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

Find the kth Largest Element in a Binary Search Tree - Algorithm, Visualization, Examples

Problem Statement

You are given a Binary Search Tree (BST) and an integer k. Your task is to find the kth largest element in the BST. In a BST, the left subtree of a node contains nodes with values less than the node’s value, and the right subtree contains nodes with values greater than the node’s value.

The tree will contain unique values, and k is guaranteed to be a positive integer no greater than the number of nodes in the tree.

Examples

Input Tree (Level Order) k Kth Largest Description
[5, 3, 7, 2, 4, 6, 8]
3 6 In descending order [8, 7, 6, 5, 4, 3, 2], the 3rd largest is 6.
[20, 10, 30, 5, 15, 25, 35]
1 35 Largest element in the BST is 35 (rightmost leaf).
[15, 10, 20, null, 12, 17, 25]
5 12 Descending order is [25, 20, 17, 15, 12, 10]; 5th largest is 12.
[50, 30, 70, 20, 40, 60, 80]
7 20 In descending order [80, 70, 60, 50, 40, 30, 20]; 7th largest is 20.
[10]
1 10 Single node is both the largest and smallest, so 1st largest is 10.
[] 1 null Empty tree has no nodes, so kth largest is undefined (null).

Visualization Player

Solution

To find the kth largest element in a BST, we can use the property that an in-order traversal gives nodes in ascending order. So, by performing a reverse in-order traversal (right → node → left), we can access nodes in descending order. This allows us to find the kth largest node without needing to store all elements.

Case 1: Normal Case

In a typical BST with multiple nodes, we perform a reverse in-order traversal. At each node visited, we increment a counter. Once the counter equals k, we record that node’s value as the answer. For example, in a BST like [5,3,6,2,4,null,null,1], if k=3, we visit nodes in the order [6,5,4,…] and stop at the 3rd visited node, which is 4.

Case 2: k = 1 (Largest Element)

When k = 1, we're looking for the largest element in the BST. The traversal begins from the rightmost node, which will be the largest due to BST properties. So, the answer is simply the value of the rightmost node.

Case 3: Small BST

In small trees like [2,1,3], reverse traversal gives us [3,2,1]. The kth largest can be identified quickly by counting the nodes visited. For k = 2, we pick 2 as the result.

Case 4: Single Node Tree

If the BST has only one node, such as [5], the only possible valid value for k is 1. In this case, the answer is the node itself, i.e., 5.

Case 5: Empty Tree

If the BST is empty (no nodes), then there are no elements to choose from. Any value of k would be invalid in this context, and we should return an error message or handle this case explicitly in code to avoid runtime errors.

Algorithm Steps

  1. Given a binary search tree (BST) and an integer k.
  2. Perform a reverse in-order traversal (visit right subtree, then node, then left subtree) to process nodes in descending order.
  3. Maintain a counter of visited nodes.
  4. When the counter equals k, record the current node's value as the kth largest element and terminate the traversal.
  5. Return the recorded value.

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 kthLargest(root, k):
    count = 0
    result = None

    def traverse(node):
        nonlocal count, result
        if not node or result is not None:
            return
        traverse(node.right)
        count += 1
        if count == k:
            result = node.val
            return
        traverse(node.left)

    traverse(root)
    return result

# Example usage:
if __name__ == '__main__':
    # Construct a sample BST:
    #         5
    #        / \
    #       3   7
    #      / \   \
    #     2   4   8
    root = TreeNode(5, TreeNode(3, TreeNode(2), TreeNode(4)), TreeNode(7, None, TreeNode(8)))
    k = 2
    print(kthLargest(root, k))