Lecture Notes: Insertion Sort

Introduction

• Channel: Gate Smashers
• Topic: Insertion Sort
• Relevance: Useful for competitive exams, college, and university exams.
• Method of Explanation: Real-life examples (playing cards analogy).

Overview of Insertion Sort

• Purpose: Sorts an array of random elements.
• Comparison: Often compared with other sorting algorithms for its utility and simplicity.
• Analogy: Similar to sorting playing cards in hand.

How Insertion Sort Works

1. Real-life Analogy:
   • Similar to arranging cards in ascending order.
   • Pick a card and place it in the correct position relative to the other cards.
   • Compare the new card with already sorted cards to find its place.
2. Example with Cards:
   • Start with the first card.
   • Compare subsequent cards with the sorted section.
   • Place them in the correct order.
3. Steps with Array Elements:
   • Begin with the array: [40, 20, 60, 10, 50, 30].
   • Place the first element without comparison.
   • Compare each new element with the previous sorted elements and insert it in the correct position.

Algorithm Details

• Algorithm:
  • Start from the second element.
  • Compare and insert into the sorted part of the array.
  • Use a key to hold the current element to be inserted.
  • Shift larger elements one position to the right.

Complexity Analysis

1. Best Case:
   • Condition: Array is in ascending order.
   • Comparisons: N - 1 comparisons.
   • Swaps: Zero swaps.
   • Time Complexity: Order of N.
2. Worst Case:
   • Condition: Array is in descending order.
   • Comparisons and Swaps: N(N-1)/2.
   • Time Complexity: Order of N².
3. Average Case:
   • Time Complexity: Order of N².

Additional Properties

• Stability: Maintains relative order of identical elements.
• In-place Sorting: No additional space for sorting.
• Online Algorithm: Can sort elements as they arrive without waiting.

Important Points for Exams and Interviews

• Best and worst-case scenarios are critical.
• Online nature makes it responsive and efficient for real-time sorting.
• Known for its simplicity and practical utility.

Conclusion

• Key Takeaway: Remember the insertion process and complexities.
• Resources: PPT slides available in the description for further reference.