idea of algorithms in python

Class – XII : Computer Science New : (Python)
Idea Algorithmic Efficiency
Introduction: The quality of algorithms we say performance of an algorithm depends on many internal and external factors.

Internal Factors: Specify algorithms efficiency .
1- Time Required to run
2- Space required to run
External Factors: affect the algorithms performance.
1- Size of the input to the algorithms
2- Speed of the computer on which it is run
3- Quality of the compiler

External factors are controllable to some extent, mainly internal factors are studied and measured in order to determine an algorithms efficiency or we can say complexity. Complexity of an algorithms is determined by studying and measuring internal factors affecting the algorithms.

Q- What is computational Complexity?
Answer: the term computational complexity is made of two words. ‘Computation’, ‘Complexity’.
The complexity involves the study of factors to determine how much resource is sufficient for the run algorithms.
Computation: involves the problems to be solved and the algorithms to solve them.
Resource included:
1- The time to run the algorithms
2- The space to needed to run the algorithms.

Estimating complexity of algorithms:
Amount of space use and the time taken.

Big-O Notation : A big O notation is used to depict and algorithms growth rate. The Growth rate determines the algorithms performance when its input size grows.
Through big-O , the upper bound of an algorithms performance is specified.
If we say an algorithms takes O(n2) time; this means that this algorithms will carry out its task taking at the most N2 steps for input size N.

Dominant Term: Big-O notation indicates the growth rate. It is mathematical formulas that describe algorithm performance.
A term which is going to affect the most on the algorithm’s performance. This term is known as the dominant term.

Common Growth Rates:
Time Complexity example
O(1) Constant Adding to the front of a list.
O(log N) log Finding an entry in a sorted array
O(N3) cubic Linear Equations
O(2N) Exponential The towers of Hanoi problem.

Guidelines of Computing Complexity:
1- Time and Memory
2- Size of the input
3- Shortest Possible time , Maximum Possible Time

Calculating Complexity: Few Guideline for finding this-
1- Loops
2- Nested Loops
3- Consecutive statements
4- If-then-else statements
5- Logarithmic complexity