Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Please assist with part  d and e. Thank you!

**Recursive Algorithm Analysis**

**Algorithm: Mystery A[0..n − 1]**
- **Input**: An array `A[0..n − 1]` of real numbers.
- **Process**:
  1. If `n = 1`, return `A[0]`.
  2. Else, set `temp ← Riddle(A[0..n−2])`.
  3. If `temp ≤ A[n−1]`, return `temp`; else, return `A[n−1]`.

**a. What does this algorithm compute?**
- The algorithm recursively calculates the minimum of the given array or list of elements. It determines the minimum for each value of `n` by comparing all elements up to `n−1`. If the returned value is less than `A[n-1]`, it returns that value; otherwise, it returns `A[n−1]`.

**b. What is its input size?**
- The input size is an array ranging from `0` to `n−1` of real numbers.

**c. What is its basic operation?**
- The basic operation is: `temp ← Riddle(A[0...n−2])`.

**d. Set up a recurrence relation for the algorithm’s basic operation count and solve it.**
- The recurrence relation is typically defined based on the recursive call structure. Here, let `T(n)` be the time complexity for an array of size `n`.
  - Base case: `T(1) = O(1)`
  - Recursive case: `T(n) = T(n-1) + O(1)`
  - Solving this recurrence relation gives `T(n) = O(n)`, which indicates linear time complexity, as each step involves a constant amount of work and depends linearly on the size of the input.

**e. What is the efficiency class of this algorithm?**
- The efficiency class of this algorithm is `O(n)`, indicating it has linear time complexity with respect to the input size.
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Transcribed Image Text:**Recursive Algorithm Analysis** **Algorithm: Mystery A[0..n − 1]** - **Input**: An array `A[0..n − 1]` of real numbers. - **Process**: 1. If `n = 1`, return `A[0]`. 2. Else, set `temp ← Riddle(A[0..n−2])`. 3. If `temp ≤ A[n−1]`, return `temp`; else, return `A[n−1]`. **a. What does this algorithm compute?** - The algorithm recursively calculates the minimum of the given array or list of elements. It determines the minimum for each value of `n` by comparing all elements up to `n−1`. If the returned value is less than `A[n-1]`, it returns that value; otherwise, it returns `A[n−1]`. **b. What is its input size?** - The input size is an array ranging from `0` to `n−1` of real numbers. **c. What is its basic operation?** - The basic operation is: `temp ← Riddle(A[0...n−2])`. **d. Set up a recurrence relation for the algorithm’s basic operation count and solve it.** - The recurrence relation is typically defined based on the recursive call structure. Here, let `T(n)` be the time complexity for an array of size `n`. - Base case: `T(1) = O(1)` - Recursive case: `T(n) = T(n-1) + O(1)` - Solving this recurrence relation gives `T(n) = O(n)`, which indicates linear time complexity, as each step involves a constant amount of work and depends linearly on the size of the input. **e. What is the efficiency class of this algorithm?** - The efficiency class of this algorithm is `O(n)`, indicating it has linear time complexity with respect to the input size.
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