Used to analyze worst-case (usually) complexity to check resource requirements for runtime as inputs increase. Not about the hardware, etc. High level view. How long: time complexity. Memory consumption: space complexity.

Common examples (time complexity):

• O(1): Constant. Input size won't have a major effect. (bookmark example, array key)
• O(n): Linear. The runtime grows linearly with the input size. (reading the book example, interating over array)
• O(n^2): Quadratic. Common in algorithms with nested loops. (many array sorting functions)
• O(log n): Logarithmic. Common in algorithms like binary search. (dictionary example)
• O(n log n): Linearithmic. Seen in efficient sorting algorithms like merge sort and quicksort.
• O(2^n): Exponential. Often seen in brute-force algorithms.
• O(n!): Factorial. Extremely inefficient and usually impractical for large inputs.

Examples:

• https://betterprogramming.pub/big-o-notation-a-simple-explanation-with-examples-a56347d1daca
• https://www.freecodecamp.org/news/big-o-cheat-sheet-time-complexity-chart/ (with graphic)