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Data Structures and Algorithms

Data Structures and Algorithms (DSA) form the foundation of computer science and software engineering. This guide covers the essential concepts you need to master for technical interviews and become a better programmer.

Data Structures​

Data structures are specialized formats for organizing and storing data. Here's an overview of the key data structures:

Arrays and Strings​

  • Contiguous memory allocation
  • Constant-time access by index
  • Common operations: insertion, deletion, traversal
  • String manipulation and pattern matching

Linked Lists​

  • Sequential elements with pointers
  • Singly and doubly linked variants
  • Dynamic size
  • Efficient insertions and deletions

Stacks and Queues​

  • Stack: LIFO (Last In, First Out)
  • Queue: FIFO (First In, First Out)
  • Applications: function calls, BFS/DFS, task scheduling

Hash Tables​

  • Key-value pairs
  • O(1) average case for insertions and lookups
  • Collision handling
  • Applications: caching, indexing

Trees​

  • Binary Search Trees (BST)
  • Balanced trees (AVL, Red-Black)
  • Tree traversals
  • Applications: databases, file systems

Heaps​

  • Priority Queues
  • Min/Max heaps
  • Heap operations
  • Applications: scheduling, graph algorithms

Graphs​

  • Vertices and edges
  • Directed vs undirected
  • Graph representations
  • Common algorithms (DFS, BFS, shortest path)

Problem Solving Patterns​

Understanding common problem-solving patterns helps tackle new problems effectively:

  1. Sliding Window

    • For contiguous sequences
    • String/array problems
    • Optimization problems

  2. Two Pointers / Multiple Pointers

    • Array manipulation
    • Linked list operations
    • Search problems

  3. Frequency Counter

    • Compare pieces of data
    • Anagram problems
    • Pattern matching

  4. Divide and Conquer

    • Breaking problems into smaller parts
    • Binary search
    • Merge sort

  5. Greedy Algorithms

    • Local optimal choices
    • Optimization problems
    • Scheduling problems

Sorting Algorithms​

Understanding various sorting algorithms and their trade-offs is crucial:

Common Sorting Algorithms​

  1. Bubble Sort

    • Time Complexity: O(n²)
    • Space Complexity: O(1)
    • Simple but inefficient

  2. Selection Sort

    • Time Complexity: O(n²)
    • Space Complexity: O(1)
    • Simple implementation

  3. Insertion Sort

    • Time Complexity: O(n²)
    • Space Complexity: O(1)
    • Efficient for small data sets

  4. Merge Sort

    • Time Complexity: O(n log n)
    • Space Complexity: O(n)
    • Divide and conquer approach

  5. Quick Sort

    • Time Complexity: O(n log n) average, O(n²) worst
    • Space Complexity: O(log n)
    • Often used in practice

  6. Heap Sort

    • Time Complexity: O(n log n)
    • Space Complexity: O(1)
    • In-place sorting

Each sorting algorithm has its use cases and trade-offs in terms of:

  • Time complexity
  • Space complexity
  • Stability
  • In-place vs. extra space
  • Adaptive behavior

Understanding when to use each algorithm is as important as knowing how they work.