ClosestPairOfPoints.py

# Task. Given 𝑛 points on a plane, find the smallest distance between a pair of two (different) points. Recall
# that the distance between points (𝑥1, 𝑦1) and (𝑥2, 𝑦2) is equal to √︀((𝑥1 − 𝑥2)² + (𝑦1 − 𝑦2)²)

import math
def dist(p1, p2):
    return math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)

def closest_split_pair(p_x, p_y, delta, best_pair):
    ln_x = len(p_x)  # store length - quicker
    mx_x = p_x[ln_x // 2][0]  # select midpoint on x-sorted array

    # Create a subarray of points not further than delta from midpoint on x-sorted array
    s_y = [x for x in p_y if mx_x - delta <= x[0] <= mx_x + delta]

    best = delta  # assign delta value to best
    ln_y = len(s_y)  # store length of subarray for quickness
    for i in range(ln_y - 1):
        for j in range(i+1, min(i + 5, ln_y)):    # We have to check only next 5 points;
            p, q = s_y[i], s_y[j]
            dst = dist(p, q)
            if dst < best:
                best_pair = p, q
                best = dst
    return best_pair[0], best_pair[1], best


def brute(ax):
    mi = dist(ax[0], ax[1])
    p1 = ax[0]
    p2 = ax[1]
    ln_ax = len(ax)
    if ln_ax == 2:
        return p1, p2, mi
    for i in range(ln_ax-1):
        for j in range(i + 1, ln_ax):
            if i != 0 and j != 1:
                d = dist(ax[i], ax[j])
                if d < mi:  # Update min_dist and points
                    mi = d
                    p1, p2 = ax[i], ax[j]
    return p1, p2, mi


def closest_pair(ax, ay):
    ln_ax = len(ax)  # It's quicker to assign variable
    if ln_ax <= 3:
        return brute(ax)  # A call to bruteforce comparison
    mid = ln_ax // 2  # Division without remainder, need int
    Qx = ax[:mid]  # Two-part split
    Rx = ax[mid:]

    midpoint = ax[mid][0]
    Qy = list()
    Ry = list()
    for x in ay:  # split ay into 2 arrays using midpoint
        if x[0] < midpoint:
           Qy.append(x)
        else:
           Ry.append(x)
    # Call recursively both arrays after split
    (p1, q1, mi1) = closest_pair(Qx, Qy)
    (p2, q2, mi2) = closest_pair(Rx, Ry)

    # Determine smaller distance between points of 2 arrays
    if mi1 <= mi2:
        d = mi1
        mn = (p1, q1)
    else:
        d = mi2
        mn = (p2, q2)

    # Call function to account for points on the boundary
    (p3, q3, mi3) = closest_split_pair(ax, ay, d, mn)
    # Determine smallest distance for the array
    if d <= mi3:
        return mn[0], mn[1], d
    else:
        return p3, q3, mi3


def solution(a):
    ax = sorted(a, key=lambda x: x[0])  # Presorting x-wise O(nlogn)
    ay = sorted(a, key=lambda x: (x[1], x[0]))  # Presorting y-wise then x-wise O(nlogn)
    p1, p2, mi = closest_pair(ax, ay)  # Recursive D&C function
    return mi


# Input
points = list()
n = int(input())
for i in range(n):
    points.append([int(i) for i in input().split()])

print(solution(points))