
- 1Overview of DSA Problem Solving Techniques
- 2Brute Force Technique in DSA
- 3Greedy Algorithm Technique in DSA
- 4Divide and Conquer Technique in DSA
- 5Dynamic Programming Technique in DSA
- 6Backtracking Technique in DSA
- 7Recursion Technique in DSA
- 8Sliding Window Technique in DSA
- 9Two Pointers Technique
- 10Binary Search Technique
- 11Tree / Graph Traversal Technique in DSA
- 12Bit Manipulation Technique in DSA
- 13Hashing Technique
- 14Heaps Technique in DSA

- 1Find Maximum and Minimum in Array using Loop
- 2Find Second Largest in Array
- 3Find Second Smallest in Array
- 4Reverse Array using Two Pointers
- 5Check if Array is Sorted
- 6Remove Duplicates from Sorted Array
- 7Left Rotate an Array by One Place
- 8Left Rotate an Array by K Places
- 9Move Zeroes in Array to End
- 10Linear Search in Array
- 11Union of Two Arrays
- 12Find Missing Number in Array
- 13Max Consecutive Ones in Array
- 14Find Kth Smallest Element
- 15Longest Subarray with Given Sum (Positives)
- 16Longest Subarray with Given Sum (Positives and Negatives)
- 17Find Majority Element in Array (more than n/2 times)
- 18Find Majority Element in Array (more than n/3 times)
- 19Maximum Subarray Sum using Kadane's Algorithm
- 20Print Subarray with Maximum Sum
- 21Stock Buy and Sell
- 22Rearrange Array Alternating Positive and Negative Elements
- 23Next Permutation of Array
- 24Leaders in an Array
- 25Longest Consecutive Sequence in Array
- 26Count Subarrays with Given Sum
- 27Sort an Array of 0s, 1s, and 2s
- 28Two Sum Problem
- 29Three Sum Problem
- 304 Sum Problem
- 31Find Length of Largest Subarray with 0 Sum
- 32Find Maximum Product Subarray

- 1Binary Search in Array using Iteration
- 2Find Lower Bound in Sorted Array
- 3Find Upper Bound in Sorted Array
- 4Search Insert Position in Sorted Array (Lower Bound Approach)
- 5Floor and Ceil in Sorted Array
- 6First Occurrence in a Sorted Array
- 7Last Occurrence in a Sorted Array
- 8Count Occurrences in Sorted Array
- 9Search Element in a Rotated Sorted Array
- 10Search in Rotated Sorted Array with Duplicates
- 11Minimum in Rotated Sorted Array
- 12Find Rotation Count in Sorted Array
- 13Search Single Element in Sorted Array
- 14Find Peak Element in Array
- 15Square Root using Binary Search
- 16Nth Root of a Number using Binary Search
- 17Koko Eating Bananas
- 18Minimum Days to Make M Bouquets
- 19Find the Smallest Divisor Given a Threshold
- 20Capacity to Ship Packages within D Days
- 21Kth Missing Positive Number
- 22Aggressive Cows Problem
- 23Allocate Minimum Number of Pages
- 24Split Array - Minimize Largest Sum
- 25Painter's Partition Problem
- 26Minimize Maximum Distance Between Gas Stations
- 27Median of Two Sorted Arrays of Different Sizes
- 28K-th Element of Two Sorted Arrays

- 1Reverse Words in a String
- 2Find the Largest Odd Number in a Numeric String
- 3Find Longest Common Prefix in Array of Strings
- 4Find Longest Common Substring
- 5Check If Two Strings Are Isomorphic - Optimal HashMap Solution
- 6Check String Rotation using Concatenation - Optimal Approach
- 7Check if Two Strings Are Anagrams - Optimal Approach
- 8Sort Characters by Frequency - Optimal HashMap and Heap Approach
- 9Find Longest Palindromic Substring - Dynamic Programming Approach
- 10Find Longest Palindromic Substring Without Dynamic Programming
- 11Remove Outermost Parentheses in String
- 12Find Maximum Nesting Depth of Parentheses - Optimal Stack-Free Solution
- 13Convert Roman Numerals to Integer - Efficient Approach
- 14Convert Integer to Roman Numeral - Step-by-Step for Beginners
- 15Implement Atoi - Convert String to Integer in Java
- 16Count Number of Substrings in a String - Explanation with Formula
- 17Edit Distance Problem
- 18Calculate Sum of Beauty of All Substrings - Optimal Approach
- 19Reverse Each Word in a String - Optimal Approach

