Py[i].x <= Xm.x)
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Yl.push(Py[i]);
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else
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Yr.push(Py[i]);
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}
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var Xl = Px.slice(0, leftN),
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Xr = Px.slice(rightN),
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Xm = Xl[leftN - 1],
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Yl = [],
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Yr = [];
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//separate Py
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for(var i = 0; i < Py.length; i += 1) {
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if(Py[i].x <= Xm.x)
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Yl.push(Py[i]);
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else
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Yr.push(Py[i]);
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}
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var dLeft = _closestPair(Xl, Yl),
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dRight = _closestPair(Xr, Yr);
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var dLeft = _closestPair(Xl, Yl),
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dRight = _closestPair(Xr, Yr);
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var minDelta = dLeft.distance,
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closestPair = dLeft.pair;
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if(dLeft.distance > dRight.distance) {
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minDelta = dRight.distance;
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closestPair = dRight.pair;
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}
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var minDelta = dLeft.distance,
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closestPair = dLeft.pair;
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if(dLeft.distance > dRight.distance) {
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minDelta = dRight.distance;
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closestPair = dRight.pair;
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}
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//filter points around Xm within delta (minDelta)
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var closeY = [];
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for(i = 0; i < Py.length; i += 1) {
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if(Math.abs(Py[i].x - Xm.x) < minDelta) closeY.push(Py[i]);
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}
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//find min within delta. 8 steps max
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for(i = 0; i < closeY.length; i += 1) {
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for(var j = i + 1; j < Math.min( (i + 8), closeY.length ); j += 1) {
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var d = Math.sqrt( Math.pow(Math.abs(closeY[j].x - closeY[i].x), 2) + Math.pow(Math.abs(closeY[j].y - closeY[i].y), 2) );
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if(d < minDelta) {
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minDelta = d;
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closestPair = [ closeY[i], closeY[j] ]
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}
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}
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}
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//filter points around Xm within delta (minDelta)
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var closeY = [];
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for(i = 0; i < Py.length; i += 1) {
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if(Math.abs(Py[i].x - Xm.x) < minDelta) closeY.push(Py[i]);
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}
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//find min within delta. 8 steps max
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for(i = 0; i < closeY.length; i += 1) {
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for(var j = i + 1; j < Math.min( (i + 8), closeY.length ); j += 1) {
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var d = Math.sqrt( Math.pow(Math.abs(closeY[j].x - closeY[i].x), 2) + Math.pow(Math.abs(closeY[j].y - closeY[i].y), 2) );
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if(d < minDelta) {
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minDelta = d;
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closestPair = [ closeY[i], closeY[j] ]
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}
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}
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||||
}
|
||||
|
||||
return {
|
||||
distance: minDelta,
|
||||
pair: closestPair
|
||||
};
|
||||
return {
|
||||
distance: minDelta,
|
||||
pair: closestPair
|
||||
};
|
||||
};
|
||||
|
||||
function getClosestPair(points) {
|
||||
@ -353,7 +359,4 @@ function getClosestPair(points) {
|
||||
|
||||
return closestPair(Px, Py);
|
||||
}
|
||||
|
||||
```
|
||||
|
||||
</section>
|
||||
|
||||
Reference in New Issue
Block a user