Summary of Big O Notation

The video discusses the basics of Big O notation, which is essential for understanding algorithm efficiency and optimizing code performance. It measures how runtime scales with input size and highlights common notations from fastest to slowest.

Key Points:

• Constant Time: Runtime stays the same regardless of input size. Examples: array indexing, hashtable operations.
• Logarithmic Time: Runtime increases slowly as input grows. Example: binary search.
• Linear Time: Runtime grows directly with input size. Example: finding the maximum in an unsorted array.
• Linearithmic Time: Efficient sorting algorithms such as merge sort, quick sort, and heap sort.
• Quadratic Time: Runtime grows with the square of the input size. Example: bubble sort. Watch for nested loops.
• Cubic Time: Runtime grows with the cube of the input size. Example: naive matrix multiplication with three nested loops.
• Exponential Time: Runtime doubles with each additional input element. Common in some recursive algorithms.
• Factorial Time: Grows extremely fast with input size, e.g., generating all permutations.
• Big O is a starting point; real-world performance can vary based on factors like caching and memory usage.
• Example 1: Array traversal row-wise is faster than column-wise due to memory access patterns.
• Example 2: Arrays are often faster than linked lists for traversal despite both having linear complexity, due to contiguous memory allocation.

Takeaway: Use Big O as a starting point, but also profile your code to understand hardware impacts and optimize for real-world conditions.

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Youtube Video: https://www.youtube.com/watch?v=x2CRZaN2xgM
Youtube Channel: ByteByteGo
Video Published: 2024-11-12T16:30:12+00:00