Data Structures Tutorial

Data Structures Tutorial Asymptotic Notation Structure and Union Array Data Structure Linked list Data Structure Type of Linked list Advantages and Disadvantages of linked list Queue Data Structure Implementation of Queue Stack Data Structure Implementation of Stack Sorting Insertion sort Quick sort Selection sort Heap sort Merge sort Bucket sort Count sort Radix sort Shell sort Tree Traversal of the binary tree Binary search tree Graph Spanning tree Linear Search Binary Search Hashing Collision Resolution Techniques

Misc Topic:

Priority Queue in Data Structure Deque in Data Structure Difference Between Linear And Non Linear Data Structures Queue Operations In Data Structure About Data Structures Data Structures Algorithms Types of Data Structures Big O Notations Introduction to Arrays Introduction to 1D-Arrays Operations on 1D-Arrays Introduction to 2D-Arrays Operations on 2D-Arrays Strings in Data Structures String Operations Application of 2D array Bubble Sort Insertion Sort Sorting Algorithms What is DFS Algorithm What Is Graph Data Structure What is the difference between Tree and Graph What is the difference between DFS and BFS Bucket Sort Dijkstra’s vs Bellman-Ford Algorithm Linear Queue Data Structure in C Stack Using Array Stack Using Linked List Recursion in Fibonacci Stack vs Array What is Skewed Binary Tree Primitive Data Structure in C Dynamic memory allocation of structure in C Application of Stack in Data Structures Binary Tree in Data Structures Heap Data Structure Recursion - Factorial and Fibonacci What is B tree what is B+ tree Huffman tree in Data Structures Insertion Sort vs Bubble Sort Adding one to the number represented an array of digits Bitwise Operators and their Important Tricks Blowfish algorithm Bubble Sort vs Selection Sort Hashing and its Applications Heap Sort vs Merge Sort Insertion Sort vs Selection Sort Merge Conflicts and ways to handle them Difference between Stack and Queue AVL tree in data structure c++ Bubble sort algorithm using Javascript Buffer overflow attack with examples Find out the area between two concentric circles Lowest common ancestor in a binary search tree Number of visible boxes putting one inside another Program to calculate the area of the circumcircle of an equilateral triangle Red-black Tree in Data Structures Strictly binary tree in Data Structures 2-3 Trees and Basic Operations on them Asynchronous advantage actor-critic (A3C) Algorithm Bubble Sort vs Heap Sort Digital Search Tree in Data Structures Minimum Spanning Tree Permutation Sort or Bogo Sort Quick Sort vs Merge Sort Boruvkas algorithm Bubble Sort vs Quick Sort Common Operations on various Data Structures Detect and Remove Loop in a Linked List How to Start Learning DSA Print kth least significant bit number Why is Binary Heap Preferred over BST for Priority Queue Bin Packing Problem Binary Tree Inorder Traversal Burning binary tree Equal Sum What is a Threaded Binary Tree? What is a full Binary Tree? Bubble Sort vs Merge Sort B+ Tree Program in Q language Deletion Operation from A B Tree Deletion Operation of the binary search tree in C++ language Does Overloading Work with Inheritance Balanced Binary Tree Binary tree deletion Binary tree insertion Cocktail Sort Comb Sort FIFO approach Operations of B Tree in C++ Language Recaman’s Sequence Tim Sort Understanding Data Processing

Lowest common ancestor in a binary search tree

Suppose you have given two values of nodes in a binary search tree. You have to find out the lowest common ancestor between the nodes.

Let’s take an example tree-

Binary Tree

For the above binary search tree, if we take inputs 3 and 5, then the output will be 4. It is supposed that there will be a particular output for every input.

Input- 0, 4

Output- 2

Explanation- 0 and 4 both nodes are in the lower level of 2. 2 is the closest node of both nodes, so it is the lowest common ancestor.

Note: -

What is the lowest common ancestor in a binary search tree?

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes m and n as the lowest node in T that has both m and n as descendants (where we allow a node to be a descendant of itself ).”


Step 1: Start

Step 2: Two values are taken from the user

Step 3: A tree is created

Step 4: A recursive function called. This function takes two input values and one tree node.

Step 5: If the values are less than the node value, the function is again called with the left node.

Step 6: If the values are greater than the node value, the function is called with the right node.

Step 7: If steps 5 and 6 are not satisfying, then the node value will be returned.

Step 8: The returned value will be printed.

Step 9: Stop.

Explanation of Algorithm: We take the above-given tree, and inputs are 0 and 5. If we call the recursive function with the root node and values, then the function is again called with the node's left node because 0 and 5 are both less than 6. After that, values are compared with node's value two, and here we get our answer because 0 is less than 2, but 5 is greater than 2. The function will return 2.


#include <bits/stdc++.h>
using namespace std;
class node
	int value;
	node* left, *right;
/* Function to find LCA of m and n.
The function assumes that both
m and n are present in BST */
node *fun(node* root, int m, int n)
	if (root == NULL) 
                return NULL;
	// If both m and n are smaller
	// than root, then LCA lies in left
	if (root->value > m && root->value > n)
		return fun(root->left, m, n);
	// If both m and n are greater than
	// root, then LCA lies in right
	if (root->value < m && root->value < n)
		return fun(root->right, n1, n2);
	return root;
/* Helper function that allocates
a new node with the given data.*/
node* insert(int data)
	node* root = new node();
	root->value = data;
	root->left = root->right = NULL;
/* Driver code*/
int main()
	// Let us construct the BST
	// shown in the above figure
	node *root = insert(6);
	root->left = insert(2);
	root->right = insert(8);
	root->left->left = insert(0);
	root->left->right = insert(4);
            root->right->left = insert(7);
	root->right->right = insert(9);
	root->left->right->left = insert(3);
	root->left->right->right = insert(5);
	int m = 0, n = 4;
	node *t = fun(root, m, n);
	cout << "LCA of " << m << " and " << n << " is " << t->value<<endl;
	m = 4, n = 7;
	t = fun(root, n1, n2);
	cout<<"LCA of " << m << " and " << n << " is " << t->value << endl;
	m = 0, n = 2;
	t = fun(root, m, n);
	cout << "LCA of " << m << " and " << n << " is " << t->value << endl;
	return 0;


LCA of 0 and 4 is 2
LCA of 4 and 7 is 6
LCA of 0 and 2 is 2

Complexity Analysis

Time complexity- Here, the recursion continues till we find the LCA. So, the complexity directly depends on the height of the tree. Complexity will be O(h).

Space complexity- In this recursive solution, we use constant memory. So, space complexity will be O(1).

Note- The above code and algorithm are based on a recursive approach. The main drawback of this solution is for recursion purposes, and we have to allocate the memory of the function stack. But if we use an iterative approach, then we can avoid this problem. In the iterative solution, we will use the loop in the main function. The loop will continue till we get the answer. The root is updated in every iteration by the left node or right node according to steps 5, 6, and 7 of the algorithm.