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

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

  1. Use a hash function to convert the key into an index.
  2. Store the value at that index in a hash table.
  3. 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.