Algorithms

Meaning and Definition of an Algorithm

An algorithm is a step-by-step procedure or a set of well-defined instructions for solving a problem or completing a task. Each step in an algorithm must be clear, unambiguous, and finite, leading to a specific result. Algorithms can be implemented using programming languages to solve computational problems or even performed manually in day-to-day activities.

• Formal Definition: An algorithm is a finite sequence of well-defined steps that take input(s) and transform them into an output to solve a problem.

• Example: A simple algorithm to find the sum of two numbers:

  1. Start
  2. Read two numbers A and B
  3. Calculate Sum = A + B
  4. Display Sum
  5. End

Reasons for Using Algorithms

1. Efficiency: Algorithms are designed to solve problems in the most efficient way possible, minimizing time and resources.

2. Clarity and Structure: Algorithms provide a clear, structured approach to problem-solving. By following a series of logical steps, you ensure that the problem is tackled systematically.

3. Automation: Algorithms can be translated into code, allowing machines to perform tasks automatically without human intervention. This is crucial in fields such as computer science, artificial intelligence, and automation.

4. Reusability: Once an algorithm is designed and proven to be correct, it can be reused to solve similar problems without rethinking the process from scratch.

5. Optimization: Algorithms help in finding optimal solutions for complex problems, especially in fields like data science, operations research, and machine learning, where optimization is key.

6. Problem-solving: Algorithms break down complex problems into smaller, manageable steps, which make them easier to solve. They act as a blueprint for designing programs.

7. Consistency: Algorithms ensure that a problem is solved the same way every time, providing predictable and consistent results, essential for software development.

8. Verification: Algorithms can be tested and verified for correctness. By analyzing the logic and flow, one can determine if the solution is correct and whether the desired outcome is achieved.

Key Properties of an Algorithm

• Finiteness: An algorithm must terminate after a finite number of steps.
• Definiteness: Each step in the algorithm must be clearly defined without ambiguity.
• Input: An algorithm must have zero or more inputs provided before execution.
• Output: The algorithm should produce at least one output.
• Effectiveness: Each operation should be simple enough to be performed in a finite time.

Algorithm to  Check Whether the given number is Palindrome ( University Question)

Input: A number num.

Initialize:

• original_num = num (to store the original number).
• reversed_num = 0 (to store the reversed number).

Repeat the following steps until num becomes 0:

• Extract the last digit of num using digit = num % 10.
• Update reversed_num by multiplying it by 10 and adding digit.
• Remove the last digit from num using num = num // 10.

Compare:

• If original_num equals reversed_num, the number is a palindrome.
• Otherwise, it is not a palindrome.

Output:

• Print "Palindrome" if original_num equals reversed_num.
• Print "Not a Palindrome" otherwise.

Example:

Input:

num = 121

Process:

• original_num = 121
• Reverse the digits:
  • digit = 121 % 10 = 1, reversed_num = 0 * 10 + 1 = 1, num = 121 // 10 = 12.
  • digit = 12 % 10 = 2, reversed_num = 1 * 10 + 2 = 12, num = 12 // 10 = 1.
  • digit = 1 % 10 = 1, reversed_num = 12 * 10 + 1 = 121, num = 1 // 10 = 0.
• Compare: original_num = 121 and reversed_num = 121.

Output:

"Palindrome"

Algorithm: Palindrome Check

1. Start the process.
2. Input the number num.
3. Store the value of num in original_num.  
4. Set reversed_num = 0.
5. Check if num == 0:
   • If true, go to Step 10.
   • If false, go to Step 6.
6. Compute the last digit: digit = num % 10.
7. Update the reversed number: reversed_num = reversed_num * 10 + digit.
8. Remove the last digit from num: num = num // 10.
9. Go back to Step 5.
10. Compare original_num and reversed_num:
    • If they are equal, go to Step 12.
    • If they are not equal, go to Step 13.
11. Print "Not a Palindrome" and go to Step 13.
12. Print "Palindrome" and go to Step 13.
13. End the process.

You are a software developer working on data analysis tool for a logistic company. The company has a list of delivery times, where each entity represents the time taken(in minutes) for a particular delivery. The team needs to identify delivery time that are divisible by 6( as they are considered optimal delivery duration) but not divisible by 4 ( as they tend to involve more complexity in scheduling). Write an algorithm to print the delivery times that are divisible by and not divisible by 4 from a given set of delivery times.

Algorithm

1. Input: A list of delivery times.
2. Iterate through each delivery time in the list.
3. Check divisibility:
   • If the delivery time is divisible by 6 (time % 6 == 0) but not divisible by 4 (time % 4 != 0):
     • Add the delivery time to the result list.
4. Output: Print the result list.