Performance Analysis of Algorithms

Overview

• Performance analysis is essential for understanding how algorithms behave under different conditions.
• Two main metrics for analyzing performance:
  • Time Complexity
  • Space Complexity

Time Complexity

• Definition: The amount of time an algorithm takes for execution.
• Types of Time Complexities:
  1. Best Case Time Complexity
     • Minimum time required for execution.
  2. Worst Case Time Complexity
     • Maximum time required for execution.
  3. Average Case Time Complexity
     • Average time required for execution.

Detailed Explanation of Time Complexities

• Best Case:

  • Example: Key element found at the first position (requires minimum time).

• Worst Case:

  • Example: Key element found at the last position (requires maximum time).

• Average Case:

  • Example: Key element found at a middle position (somewhere between best and worst case).

Example: Linear Search

• Linear Search Definition:

  • Searching elements one by one until the key element is found or the array is exhausted.

• Best Case Example:

  • Key element is at the first position (e.g., searching for 10).
  • Requires only 1 unit of time.

• Worst Case Example:

  • Key element is at the last position (e.g., searching for 50 in an array of 10, 20, 30, 40, 50).
  • Requires maximum time (5 units of time).

• Average Case Example:

  • Key element found at a middle position (e.g., searching for 30, 40).

Approaches to Calculate Time Complexity

1. Frequency Count or Step Count
2. Asymptotic Notations

• These approaches will be discussed in future videos.

Space Complexity

• Definition: The amount of space an algorithm requires for execution.
• Similar to time complexity, space complexity will also be analyzed using frequency count and asymptotic notations in future discussions.

Conclusion

• Performance analysis can be conducted through time and space complexity.
• Understanding the different types of time complexity (best, worst, average) is crucial for algorithm evaluation.