DSA Cheat Sheet Free pdf

Chapter 1: Introduction to DSA

What is DSA? and Its Importance:

DSA (Data Structures and Algorithms) is the foundational concept in computer science, which is essential for solving problems efficiently and optimizing code performance.

Time Complexity:

Time complexity measures the execution time of an algorithm as a function of the input size, helping evaluate efficiency.

Space Complexity:

Space complexity measures the memory usage of an algorithm, crucial for understanding its storage requirements.

Big O, Big Θ, Big Ω Notations:

• First, Big O (O): This describes the upper bound of an algorithm’s runtime.
• Second, Big Θ (Θ): Here This describes the exact bound (both upper and lower) of an algorithm’s runtime.
• Third, Big Ω (Ω): Describes the lower bound of an algorithm’s runtime.

Chapter 2: Arrays

What are Arrays? and Their Importance:

Arrays are a collection of elements which is used for stored in contiguous memory locations, allowing fast access via indices.

Types of Arrays:

• 1D Arrays: Linear array of elements.
• 2D Arrays: Matrix of elements arranged in rows and columns.
• 3D Arrays: Collection of 2D arrays stacked upon each other.

Chapter 3: Linked Lists

What are Linked Lists? and Their Importance:

Linked lists are linear data structures where each element points to the next, which allows dynamic memory allocation and efficient insertions/deletions operations.

Types of Linked Lists:

• Singly Linked List: Each node points to the next node.
• Doubly Linked List: Each node points to both the next and previous nodes.
• Circular Linked List: Last node points back to the first node.

Chapter 4: Stacks

Introduction to Stacks:

A stack is a LIFO (Last In, First Out) Data Structure which are used for managing function calls, expression evaluation, and undo mechanisms.

Stack Operations:

• Push: Add an element to the top.
• Pop: Remove the top element.
• Peek: View the top element without removing it.
• isEmpty: Check if the stack is empty.

Chapter 5: Queues

Introduction to Queues:

A queue is a FIFO (First In, First Out) Data Structure which are used for scheduling, buffering, and breadth-first search algorithms.

Queue Operations:

• Enqueue: Add an element to the rear.
• Dequeue: Remove an element from the front.
• Front: View the front element without removing it.
• Rear: View the rear element without removing it.
• isEmpty: Check if the queue is empty.

Types of Queues:

• Circular Queue: The last position is connected back to the first.
• Priority Queue: Elements are processed based on priority.
• Deque: Double-ended queue allowing insertion and deletion from both ends.

Chapter 6: Trees

Introduction to Trees:

Trees are a Hierarchical Data Structure which have root node and sub-nodes, that’s why it is used in databases, file systems, and expression parsing.

Tree Traversal:

• Preorder: Visit root, traverse left, traverse right.
• Inorder: Traverse left, visit root, traverse right.
• Postorder: Traverse left, traverse right, visit root.
• Level Order: Visit nodes level by level.

Advanced Trees:

• AVL Trees: Self-balancing binary search trees.
• Red-Black Trees: Balanced binary search trees with color properties.
• B-Trees: Balanced tree data structures for database indexing.

Chapter 7: Heaps

Introduction to Heaps:

A complete binary tree used to implement priority queues, where each parent node is either greater or smaller than its children (max-heap or min-heap).

Types of Heaps:

• Min-Heap: Parent node is smaller than its children.
• Max-Heap: Parent node is larger than its children.

Chapter 8: Graphs

Introduction to Graphs:

A Graph is a collection of nodes (vertices) and edges connecting pairs of nodes, used to model networks and relationships.

Types of Graphs:

• Adjacency Matrix: 2D array to represent edge connections.
• Adjacency List: List of lists to represent edge connections.

Graph Traversal Algorithms:

• DFS (Depth-First Search): Explore as far as possible along each branch before backtracking.
• BFS (Breadth-First Search): Explore all neighbors at the present depth before moving on to nodes at the next depth level.

Chapter 9: Hashing

Introduction to Hashing:

Hashing is a technique which is used for map the data of arbitrary size to fixed-size values (hash codes), enabling fast data retrieval.

Hash Functions:

Functions that convert input into a fixed-size string of bytes, typically used to index data.

Collision Resolution Techniques:

• Chaining: Store colliding elements in linked lists.
• Open Addressing: Probe alternative locations in the array.

Chapter 10: Sorting Algorithms

Introduction to Sorting:

Sorting algorithms arrange elements in a specified order, essential for searching and organizing data.

Comparison-based Sorting Algorithms:

• Bubble Sort: Repeatedly swap adjacent elements if they are in the wrong order.
• Selection Sort: Select the minimum element and place it at the beginning.
• Insertion Sort: Insert elements into their correct position.
• Quick Sort: Divide and conquer by selecting a pivot and partitioning the array.
• Merge Sort: Divide and merge sorted halves.
• Heap Sort: Convert array to heap and extract elements.

Non-comparison-based Sorting Algorithms:

• Counting Sort: Count occurrences of each element.
• Radix Sort: Sort elements digit by digit.
• Bucket Sort: Distribute elements into buckets and sort each bucket.

Chapter 11: Searching Algorithms

Linear Search:

Sequentially check each element until the target is found or the end is reached.

Binary Search:

Efficiently search a sorted array by repeatedly dividing the search interval in half.

Advanced Searching Algorithms:

Techniques like interpolation search and exponential search for specific scenarios.

Chapter 12: Dynamic Programming

Introduction to Dynamic Programming:

Dynamic Programming are the technique to solve problems by breaking them down into simpler subproblems, storing results to avoid recomputation.

DP Techniques:

• Memoization: Store results of subproblems in a table to avoid redundant calculations.
• Tabulation: Build a table bottom-up to solve the problem.

Chapter 13: Greedy Algorithm

Introduction to Greedy Algorithm:

Greedy Algorithm are make locally optimal choices at each step to find a global optimum solution.

Chapter 14: Advanced Topics

Backtracking:

Backtracking are the algorithmic technique which is used for solving problems recursively by trying to build a solution incrementally and removing solutions that fail.

Bit Manipulation:

Bit Manipulation are the techniques which perform the operations at the bit level for optimization.

Advanced Graph Algorithms:

Algorithms like Floyd-Warshall for shortest paths and Tarjan’s algorithm for strongly connected components.

String Manipulation:

String Manipulation are the techniques which is used for processing and analyzing strings, such as KMP pattern matching and Rabin-Karp algorithm.

Computational Geometry:

Computational Geometry are the algorithms for solving geometric problems, like convex hull and closest pair of points.

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