# Validate Binary Search Tree in Python

Suppose we have a binary tree, determine to check whether it is a valid binary search tree (BST) or not. Assume a BST is defined as follows –

• The left subtree of a node holds only nodes with keys smaller than the node's key.
• The right subtree of a node holds only nodes with keys larger than the node's key.
• Both the left and right subtrees must also be binary search trees.

So if the tree is like –

The output will be true.

To solve this, we will follow these steps –

• Create one recursive function called solve(), this will take root, min and max, the method will be like
• if root is null, then return true
• if value of root <= min or value of root >= max, then return false
• return the (solve(left of root, min, root value) AND solve(right of root, root value, max))
• call the solve() method initially, by passing root, and – inf as min and inf as max.

## Example(Python)

Let us see the following implementation to get a better understanding −

Live Demo

class TreeNode:
def __init__(self, data, left = None, right = None):
self.data = data
self.left = left
self.right = right
def insert(temp,data):
que = []
que.append(temp)
while (len(que)):
temp = que[0]
que.pop(0)
if (not temp.left):
if data is not None:
temp.left = TreeNode(data)
else:
temp.left = TreeNode(0)
break
else:
que.append(temp.left)
if (not temp.right):
if data is not None:
temp.right = TreeNode(data)
else:
temp.right = TreeNode(0)
break
else:
que.append(temp.right)
def make_tree(elements):
Tree = TreeNode(elements[0])
for element in elements[1:]:
insert(Tree, element)
return Tree
class Solution(object):
def isValidBST(self, root):
return self.solve(root,-1000000000000000000000,1000000000000000000000)
def solve(self,root,min_val,max_val):
if root == None or root.data == 0:
return True
if (root.data <= min_val or root.data >=max_val):
return False
return self.solve(root.left,min_val,root.data) and self.solve(root.right,root.data,max_val)
ob1 = Solution()
tree = make_tree([3,1,4,None,2,None,5])
print(ob1.isValidBST(tree))
tree = make_tree([5,1,4,None,None,3,6])
print(ob1.isValidBST(tree))

## Input

[3,1,4,null,2,null,5]
[5,1,4,null,null,3,6]

## Output

true
false