1. Definition

Mathematical notation that describes the upper limit of execution time or the use of an algorithm space. It is denoted as or (f (n)) , where f (n) is a function that represents time or space depending on the input size n .

2. Purpose

Algorithms comparison
• : Allows you to compare different algorithms and choose the most efficient for a given problem. Scalability
: It helps predict how an algorithm will behave when the amount of data increases.
• 3. Complexity analysis

Worse case

• Better case and average case : Although they are important, they are used less frequently for the Big O.
• 4. Space vs. Time

Temporary complexity

• Spatial complexity : refers to the amount of additional memory you use. You can have notations such as or (1)
(constant space) or
• (linear space). Example: Import Timeit IMPORT MATPLOTLIB.PYPLOT AS PLT Import CProfile # O (1) Def Constant_time_operation (): return 42 # O (log n) Def logarithmic_time_operation (n): Count = 0 While N> 1: N // = 2 Count = 1 return count # Or (n) def linear_time_operation (n): Total = 0 for i in range (n): Total = i Total return # O (n log n) def linear_logarithmic_time_operation (n): if n

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