Algorithm Analysis (Time complexity)

Software development cycle

-Four phases:1. Analysis 2. Design

Design an algorithm to solve the problem or sub- problem. Algorithm is step by step problem-solving process, and solution obtained in finite amount of time.

3. Implementation4. Testing and Debugging

Algorithm Analysis: The Big-O Notation (cont’d.)

- By analyzing a particular algorithm, we usually count the number of Primitive Operations:

1. Assigning a value to a variable2.Calling a function3.Performing an arithmetic operation4.Comparing two values5.Returning from a function

The Big-O Notation (cont’d.)

- The following table shows each of the seven common functions used in algorithm analysis in order of growth rates.

Examples:

1- F(n) = 5n2 + 3n log n + 2n + 5We say the function F(n) is O(n2) or Big-O of n2

2- F(n)= 3 log n + 2 We say the function F(n) is O(log n) or Big-O of log n

3- F(n)= 2n + 100 log n We say the function F(n) is O(n) or Big-O of n

constant logarithm linear n-log-n quadratic cubic exponential

1 log n n n log n n2 n3 an, a>1