ALGORITHMIC THINKING

Session 1: Algorithmic Thinking 1 – Problem Identification and Analysis

What is Algorithmic Thinking?
Algorithmic thinking is a structured approach to problem-solving that involves creating a sequence of instructions or algorithms. It helps in breaking down complex tasks into smaller, manageable parts, designing logical steps to efficiently reach a solution.

Key Abilities in Algorithmic Thinking:

• Problem Analysis: Specify the problem precisely.
• Basic Action Identification: Determine the fundamental actions needed.
• Algorithm Construction: Develop a correct algorithm using the identified actions.
• Case Consideration: Think through all possible special and normal cases.
• Efficiency Improvement: Enhance the algorithm’s efficiency.

Problem Identification and Analysis

This process entails understanding and defining the problem, identifying inputs and outputs, and recognizing constraints. It requires breaking the problem down into smaller components and analyzing its structure for the best approach.

Steps in Problem Identification and Analysis

1. Define the Problem:
   Identify the inputs, expected outputs, requirements, and constraints.

2. Break Down the Problem:
   Decompose the problem into smaller, manageable sub-problems. Visualization through flowcharts or pseudocode can be helpful.

3. Design the Algorithm:
   Decide on algorithms and data structures to use. Outline the necessary steps for each sub-problem.

4. Implement the Algorithm:
   Write the algorithm in Python, following the steps outlined in the design phase.

5. Test the Algorithm:
   Run tests to ensure the algorithm produces the expected outputs for various inputs.

6. Analyze the Algorithm:
   Evaluate the algorithm’s efficiency by calculating its time and space complexity.

Example: Finding Two Numbers that Add Up to a Target

Problem Statement:
Given a list of numbers, find two numbers that add up to a specific target.

1. Define the Problem:

   • Input: List of numbers and a target number.
   • Output: Indices of the two numbers that add up to the target.

2. Break Down the Problem:
   Iterate through the list and find pairs of numbers that meet the criteria.

3. Design the Algorithm:
   Consider edge cases where no two numbers add up to the target and ensure efficiency for large lists.

4. Implement the Algorithm:

   python

   Copy code

   def two_sum(nums, target):
   num_dict = {}
   for i, num in enumerate(nums):
   complement = target - num
   if complement in num_dict:
   return [num_dict[complement], i]
   num_dict[num] = i
   return None

   # Example usage
numbers = [2, 7, 11, 15]
target = 9
result = two_sum(numbers, target)
print("Indices of numbers adding up to target:", result)


Explanation:
This function checks each number in the array against its complement to see if they add up to the target value.

Activity: Shortest Route for Multiple Cities

You are tasked with using heuristics and various problem-solving methods to find the shortest route to visit multiple cities. This activity enhances intuition for solving optimization problems with heuristic techniques.

Activity Feedback

• Understand how heuristics can provide practical solutions for complex optimization challenges.
• Learn to apply different problem-solving strategies and evaluate their effectiveness.
• Gain experience balancing solution quality with computational efficiency.
• Develop critical thinking and algorithmic intuition in a practical context.

Conclusion

This session introduces foundational concepts in algorithmic thinking and problem-solving. In the next lesson, we will explore Problem Solving Approaches and Heuristics.

Thank you!