Merge pull request #566 from AlexAdvent/ClosestPairOfPoints

Create ClosestPairOfPoints

Author: smv1999

Divide and Conquer/ClosestPairOfPoints.py

@@ -0,0 +1,94 @@
+# 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))