Solution

The correct answer is Option 1.

Key Points

• The correct order of increasing time complexity of algorithms is: B, C, D, A.
• Binary Search: The time complexity of binary search is O(log n), as it divides the search space into half with every iteration.
• Heap Sort: In the worst case, the time complexity of heap sort is O(n log n), as it involves building a heap and performing repeated heapify operations.
• Addition of Two n x n Matrices: The time complexity of adding two matrices is O(n²), as each element of the matrices is accessed once.
• Tower of Hanoi: The time complexity of solving the Tower of Hanoi problem with n disks is O(2ⁿ), as it involves exponential recursion.

Additional Information

• Time Complexity Overview:
  • Binary Search (O(log n)): Efficient for searching in sorted data, requires logarithmic time.
  • Heap Sort (O(n log n)): A comparison-based sorting algorithm with good performance in the worst case.
  • Matrix Addition (O(n²)): Involves iterating through all n² elements of the matrices to compute the sum.
  • Tower of Hanoi (O(2ⁿ)): A classic recursive problem with exponential growth in the number of moves as n increases.
• Practical Implications:
  • Binary Search is highly efficient for large datasets and is commonly used in search algorithms.
  • Heap Sort is a reliable sorting algorithm with consistent performance across different cases.
  • Matrix addition is computationally intensive for large matrices, but it is straightforward to implement.
  • The Tower of Hanoi problem demonstrates the limitations of recursive algorithms for large inputs.
• Important Points:
  • Understanding time complexity helps in selecting the right algorithm for specific problems.
  • Algorithms with exponential time complexity, like the Tower of Hanoi, become impractical for large input sizes.
  • Efficient algorithms like Binary Search and Heap Sort are crucial in optimizing performance in real-world applications.