Algorithm Evaluation

Step 1: Match the time complexities with algorithms.
- **A. Logarithmic (O(lg n))**: The Tower of Hanoi problem has a time complexity of .

- **B. Quadratic (O(n²))**: Finding an element in a sorted array has a time complexity of , which is related to algorithms like bubble sort or insertion sort.

- **C. Cubic (O(n³))**: Bubble sort in the worst case has a time complexity of .

- **D. Exponential (O(2^n))**: Matrix multiplication has an exponential time complexity of .

Step 2: Conclusion.
Thus, the correct matching is:

- A - I: Logarithmic time complexity is associated with the Tower of Hanoi problem.

- B - II: Quadratic time complexity is associated with finding an element in a sorted array.

- C - III: Cubic time complexity is associated with Bubble sort in the worst case.

- D - IV: Exponential time complexity is associated with Matrix Multiplication.

The correct answer is option (1).