Add Divide and Conquer: Closest Pair of Points algorithm

divide_and_conquer/closest_pair_of_points.cpp

@@ -0,0 +1,88 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// Structure to represent a 2D point
+struct Point {
+    int x, y;
+};
+
+// Function to compare points based on X coordinate
+bool compareX(Point a, Point b) {
+    return a.x < b.x;
+}
+
+// Function to compare points based on Y coordinate
+bool compareY(Point a, Point b) {
+    return a.y < b.y;
+}
+
+// Utility function to calculate Euclidean distance
+double dist(Point p1, Point p2) {
+    return sqrt((p1.x - p2.x) * 1.0 * (p1.x - p2.x) +
+                (p1.y - p2.y) * 1.0 * (p1.y - p2.y));
+}
+
+// Brute force method for small number of points
+double bruteForce(Point points[], int left, int right) {
+    double minDist = DBL_MAX;
+    for (int i = left; i < right; ++i) {
+        for (int j = i + 1; j < right; ++j) {
+            minDist = min(minDist, dist(points[i], points[j]));
+        }
+    }
+    return minDist;
+}
+
+// Function to find the closest points in the strip
+double stripClosest(vector<Point>& strip, double d) {
+    double minDist = d;
+    int n = strip.size();
+
+    sort(strip.begin(), strip.end(), compareY);
+
+    for (int i = 0; i < n; ++i)
+        for (int j = i + 1; j < n && (strip[j].y - strip[i].y) < minDist; ++j)
+            minDist = min(minDist, dist(strip[i], strip[j]));
+
+    return minDist;
+}
+
+// Recursive function using Divide and Conquer
+double closestUtil(Point points[], int left, int right) {
+    if (right - left <= 3)
+        return bruteForce(points, left, right);
+
+    int mid = (left + right) / 2;
+    Point midPoint = points[mid];
+
+    double dl = closestUtil(points, left, mid);
+    double dr = closestUtil(points, mid, right);
+
+    double d = min(dl, dr);
+
+    vector<Point> strip;
+    for (int i = left; i < right; ++i) {
+        if (abs(points[i].x - midPoint.x) < d)
+            strip.push_back(points[i]);
+    }
+
+    return min(d, stripClosest(strip, d));
+}
+
+// Main function to be called
+double closestPair(Point points[], int n) {
+    sort(points, points + n, compareX);
+    return closestUtil(points, 0, n);
+}
+
+// --------- Sample Driver Code ---------
+int main() {
+    Point points[] = {{2, 3}, {12, 30}, {40, 50},
+                      {5, 1}, {12, 10}, {3, 4}};
+    int n = sizeof(points) / sizeof(points[0]);
+
+    cout << fixed << setprecision(4);
+    cout << "The smallest distance is " << closestPair(points, n) << endl;
+
+    return 0;
+}