128 lines
4.9 KiB
Markdown
128 lines
4.9 KiB
Markdown
|
---
|
|||
|
title: Closest-pair problem
|
|||
|
id: 5951a53863c8a34f02bf1bdc
|
|||
|
challengeType: 5
|
|||
|
videoUrl: ''
|
|||
|
localeTitle: 最近对的问题
|
|||
|
---
|
|||
|
|
|||
|
## Description
|
|||
|
<section id="description">任务: <p>提供一个函数来在二维中找到一组给定点中最接近的两个点,即求解平面情况下的<a href="https://en.wikipedia.org/wiki/Closest pair of points problem" title="wp:最近点的问题">最近点对问题</a> 。 </p><p>直接的解决方案是O(n <sup>2</sup> )算法(我们可以称之为强力算法);伪代码(使用索引)可以简单地: </p><pre> bruteForceClosestPair of P(1),P(2),... P(N)
|
|||
|
如果N <2那么
|
|||
|
返回∞
|
|||
|
其他
|
|||
|
minDistance←| P(1) - P(2)|
|
|||
|
minPoints←{P(1),P(2)}
|
|||
|
foreachi∈[1,N-1]
|
|||
|
foreachj∈[i + 1,N]
|
|||
|
if | P(i) - P(j)| <minDistance然后
|
|||
|
minDistance←| P(i) - P(j)|
|
|||
|
minPoints←{P(i),P(j)}
|
|||
|
万一
|
|||
|
ENDFOR
|
|||
|
ENDFOR
|
|||
|
return minDistance,minPoints
|
|||
|
万一
|
|||
|
</pre><p>一个更好的算法是基于递归分而治之的方法,正如<a href="https://en.wikipedia.org/wiki/Closest pair of points problem#Planar_case" title="wp:最近点的问题#Planar_case">维基百科最近的一对点问题</a>所解释的那样,即O(n log n);伪代码可以是: </p><pre>最近的(xP,yP)
|
|||
|
其中xP是P(1).. P(N)按x坐标排序,和
|
|||
|
yP是P(1).. P(N)按y坐标排序(升序)
|
|||
|
如果N≤3那么
|
|||
|
使用强力算法返回xP的最近点
|
|||
|
其他
|
|||
|
xL←xP点从1到⌈N/2⌉
|
|||
|
xR←xP点从⌈N/2⌉+ 1到N.
|
|||
|
xm←xP(⌈N/2⌉) <sub>x</sub>
|
|||
|
基←{P∈YP:P <sub>X≤XM}</sub>
|
|||
|
yR←{p∈yP:p <sub>x</sub> > xm}
|
|||
|
(dL,pairL)←nearestPair(xL,yL)
|
|||
|
(dR,pairR)←nearestRair(xR,yR)
|
|||
|
(dmin,pairMin)←(dR,pairR)
|
|||
|
如果dL <dR则
|
|||
|
(dmin,pairMin)←(dL,pairL)
|
|||
|
万一
|
|||
|
yS←{p∈yP:| xm - p <sub>x</sub> | <dmin}
|
|||
|
nS←yS中的点数
|
|||
|
(最近,最近的公里)←(dmin,pairMin)
|
|||
|
我从1到nS - 1
|
|||
|
k←i + 1
|
|||
|
而k≤nS和yS(k) <sub>y</sub> -yS(i) <sub>y</sub> <dmin
|
|||
|
if | yS(k) - yS(i)| <最接近的
|
|||
|
(最近,最近的公里)←(| yS(k) - yS(i)|,{yS(k),yS(i)})
|
|||
|
万一
|
|||
|
k←k + 1
|
|||
|
ENDWHILE
|
|||
|
ENDFOR
|
|||
|
返回最近,最近的
|
|||
|
万一
|
|||
|
</pre>参考和进一步阅读: <a href="https://en.wikipedia.org/wiki/Closest pair of points problem" title="wp:最近点的问题">最近的一对点问题</a> <a href="http://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html" title="链接:http://www.cs.mcgill.ca/~cs251/ClosestPair/ClosestPairDQ.html">最近的一对(麦吉尔)</a> <a href="http://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf" title="链接:http://www.cs.ucsb.edu/~suri/cs235/ClosestPair.pdf">最近的一对(UCSB)</a> <a href="http://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf" title="链接:http://classes.cec.wustl.edu/~cse241/handouts/closestpair.pdf">最近的一对(WUStL)</a> <a href="http://www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt" title="链接:http://www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt">最近的一对(IUPUI)</a> <p>对于输入,期望参数是一个对象(点)数组,其中<code>x</code>和<code>y</code>成员设置为数字。对于输出,返回一个包含键的对象: <code>distance</code>和<code>pair</code>值对(即两对最近点的对)。 </p></section>
|
|||
|
|
|||
|
## Instructions
|
|||
|
<section id="instructions">
|
|||
|
</section>
|
|||
|
|
|||
|
## Tests
|
|||
|
<section id='tests'>
|
|||
|
|
|||
|
```yml
|
|||
|
tests:
|
|||
|
- text: <code>getClosestPair</code>是一个函数。
|
|||
|
testString: 'assert(typeof getClosestPair === "function", "<code>getClosestPair</code> is a function.");'
|
|||
|
- text: 距离应如下。
|
|||
|
testString: 'assert.equal(getClosestPair(points1).distance, answer1.distance, "Distance should be the following.");'
|
|||
|
- text: 要点应如下。
|
|||
|
testString: 'assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points1))).pair, answer1.pair, "Points should be the following.");'
|
|||
|
- text: 距离应如下。
|
|||
|
testString: 'assert.equal(getClosestPair(points2).distance, answer2.distance, "Distance should be the following.");'
|
|||
|
- text: 要点应如下。
|
|||
|
testString: 'assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points2))).pair, answer2.pair, "Points should be the following.");'
|
|||
|
|
|||
|
```
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
## Challenge Seed
|
|||
|
<section id='challengeSeed'>
|
|||
|
|
|||
|
<div id='js-seed'>
|
|||
|
|
|||
|
```js
|
|||
|
const Point = function (x, y) {
|
|||
|
this.x = x;
|
|||
|
this.y = y;
|
|||
|
};
|
|||
|
Point.prototype.getX = function () {
|
|||
|
return this.x;
|
|||
|
};
|
|||
|
Point.prototype.getY = function () {
|
|||
|
return this.y;
|
|||
|
};
|
|||
|
|
|||
|
function getClosestPair (pointsArr) {
|
|||
|
// Good luck!
|
|||
|
return true;
|
|||
|
}
|
|||
|
|
|||
|
```
|
|||
|
|
|||
|
</div>
|
|||
|
|
|||
|
|
|||
|
### After Test
|
|||
|
<div id='js-teardown'>
|
|||
|
|
|||
|
```js
|
|||
|
console.info('after the test');
|
|||
|
```
|
|||
|
|
|||
|
</div>
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
## Solution
|
|||
|
<section id='solution'>
|
|||
|
|
|||
|
```js
|
|||
|
// solution required
|
|||
|
```
|
|||
|
</section>
|