# Python Algorithms

A quote goes, "A goal without a plan is just a wish." To achieve anything in life, we can't simply go for it without making a plan and sticking to it with persistence because life is complex. In the same way, programmers have to solve many complex problems that require thousands of lines of code. When we don't have a plan to solve the problem, we won't be able to keep track of whether we are writing the right logic. If we get stuck in the middle of writing a program, it becomes even more complex.

But, how do we make a plan? To write a program, the programmer has to understand what he wants to achieve by writing the code- the goal. Then, he needs to think about the procedure, and the step-by-step sequential procedure to solve a problem is an algorithm.

There can be any number of algorithms for a particular problem, as there can be any number of methods to solve a problem. After writing the algorithms, we choose the best efficient algorithm based on time and space complexities.

Definition: A set of instructions or rules expressed in a step-by-step fashion that represents the procedure to solve the problem to reach the required output is called an Algorithm.

• Irrespective of the programming language, the algorithm is the first step to solve any problem. Hence, an algorithm is independent of the language in which we want to write the program.
• We can develop a flowchart from the algorithm to analyze the problem.

### Characteristics of algorithms:

The difference between just a random explanation of how to solve a problem and representing an algorithm lies in the characteristics of an algorithm.

An algorithm must be:

1. Clear and unambiguous: Writing an algorithm aims to get a clarified view of the problem. Hence, the algorithms must be an explanation and should not rise to more confusion. The steps must be clear and should have a straightforward meaning.
2. Well-defined I/p and O/p: The inputs and the outputs must be mentioned, and every algorithm must have 0 or more inputs and should generate at least 1 output.
3. Finite: The algorithm can be lengthy depending on the need of the problem, but it should have a finite number of steps.
4. Feasible: Writing a program based on the algorithm must be feasible for the programmer.
5. Independent of the platform: The algorithm for a particular problem must work the same in all programming languages.

### Developing an algorithm:

There are no standards on how an algorithm must be. Any algorithm must have all the characteristics mentioned above and be understandable to a new reader. We can use common concepts of programming languages like conditional statements and loops while developing an algorithm.

## Aim: To add two integer numbers.

Algorithm:

Step 1: START

Step 2: Declare three integers: a, b and sum.

Step 3: Take the values of the two numbers a and b from the user.

Step 4: Add a and b and store the value in the variable sum.

Step 5: Print the value of the sum

Step 6: STOP

Adding two numbers is easy. Hence, this algorithm does not have much to gain to write the program. But algorithms play a major role in solving bigger and more complex problems.

Rather than writing definitions, we can even simplify an algorithm as below:

Step 1: START

Step 2: Take values of a and b

Step 3: sum <- a + b

Step 4: Display the sum

Step 5: STOP

1. Gives a clear view to the programmer as it makes the program easy to understand.

1. Creating an algorithm for big problems can be time-taking.
2. As the problem becomes complex, the algorithm becomes bulky, and the level of simplicity decreases, making it hard to grasp.
3. Loops and branches are hard to show in the algorithms.

To test if the written algorithm works fine, we need to implement it by writing a program in any language.

### Analysis:

1. Priori Analysis – Before:
It is the final check of the algorithm before writing the program. The algorithm designer analyzes the algorithm and determines the complexity. While analyzing, the factors like processor speed are kept constant.
2. Posterior Analysis – After:
It is to check the algorithm via the program developed from it. We can compare the algorithm analysis and the code analysis in terms of time, space, and speed by analyzing the program.
The two major factors that are used to analyze an algorithm are:
1. Time complexity: It is the total time taken to execute the algorithm.
2. Space complexity: It is the total memory required by all types of program variables for execution.
Calculating time and space complexities is a procedure, and based on time complexity, we make asymptotic notations to analyze different algorithms, which are another concept.

### Famous algorithms in Python:

1. Searching and sorting algorithms
2. Divide and conquer algorithms
3. Greedy algorithms

In data structures, we need to create algorithms for 5 operations:

1. Search
2. Sort
3. Insert
4. Update
5. Delete