# Is This a Binary Search Tree?

### Problem Statement :

```For the purposes of this challenge, we define a binary tree to be a binary search tree with the following ordering requirements:

The data value of every node in a node's left subtree is less than the data value of that node.
The data value of every node in a node's right subtree is greater than the data value of that node.
Given the root node of a binary tree, can you determine if it's also a binary search tree?

Complete the function in your editor below, which has 1 parameter: a pointer to the root of a binary tree. It must return a boolean denoting whether or not the binary tree is a binary search tree. You may have to write one or more helper functions to complete this challenge.

Input Format

You are not responsible for reading any input from stdin. Hidden code stubs will assemble a binary tree and pass its root node to your function as an argument.

Constraints

0 <= data <= 10^4

Output Format

You are not responsible for printing any output to stdout. Your function must return true if the tree is a binary search tree; otherwise, it must return false. Hidden code stubs will print this result as a Yes or No answer on a new line.```

### Solution :

```                            ```Solution in C :

In C ++ :

The Node struct is defined as follows:
struct Node {
int data;
Node* left;
Node* right;
}
*/  enum comp {LESS, GREATER};
bool checkBST(Node* root,int minVal, int maxVal ){
if(root==0)
return true;
int nVal=root->data;
if(nVal<=minVal || nVal>=maxVal)
return false;
return checkBST(root->left,minVal,nVal) && checkBST(root->right,nVal, maxVal);
}
bool checkBST(Node* root) {
if(root==0)
return true;
return checkBST(root->left, -1, root->data) && checkBST(root->right,root->data, 10001);
}

In Java :

The Node class is defined as follows:
class Node {
int data;
Node left;
Node right;
}
*/
private boolean checkBST(Node n, int min, int max) {
if(n == null) return true;
return n.data > min && n.data < max && checkBST(n.left, min, n.data) && checkBST(n.right, n.data, max);
}

boolean checkBST(Node root) {
if(root == null) return true;
if(count == 0) return true;
return checkBST(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
}

In  python3 :

from collections import deque
""" Node is defined as
class node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
"""
def check_binary_search_tree_(root, lowest_value=0, highest_value=10000):
min_v = lowest_value - 1
max_v = highest_value + 1
q = deque([(root, min_v, max_v)])
while q:
node, min_val, max_val = q.popleft()
if not node: continue
if node.data >= max_val or node.data <= min_val: return False
if node.left: q.append((node.left, min_val, node.data))
if node.right: q.append((node.right, node.data, max_val))
return True```
```

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