closest pair program

Author: bri-harris

src/main/java/com/thealgorithms/randomized/ClosestPair.java

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+package com.thealgorithms.randomized;
+import java.util.*;
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+/**
+* This class implements the randomized Closest Pair Algorithm; given some number of points
+ * in a plane find the pair with minimum euclidean distance from each other. This solution
+ * uses the divide and conquer approach.
+ * @author Bri Harris
+*/
+
+import java.util.*;
+
+class Point implements Comparable<Point> {
+    double x, y;
+
+    // Constructor to initialize a point with x and y coordinates
+    Point(double x, double y) {
+        this.x = x;
+        this.y = y;
+    }
+
+    // Compare points based on x-coordinates (for sorting)
+    public int compareTo(Point other) {
+        return Double.compare(this.x, other.x);
+    }
+
+    // Compute Euclidean distance between two points
+    static double distance(Point p1, Point p2) {
+        return Math.sqrt(Math.pow(p1.x - p2.x, 2) + Math.pow(p1.y - p2.y, 2));
+    }
+}
+
+public class ClosestPair {
+    public static double closest(List<Point> points) {
+        Collections.sort(points);
+        double result = closestRecursiveHelper(points, 0, points.size() - 1);
+
+        //Return distance of closest pair rounded to 2 decimal places
+        return new BigDecimal(result).setScale(2, RoundingMode.HALF_UP).doubleValue();
+    }
+
+    private static double closestRecursiveHelper(List<Point> points, int left, int right) {
+        //Base Case occurs with 3 or fewer points
+        if (right - left <= 2) return baseCase(points, left, right);
+
+
+        //Divide and conquer
+        int mid = (left + right) / 2;
+        double midX = points.get(mid).x;
+
+        double leftDist = closestRecursiveHelper(points, left, mid);
+        double rightDist = closestRecursiveHelper(points, mid + 1, right);
+
+        double minDist = Math.min(leftDist, rightDist);
+
+        return checkBoundary(points, left, right, midX, minDist);
+    }
+
+    private static double baseCase(List<Point> points, int left, int right) {
+        // Sub-problems fitting the base case can use brute force
+        double minDist = Double.MAX_VALUE;
+        for (int i = left; i <= right; i++) {
+            for (int j = i + 1; j <= right; j++) {
+                minDist = Math.min(minDist, Point.distance(points.get(i), points.get(j)));
+            }
+        }
+        return minDist;
+    }
+
+    private static double checkBoundary(List<Point> points, int left, int right, double midX, double minDist) {
+        //Consider a boundary by the dividing line
+        List<Point> boundary = new ArrayList<>();
+        for (int i = left; i <= right; i++) {
+            if (Math.abs(points.get(i).x - midX) < minDist) boundary.add(points.get(i));
+        }
+
+        //sort by y coordinate within the boundary and check for closer points
+        boundary.sort(Comparator.comparingDouble(p -> p.y));
+        for (int i = 0; i < boundary.size(); i++) {
+            for (int j = i + 1; j < boundary.size() && (boundary.get(j).y - boundary.get(i).y) < minDist; j++) {
+                minDist = Math.min(minDist, Point.distance(boundary.get(i), boundary.get(j)));
+            }
+        }
+        return minDist;
+    }
+}