L3: Introduction To Algorithms In Python | Lesson 3 | DSA In Python | @CodingNinjasIndia

Characteristics of an algorithm

• An algorithm should be independent of any coding language.

• It should have a definite answer and clear, unambiguous steps.

• It should solve the problem in a proper and efficient manner.

"An algorithm should be crystal clear, definite, and unambiguous. It should solve the problem efficiently."

Criteria of an algorithm

• An algorithm should have a finite number of inputs.

• It should produce an output.

• It should complete in finite time.

"An algorithm should have finite inputs and produce an output. It should also complete within a finite time."

Steps to design an algorithm

• Identify the problem and its requirements.

• Break down the problem into smaller subproblems.

• Determine the necessary inputs and outputs.

• Plan the algorithm by defining the steps and logical flow.

• Test and refine the algorithm for correctness and efficiency.

"To design an algorithm, first identify the problem, break it down, determine the inputs and outputs, plan the steps, and then test and refine it."

Definition of an algorithm

• An algorithm is a step-by-step procedure for solving a problem.

• It can be used for a wide range of problems, not just computer programs.

"An algorithm is a step-by-step procedure for solving a problem, not limited to computer programs."

Characteristics of an algorithm

• An algorithm should have definiteness, meaning that every step of the algorithm should be unambiguous.

• The output of the algorithm should also be unambiguous, meaning that there should be only one answer for a particular input.

• The algorithm should be completed in finite time, meaning that the process of converting the input into the output should not go on indefinitely.

"An algorithm should be unambiguous and provide a definite output in finite time."

Steps to design an algorithm

1. Devise an algorithm: Find the best technique to solve the problem or design the algorithm.

2. Validation: Check if the algorithm is giving the correct answer.

3. Analysis of an algorithm: Estimate the CPU execution time and space required by the algorithm and determine if it suits the problem well.

"The steps to design an algorithm include devising the algorithm, validating it, and analyzing its efficiency."

Time complexity of an algorithm

• Time complexity of an algorithm refers to the number of CPU computations required to execute the algorithm.

• The time complexity is determined by the frequency count of each instruction in the algorithm.

• The time complexity is expressed as O(n), representing the worst case scenario for the number of computations, where n is the input size.

"Time complexity measures the number of CPU computations needed for an algorithm and is expressed as O(n)."

Time Complexity

• The time complexity of an algorithm measures the highest power term in its time complexity equation.

• For example, if the time complexity is given as 3n^2 + 4n + 5, the highest power term is n^2.

• The highest power term represents the worst-case time complexity of the algorithm.

• Asymptotic notations, like big O notation, are used to represent time complexity.

"The time complexity of an algorithm is determined by the highest power term in its time complexity equation."

Space Complexity

• Space complexity is the estimation of the memory space required by an algorithm to execute itself.

• It includes the space required by variables used in the algorithm.

• It also considers the space required by data structures used in the algorithm.

• For recursive algorithms, the space used by the stack is also considered in space complexity.

"Space complexity is the estimation of memory space required by an algorithm, including variables and data structures used in the algorithm."

Example of Space Complexity

• Let's consider an algorithm that sums up the values of an array.

• This algorithm requires two variables (i and sum) and uses an array (arr) as a data structure.

• In this case, the space complexity would be n + n + 3, where n is the size of the array.

• The space complexity is determined by the highest power term or the most significant factor, which in this case is n.

"The space complexity of the algorithm for summing up the values of an array is determined by the size of the array, n."

Palindrome Checking Algorithm

• The problem statement is to check whether a given string is a palindrome or not.

• A palindrome is a string that reads the same forward and backward.

• The algorithm can be implemented by comparing the characters from the beginning and end of the string.

• Traverse the string from index 0 to half of the length of the string.

• Compare the characters at index i with the character at index n-i-1.

• If all the characters match, return 1; otherwise, return 0.

"The algorithm for checking whether a string is a palindrome involves comparing characters from the beginning and end of the string."

Writing algorithms in Python

• When writing algorithms, we can write them independently of the programming language we will use later.

• In this case, we will write the algorithm in Python.

"We can write algorithms independently of the programming language we will use later."

Checking the palindrome condition

• To check if a string is a palindrome, we need to compare characters at symmetric positions in the string.

• We start by comparing the character at position i with the character at position n - 1 - i.

• If the characters don't match, we break out of the loop.

"To check if a string is a palindrome, we compare characters at symmetric positions in the string."

Returning the result

• After comparing all the characters in the string, we check if the loop has reached i = n/2 - 1.

• If it has, we return True, indicating that the string is a palindrome.

• If not, we return False.

"After comparing all the characters, we check if the loop has reached the halfway point."

The pass keyword in Python

• In Python, the pass keyword allows us to have empty blocks of code.

• It is used when we want to have a placeholder block, but don't need to execute any code.

"The pass keyword in Python allows us to have empty code blocks."

Calculating the length of a string

• To calculate the length of a string in Python, we can use the len() function.

• We pass the string as an argument, and the function returns the length of the string.

"To calculate the length of a string in Python, we use the len() function."

Using floor division

• Floor division in Python is denoted by //.

• It returns the quotient of the division, rounded down to the nearest integer.

• In this case, we use floor division to divide n by 2.

"Floor division in Python is denoted by // and returns the rounded down quotient."

Executing the palindrome-checking loop

• We use a for loop to iterate over the range of values from 0 to n//2.

• Inside the loop, we compare characters at symmetric positions.

• If they don't match, we break out of the loop.

"We use a for loop to iterate over the range of values from 0 to n//2."

Completing the code and running it

• After writing the algorithm in Python code, we test the code by running it.

• The code successfully checks if a given string is a palindrome or not.

"After completing the code, we run it to test its functionality."