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 in the planar case.
The straightforward solution is a O(n2) algorithm (which we can call brute-force algorithm); the pseudo-code (using indexes) could be simply:
bruteForceClosestPair of P(1), P(2), ... P(N) if N < 2 then return ∞ else minDistance ← |P(1) - P(2)| minPoints ← { P(1), P(2) } foreach i ∈ [1, N-1] foreach j ∈ [i+1, N] if |P(i) - P(j)| < minDistance then minDistance ← |P(i) - P(j)| minPoints ← { P(i), P(j) } endif endfor endfor return minDistance, minPoints endif
A better algorithm is based on the recursive divide&conquer approach, as explained also at Wikipedia's Closest pair of points problem, which is O(n log n); a pseudo-code could be:
closestPair of (xP, yP) where xP is P(1) .. P(N) sorted by x coordinate, and yP is P(1) .. P(N) sorted by y coordinate (ascending order) if N ≤ 3 then return closest points of xP using brute-force algorithm else xL ← points of xP from 1 to ⌈N/2⌉ xR ← points of xP from ⌈N/2⌉+1 to N xm ← xP(⌈N/2⌉)x yL ← { p ∈ yP : px ≤ xm } yR ← { p ∈ yP : px > xm } (dL, pairL) ← closestPair of (xL, yL) (dR, pairR) ← closestPair of (xR, yR) (dmin, pairMin) ← (dR, pairR) if dL < dR then (dmin, pairMin) ← (dL, pairL) endif yS ← { p ∈ yP : |xm - px| < dmin } nS ← number of points in yS (closest, closestPair) ← (dmin, pairMin) for i from 1 to nS - 1 k ← i + 1 while k ≤ nS and yS(k)y - yS(i)y < dmin if |yS(k) - yS(i)| < closest then (closest, closestPair) ← (|yS(k) - yS(i)|, {yS(k), yS(i)}) endif k ← k + 1 endwhile endfor return closest, closestPair endifReferences and further readings: Closest pair of points problem Closest Pair (McGill) Closest Pair (UCSB) Closest pair (WUStL) Closest pair (IUPUI)
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
(i.e., the pair of two closest points).
getClosestPair
is a function.
testString: assert(typeof getClosestPair === 'function', 'getClosestPair
is a function.');
- text: Distance should be the following.
testString: assert.equal(getClosestPair(points1).distance, answer1.distance, 'Distance should be the following.');
- text: Points should be the following.
testString: assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points1))).pair, answer1.pair, 'Points should be the following.');
- text: Distance should be the following.
testString: assert.equal(getClosestPair(points2).distance, answer2.distance, 'Distance should be the following.');
- text: Points should be the following.
testString: assert.deepEqual(JSON.parse(JSON.stringify(getClosestPair(points2))).pair, answer2.pair, 'Points should be the following.');
```