Rubidium2018.py

# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")

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 best value to delta
    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 + 7, ln_y)):
            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 dist(p1, p2):
    return max(abs(p1[0] - p2[0]), abs(p1[1] - p2[1]))

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:]

    # Determine midpoint on x-axis

    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(X, Y):
    a = list(zip(X, Y))
    ax = sorted(a, key=lambda x: x[0])  # Presorting x-wise
    ay = sorted(a, key=lambda x: x[1])  # Presorting y-wise
    (x1, y1), (x2, y2), mi = closest_pair(ax, ay)  # Recursive D&C function
    
    lo = 0
    high = 10 ** 5
    while lo < high:
        mid = (lo + high + 1) // 2
        if abs(x1 - x2) < 2 * mid and abs(y1 - y2) < 2 * mid:
            high = mid - 1
        else:
            lo = mid
    return lo