- 1Check if i-th bit is set
- 2Check if a Number is Even/Odd
- 3Check if a Number is Power of 2
- 4Count Number of Set Bits
- 5Swap Two Numbers using XOR
- 6Divide Two Integers without using Multiplication, Division and Modulus Operator
- 7Count Number of Bits to Flip to Convert A to B
- 8Find the Number that Appears Odd Number of Times
- 9Power Set
- 10Find XOR of Numbers from L to R
- 11Prime Factors of a Number
- 12All Divisors of Number
- 13Sieve of Eratosthenes
- 14Find Prime Factorisation of a Number using Sieve
- 15Power(n,x)


- 1Preorder Traversal of a Binary Tree using Recursion
- 2Preorder Traversal of a Binary Tree using Iteration
- 3Inorder Traversal of a Binary Tree using Recursion
- 4Inorder Traversal of a Binary Tree using Iteration
- 5Postorder Traversal of a Binary Tree Using Recursion
- 6Postorder Traversal of a Binary Tree using Iteration
- 7Level Order Traversal of a Binary Tree using Recursion
- 8Level Order Traversal of a Binary Tree using Iteration
- 9Reverse Level Order Traversal of a Binary Tree using Iteration
- 10Reverse Level Order Traversal of a Binary Tree using Recursion
- 11Find Height of a Binary Tree
- 12Find Diameter of a Binary Tree
- 13Find Mirror of a Binary Tree
- 14Left View of a Binary Tree
- 15Right View of a Binary Tree
- 16Top View of a Binary Tree
- 17Bottom View of a Binary Tree
- 18Zigzag Traversal of a Binary Tree
- 19Check if a Binary Tree is Balanced
- 20Diagonal Traversal of a Binary Tree
- 21Boundary Traversal of a Binary Tree
- 22Construct a Binary Tree from a String with Bracket Representation
- 23Convert a Binary Tree into a Doubly Linked List
- 24Convert a Binary Tree into a Sum Tree
- 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
- 26Check if a Binary Tree is a Sum Tree
- 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
- 28Lowest Common Ancestor (LCA) in a Binary Tree
- 29Solve the Tree Isomorphism Problem
- 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
- 31Check if Two Binary Trees are Mirror Images
- 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
- 33Print All Paths in a Binary Tree with a Given Sum
- 34Find the Distance Between Two Nodes in a Binary Tree
- 35Find the kth Ancestor of a Node in a Binary Tree
- 36Find All Duplicate Subtrees in a Binary Tree

- 1Find a Value in a Binary Search Tree
- 2Delete a Node in a Binary Search Tree
- 3Find the Minimum Value in a Binary Search Tree
- 4Find the Maximum Value in a Binary Search Tree
- 5Find the Inorder Successor in a Binary Search Tree
- 6Find the Inorder Predecessor in a Binary Search Tree
- 7Check if a Binary Tree is a Binary Search Tree
- 8Find the Lowest Common Ancestor of Two Nodes in a Binary Search Tree
- 9Convert a Binary Tree into a Binary Search Tree
- 10Balance a Binary Search Tree
- 11Merge Two Binary Search Trees
- 12Find the kth Largest Element in a Binary Search Tree
- 13Find the kth Smallest Element in a Binary Search Tree
- 14Flatten a Binary Search Tree into a Sorted List

