The document discusses algorithm complexity analysis using Big O notation, which describes the growth rate of an algorithm in terms of time and space. It highlights different complexities such as constant (O(1)), linear (O(n)), and quadratic (O(n²)) algorithms, and provides benchmarks for data structures and sorting operations. Additionally, it emphasizes the importance of choosing the appropriate data structure and simplifying complexities, especially in the presence of nested loops.

1. Algorithm Complexity
Analyzing
By Haluan Mohammad Irsad

2. Algorithm Complexity
• Commonly expressed in Big O Notation
“is a mathematical notation that describes the limiting behavior of
a function when the argument tends towards a particular value or infinity.”
“Representing the growth rate of an algorithm based on time and space”

3. Measurement
• Time complexity: how long does the algorithm run?
• Space complexity: the number of memory cells which an algorithm
needs

4. Exclude
• Platform ( machine/hardware & OS)
• Programming Language
• Compiler Quality
• Programming Paradigm

5. Code Example

6. Constant Algorithm O(1)

7. Linear Algorithm O(n)

8. Algorithm O(logn)

9. Quadratic Algorithm O(n2)

10. Cubic Algorithm O(n3)

11. Benchmark by Data Structure

12. Benchmark by Sorting Operation

13. DataTest

14. Problem
Count 1 and 0 in a line. If in the line have 1 digit in even then print 1,
else print 0.

15. Example Result
Input Output

16. Data Test
Size of data
1
9

17. Results

18. Graphic Linear Algorithm O(n)

19. Graphic Algorithm O(nlogn)

20. Graphic Quadratic Algorithm O(n2)

21. Graphic Cubic Algorithm O(n3)

22. Graphic Resume

23. Resume
• Linear algorithm is stable for any size of data
• Simplify your complexity if you found Quadratic and Cubic algorithm
in your code. Avoid nested looping.
• Choose the right data structure for the right operation.