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package algs9; // section 9.8
import stdlib.*;
import java.util.Arrays;
import algs12.Point2D;
import algs22.Merge;
/* ***********************************************************************
 *  Compilation:  javac ClosestPair.java
 *  Execution:    java ClosestPair < input.txt
 *  Dependencies: Point2D.java
 *
 *  Given N points in the plane, find the closest pair in N log N time.
 *
 *  Note: could speed it up by comparing square of Euclidean distances
 *  instead of Euclidean distances.
 *
 *  % java ClosestPair < rs1423.txt
 *  15.0 from (11364.0, 12693.0) to (11373.0, 12705.0)
 *
 *************************************************************************/


public class ClosestPair {
  // closest pair of points and their Euclidean distance
  private Point2D best1, best2;
  private double bestDistance = Double.POSITIVE_INFINITY;

  public ClosestPair(Point2D[] points) {
    int N = points.length;
    if (N <= 1) return;

    // sort by x-coordinate (breaking ties by y-coordinate)
    Point2D[] pointsByX = new Point2D[N];
    for (int i = 0; i < N; i++) pointsByX[i] = points[i];
    Arrays.sort(pointsByX, Point2D.X_ORDER);

    // check for coincident points
    for (int i = 0; i < N-1; i++) {
      if (pointsByX[i].equals(pointsByX[i+1])) {
        bestDistance = 0.0;
        best1 = pointsByX[i];
        best2 = pointsByX[i+1];
        return;
      }
    }

    // sort by y-coordinate (but not yet sorted)
    Point2D[] pointsByY = new Point2D[N];
    for (int i = 0; i < N; i++) pointsByY[i] = pointsByX[i];

    // auxiliary array
    Point2D[] aux = new Point2D[N];

    closest(pointsByX, pointsByY, aux, 0, N-1);
  }

  // find closest pair of points in pointsByX[lo..hi]
  // precondition:  pointsByX[lo..hi] and pointsByY[lo..hi] are the same sequence of points
  // precondition:  pointsByX[lo..hi] sorted by x-coordinate
  // postcondition: pointsByY[lo..hi] sorted by y-coordinate
  private double closest(Point2D[] pointsByX, Point2D[] pointsByY, Point2D[] aux, int lo, int hi) {
    if (hi <= lo) return Double.POSITIVE_INFINITY;

    int mid = lo + (hi - lo) / 2;
    Point2D median = pointsByX[mid];

    // compute closest pair with both endpoints in left subarray or both in right subarray
    double delta1 = closest(pointsByX, pointsByY, aux, lo, mid);
    double delta2 = closest(pointsByX, pointsByY, aux, mid+1, hi);
    double delta = Math.min(delta1, delta2);

    // merge back so that pointsByY[lo..hi] are sorted by y-coordinate
    Merge.merge(pointsByY, aux, lo, mid, hi);

    // aux[0..M-1] = sequence of points closer than delta, sorted by y-coordinate
    int M = 0;
    for (int i = lo; i <= hi; i++) {
      if (Math.abs(pointsByY[i].x() - median.x()) < delta)
        aux[M++] = pointsByY[i];
    }

    // compare each point to its neighbors with y-coordinate closer than delta
    for (int i = 0; i < M; i++) {
      // a geometric packing argument shows that this loop iterates at most 7 times
      for (int j = i+1; (j < M) && (aux[j].y() - aux[i].y() < delta); j++) {
        double distance = aux[i].distanceTo(aux[j]);
        if (distance < delta) {
          delta = distance;
          if (distance < bestDistance) {
            bestDistance = delta;
            best1 = aux[i];
            best2 = aux[j];
            // StdOut.println("better distance = " + delta + " from " + best1 + " to " + best2);
          }
        }
      }
    }
    return delta;
  }

  public Point2D either() { return best1; }
  public Point2D other()  { return best2; }

  public double distance() {
    return bestDistance;
  }


  public static void main(String[] args) {
    StdIn.fromFile ("data/rs1423.txt");

    int N = StdIn.readInt();
    Point2D[] points = new Point2D[N];
    for (int i = 0; i < N; i++) {
      double x = StdIn.readDouble();
      double y = StdIn.readDouble();
      points[i] = new Point2D(x, y);
    }
    ClosestPair closest = new ClosestPair(points);
    StdOut.println(closest.distance() + " from " + closest.either() + " to " + closest.other());
  }

}