# Display List Code Below:
def height(node):
	if (node == None):
		return 0
	return 1 + max(height(node.left), height(node.right))

def draw_node(output, link_above, node, level, p, link_char):
	if (node == None): 
 		return

	out = "["
	h = len(output)
	SP = " "

	if (p < 0):
		for s in output:
			if (s):
				s = " "*(-1*p) + s
    
		for s in link_above:
			if (s):
				s = " "*(-1*p) + s

	if level < h - 1:
		p = max(p, len(output[level + 1]))
	if (level > 0):
		p = max(p, len(output[level - 1]))
	p = max(p, len(output[level]))

	# Fill in to left
	if (node.left):
		leftData = SP + str(node.left.data) + SP
		draw_node(output, link_above, node.left, level + 1, p - len(leftData),'L')
		p = max(p, len(output[level + 1]))

	# Enter this data
	space = p - len(output[level])
	if (space > 0):
		output[level] += (' ' * space)
	node_data = SP + str(node.data) + SP
	output[level] += node_data

	# Add vertical link above
	space = p + len(SP) - len(link_above[level])
	if (space > 0):
		link_above[level] += (' ' * space)
	link_above[level] += link_char

	# Fill in to right
	if (node.right):
		draw_node(output, link_above, node.right, level + 1, len(output[level]),'R')
  
def display_tree(root):
	if (root == None):
		print("\tNone")
	h = height(root)
	output = []
	link_above = []
	for i in range(0,h): 
				output.append("")
				link_above.append("")
	draw_node(output, link_above, root, 0, 5, ' ')

	# Create link lines
	for i in range(h):
		for j in range(len(link_above[i])):
			if (link_above[i][j] != ' '):
				size = len(output[i - 1])
				if (size < j + 1):
					output[i - 1] += " " *(j + 1 - size)
				jj = j
				if (link_above[i][j] == 'L'):
					while (output[i - 1][jj] == ' '):
						jj += 1
					for k in range(j+1, jj-1):
						str1 = output[i - 1]
						list1 = list(str1)
						list1[k] = '_'
						output[i - 1] = ''.join(list1)
				elif(link_above[i][j] == 'R'):
					while (output[i - 1][jj] == ' '):
						jj-=1
					
					# k = j-1
					for k in range(j-1,jj+1,-1):
						temp = output[i - 1]
						list1 = list(temp)
						list1[k] = '_'
						output[i - 1] = ''.join(list1)
						k = k - 1
      
				str1 = link_above[i]
				list1 = list(str1)
				list1[j] = '|'
				link_above[i] = ''.join(list1)
					
	# Output
	for i in range(h):
		if (i):
			print("\t" , link_above[i])
		print("\t" , output[i])

from TreeNode import *
from BinaryTree import *
import math

# Function to check if a given binary tree is a valid BST or not
def validate_bst(root):
    # Explicitly using List object to pass prev by reference because
    # in python, Pass-by-object-reference is used and simple variable is not an object
    prev = [-math.inf]
    return validate_bst_helper(root, prev)

# Helper function for validate_bst
def validate_bst_helper(root, prev):
    if not root:
         return True
    # If left subtree is not a valid BST, return False
    if not validate_bst_helper(root.left, prev):
        return False
    # If current node is less than or equal to previous node, the tree is not a valid BST
    if root.data <= prev[0]:
        return False
    prev[0] = root.data
    # Checking right subtree
    return validate_bst_helper(root.right, prev)

# Driver code
def main():
    # Create a list of list of TreeNode objects to represent binary trees
    list_of_trees = [ [TreeNode(5), TreeNode(3), TreeNode(2), TreeNode(6), TreeNode(4)],
                    [TreeNode(6), TreeNode(2), TreeNode(5), TreeNode(4), TreeNode(7)],
                    [TreeNode(4), TreeNode(2), TreeNode(5), TreeNode(1), TreeNode(3)],
                    [TreeNode(7), TreeNode(2), TreeNode(5), TreeNode(4), TreeNode(8)],
                    [TreeNode(9), TreeNode(5), TreeNode(7), TreeNode(1), TreeNode(3)],
                    [TreeNode(5), TreeNode(3), TreeNode(8), TreeNode(2), TreeNode(4), None, TreeNode(9)]
    ]

    # Create the binary trees using the BinaryTree class
    input_trees = []
    for list_of_nodes in list_of_trees:
        tree = BinaryTree(list_of_nodes)
        input_trees.append(tree)

    # Print the input trees
    x = 1
    for tree in input_trees:
        print(x, ".\tInput Tree:", sep = "")
        display_tree(tree.root)
        x += 1
        print("\n\tValid BST: ", validate_bst(tree.root), sep = "")
        print("-" * 100)
    
if __name__ == '__main__':
    main()