Binary TreesBinary Trees36
❯
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
❯
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Check if a Binary Tree is a Binary Search Tree

Binary Search Trees

Contents

ProblemExamplesVisualizationSolutionAlgorithmCode

Problem Statement❯

Given the root node of a binary tree, determine whether it satisfies the properties of a Binary Search Tree (BST).

  • In a BST, for every node:
    • All nodes in its left subtree have values less than the node's value.
    • All nodes in its right subtree have values greater than the node's value.
  • Additionally, both the left and right subtrees must also be binary search trees.

Examples❯

Input Tree Is BST? Description
[10, 5, 15, 2, 7, 12, 20]
true All nodes satisfy BST properties: left subtree < root < right subtree at every node.
[10, 5, 8]
false Right child 8 of root 10 violates BST rule since 8 < 10.
[5]
true Single node is a valid BST by definition.
[] true An empty tree is considered a valid BST.
[10, 5, 15, 1, 12, 6, 20]
false Node 12 in left subtree of 15 violates BST rule since it's less than 15 but appears in right subtree.
[8, 3, 10, 1, 6, null, 14, null, null, 4, 7, 13]
true All left & right subtrees maintain valid ranges. This is a classic valid BST example.

Visualization Player

Solution❯

Case 1: The Tree is Empty

An empty tree (i.e., the root node is null) is considered a valid Binary Search Tree by definition. Since there are no nodes, the BST property is trivially satisfied.

Answer: true

Case 2: The Tree is a Valid BST

If the tree follows all the rules of a BST—where for each node, all values in the left subtree are strictly less than the node, and all values in the right subtree are strictly greater—it qualifies as a valid BST.

This condition must hold not just at the root, but throughout the tree. For example, in the tree:

        2
       / \
      1   3

Both children follow the rules with respect to the root 2, and since they don’t have further children, the validation ends successfully.

Answer: true

Case 3: The Tree Violates BST Rules

A tree may appear locally valid but fail to follow BST rules deeper down the subtree. For instance:

        5
       / \
      1   4
         / \
        3   6

Here, the node 3 is in the right subtree of 5 but is less than 5. This violates the BST property that all right children (and their descendants) must be greater than the root.

Answer: false

Case 4: Subtle Violations from Deep Nodes

Sometimes violations are not obvious at the first level. Consider this tree:

        10
       / \
      5  15
         / \
        6  20

At first glance, all immediate children seem valid. However, node 6 is in the right subtree of 10 but is less than 10, which breaks the BST rule.

Such errors can only be detected by checking the value of each node against a range defined by its ancestors—not just its immediate parent.

Answer: false

Case 5: Perfectly Valid and Balanced BST

In a complete BST like this:

        8
       / \
      4   12
     / \  / \
    2  6 10 14

Each node correctly places its children to the left (smaller) and right (greater), and this is true recursively throughout the tree. It passes all BST checks.

Answer: true

Algorithm Steps❯

  1. If the tree is empty, return true.
  2. For each node, check if its value is within the valid range (min and max).
  3. If the node's value does not satisfy min < node.val < max, return false.
  4. Recursively verify the left subtree with an updated upper bound (max = node.val) and the right subtree with an updated lower bound (min = node.val).
  5. If all nodes satisfy the BST property, return true.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def isBST(root, min_val=float('-inf'), max_val=float('inf')):
    if not root:
        return True
    if not (min_val < root.val < max_val):
        return False
    return isBST(root.left, min_val, root.val) and isBST(root.right, root.val, max_val)

# Example usage:
if __name__ == '__main__':
    # Construct BST:      2
    #                   /   \
    #                  1     3
    root = TreeNode(2, TreeNode(1), TreeNode(3))
    print(isBST(root))