# A Python program to demonstrate operations of KD tree

import sys

# Number of dimensions

k = 2

# A structure to represent node of kd tree

class Node:

    def __init__(self, point):

        self.point = point

        self.left = None

        self.right = None

# A method to create a node of K D tree

def newNode(point):

    return Node(point)

# Inserts a new node and returns root of modified tree

# The parameter depth is used to decide axis of comparison

def insertRec(root, point, depth):

    # Tree is empty?

    if not root:

        return newNode(point)

    # Calculate current dimension (cd) of comparison

    cd = depth % k

    # Compare the new point with root on current dimension 'cd'

    # and decide the left or right subtree

    if point[cd] < root.point[cd]:

        root.left = insertRec(root.left, point, depth + 1)

    else:

        root.right = insertRec(root.right, point, depth + 1)

    return root

# Function to insert a new point with given point in

# KD Tree and return new root. It mainly uses above recursive

# function "insertRec()"

def insert(root, point):

    return insertRec(root, point, 0)

# A utility method to determine if two Points are same

# in K Dimensional space

def arePointsSame(point1, point2):

    # Compare individual coordinate values

    for i in range(k):

        if point1[i] != point2[i]:

            return False

    return True

# Searches a Point represented by "point[]" in the K D tree.

# The parameter depth is used to determine current axis.

def searchRec(root, point, depth):

    # Base cases

    if not root:

        return False

    if arePointsSame(root.point, point):

        return True

    # Current dimension is computed using current depth and total

    # dimensions (k)

    cd = depth % k

    # Compare point with root with respect to cd (Current dimension)

    if point[cd] < root.point[cd]:

        return searchRec(root.left, point, depth + 1)

    return searchRec(root.right, point, depth + 1)

# Searches a Point in the K D tree. It mainly uses

# searchRec()

def search(root, point):

    # Pass current depth as 0

    return searchRec(root, point, 0)

# Driver program to test above functions

if __name__ == '__main__':

    root = None

    points = [[3, 6], [17, 15], [13, 15], [6, 12], [9, 1], [2, 7], [10, 19]]

    n = len(points)

    for i in range(n):

        root = insert(root, points[i])

    point1 = [10, 19]

    if search(root, point1):

        print("Found")

    else:

        print("Not Found")

    point2 = [12, 19]

    if search(root, point2):

        print("Found")

    else:

        print("Not Found")

# This code is contributed by Prajwal Kandekar