- 1Breadth-First Search in Graphs
- 2Depth-First Search in Graphs
- 3Number of Provinces in an Undirected Graph
- 4Connected Components in a Matrix
- 5Rotten Oranges Problem - BFS in Matrix
- 6Flood Fill Algorithm - Graph Based
- 7Detect Cycle in an Undirected Graph using DFS
- 8Detect Cycle in an Undirected Graph using BFS
- 9Distance of Nearest Cell Having 1 - Grid BFS
- 10Surrounded Regions in Matrix using Graph Traversal
- 11Number of Enclaves in Grid
- 12Word Ladder - Shortest Transformation using Graph
- 13Word Ladder II - All Shortest Transformation Sequences
- 14Number of Distinct Islands using DFS
- 15Check if a Graph is Bipartite using DFS
- 16Topological Sort Using DFS
- 17Topological Sort using Kahn's Algorithm
- 18Cycle Detection in Directed Graph using BFS
- 19Course Schedule - Task Ordering with Prerequisites
- 20Course Schedule 2 - Task Ordering Using Topological Sort
- 21Find Eventual Safe States in a Directed Graph
- 22Alien Dictionary Character Order
- 23Shortest Path in Undirected Graph with Unit Distance
- 24Shortest Path in DAG using Topological Sort
- 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
- 26Dijkstra’s Algorithm Using Priority Queue
- 27Shortest Distance in a Binary Maze using BFS
- 28Path With Minimum Effort in Grid using Graphs
- 29Cheapest Flights Within K Stops - Graph Problem
- 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
- 31Minimum Multiplications to Reach End - Graph BFS
- 32Bellman-Ford Algorithm for Shortest Paths
- 33Floyd Warshall Algorithm for All-Pairs Shortest Path
- 34Find the City With the Fewest Reachable Neighbours
- 35Minimum Spanning Tree in Graphs
- 36Prim's Algorithm for Minimum Spanning Tree
- 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
- 38Kruskal's Algorithm - Minimum Spanning Tree
- 39Minimum Operations to Make Network Connected
- 40Most Stones Removed with Same Row or Column
- 41Accounts Merge Problem using Disjoint Set Union
- 42Number of Islands II - Online Queries using DSU
- 43Making a Large Island Using DSU
- 44Bridges in Graph using Tarjan's Algorithm
- 45Articulation Points in Graphs
- 46Strongly Connected Components using Kosaraju's Algorithm
Hashing Technique in DSA | Basics, Applications & Pseudocode
Hashing in a Nutshell
- Maps data of arbitrary size to fixed-size values using hash functions.
- Supports fast lookup, insertion, and deletion — usually in constant time O(1).
- Commonly used in data structures like hash tables, sets, and maps.
What is Hashing Technique?
Hashing is a technique used to convert a given input into a fixed-size value (called a hash code or hash value) using a function known as a hash function. The result of the hash function is typically used as an index to store the data in an array-like data structure (commonly a hash table).
Hashing allows us to perform operations like search, insert, and delete in O(1) average time, making it one of the most powerful techniques in data structure design and algorithmic problem solving.
How Hashing Works
- Use a hash function to convert the key into an index.
- Store the value at that index in a hash table.
- If two keys hash to the same index, resolve the collision using a method like chaining or open addressing.
Pseudocode
// Basic Hash Table Insertion using Chaining
function insert(key, value):
index = hashFunction(key)
if hashTable[index] is empty:
hashTable[index] = new list
hashTable[index].append((key, value))
// Search for a value
function search(key):
index = hashFunction(key)
for (k, v) in hashTable[index]:
if k == key:
return v
return null
Hash Function
A hash function is used to map a large set of possible keys to a smaller range of indices. A good hash function should:
- Be fast to compute
- Distribute keys uniformly across the table
- Minimize collisions (cases where multiple keys hash to the same index)
Example: For strings, a simple hash function might be:
function hashFunction(key):
hash = 0
for char in key:
hash = (hash * 31 + ASCII(char)) % TABLE_SIZE
return hash
Collision Resolution Techniques
Since multiple keys can hash to the same index, collisions must be handled. Common strategies include:
1. Chaining
- Each bucket holds a linked list of key-value pairs.
- Insert new elements at the head or tail of the list.
2. Open Addressing
- When a collision occurs, search the table for the next free slot.
- Variants include:
- Linear Probing: Check next slot, then next, etc.
- Quadratic Probing: Check index + 1², 2², etc.
- Double Hashing: Use second hash function to compute step size.
Applications of Hashing
- Implementing dictionaries/maps (e.g., HashMap, HashSet)
- Checking for duplicates in an array
- Counting frequency of elements
- Detecting cycles in graphs (e.g., using visited sets)
- Caching with LRU (Least Recently Used) strategies
Example: Frequency Counter
Given an array of integers, count how many times each number appears:
function countFrequency(arr):
freq = {}
for num in arr:
if num in freq:
freq[num] += 1
else:
freq[num] = 1
return freq
Time and Space Complexity
- Time Complexity: O(1) average for insert, search, and delete
- Worst Case: O(n) — when all keys collide
- Space Complexity: O(n) — where n is number of elements
When to Use Hashing
- You need fast lookup or membership tests
- You want to count frequencies or group values quickly
- You need to detect duplicates efficiently
Advantages and Disadvantages of Hashing
Advantages
- Extremely Fast: Constant-time access in average case
- Simple Implementation: Especially with built-in hash maps
- Flexible: Works with any key type that can be hashed
Disadvantages
- Not Sorted: Does not preserve order of keys
- Collisions: Require extra handling logic
- Depends on Good Hash Function: Poor design can degrade performance
Conclusion
Hashing is a powerful technique widely used in software engineering, data structures, and system design. Its ability to perform operations in constant time makes it ideal for performance-critical applications. However, careful attention must be given to collision handling and hash function design to maintain efficiency.