Basics of Data Structures and Algorithms

Introduction

• Presenter: Mosh
• Topic: Basics of data structures and algorithms.
• Importance: Frequently asked in coding interviews by companies like Google, Microsoft, Amazon.
• Prerequisites: Basic programming knowledge (Java used, but any language can be used).
• Encouragement to enroll in the ultimate data structures and algorithms course.

Big O Notation

Definition

• Big O notation describes the performance of an algorithm, especially how it scales with input size.
• Classic definition: Describes the limiting behavior of a function as the argument approaches a value or infinity.

Importance of Big O

• Helps determine if an algorithm is scalable.
• Fast execution on small datasets does not guarantee performance on larger datasets.
• Big companies emphasize understanding Big O in interviews.
• Knowing Big O improves developer skills.

Examples of Big O

• Constant Time: O(1)

  • Example: Method printing the first item in an array, always takes constant time regardless of input size.

• Linear Time: O(n)

  • Example: Loop iterating through an array (n items), runtime grows linearly with the number of items.
  • Adding constant operations in a loop does not change it to O(n) + O(1).

• Nested Loops: O(n^2)

  • Example: Two nested loops iterating over an array results in quadratic complexity.

• Logarithmic Time: O(log n)

  • More efficient than linear time.
  • Example: Binary search on a sorted array reduces problem size by half each time (max comparisons = 19 for 1 million items).

• Exponential Time: O(2^n)

  • Opposite of logarithmic growth, becomes very slow quickly.

Trade-offs

• Ideal algorithms: Fast, scalable, and memory-efficient.
• Reality: Trade-off between time and space (resource limitations).

Data Structures: Arrays

Overview

• Arrays store lists of items sequentially and have fixed sizes.
• Strengths: Fast access by index (O(1)).
• Weaknesses:
  • Static size limits flexibility.
  • Resizing (copying to a new array) costs O(n).
  • Removing items may require shifting elements (O(n) in the worst case).

Demonstration in Java

• Creating and initializing arrays, and accessing elements.
• Operations include declaring, initializing, printing, and setting values.
• Emphasis on understanding array limitations.
• Exercise: Build an array class with dynamic size.

Linked Lists

Overview

• Linked lists: Collections of nodes that can grow/shrink dynamically.
• Each node holds a value and a reference to the next node.
• Head (first node) and tail (last node).

Time Complexity of Operations

• Searching: O(n) (need to traverse the list).
• Index Lookup: O(n) (not sequential in memory).
• Insertions:
  • At End: O(1) (if tail is referenced).
  • At Beginning: O(1).
  • In Middle: O(n) (requires traversal).
• Deletions:
  • From Beginning: O(1).
  • From End: O(n) (need previous node).
  • From Middle: O(n).

Implementation in Java

• Java provides a LinkedList class that uses generics to store objects.
• Discussion of operations such as adding, removing, and searching within the linked list.

Exercise

• Implement a linked list from scratch with methods for adding, removing, and finding items.

Conclusion

• Importance of mastering basic data structures (arrays, linked lists) as building blocks for more complex structures.
• Encouragement to pursue deeper knowledge through the complete course offered, including various data structures and algorithms.