4. Consider the following recursive algorithm. Algorithm Mystery A[0..n - 1]) //Input: An array A[0..n - 1] of real numbers if n = 1 return A[0] else temp ← Riddle(A[0..n - 2]) if temp ≤ A[n 1] return temp else return A[n − 1] a. What does this algorithm compute? The given algorithm will recursively calculate the minimum of the given array or list of elements. For every value of n. It calculates the minimum of all values preceding n(ie. <= n- 1). If the value returned is less than the value[n], it returns that value else it returns value[n]. b. What is its input size? Input size: an array of size 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. e. What is the efficiency class of this algorithm?
4. Consider the following recursive algorithm. Algorithm Mystery A[0..n - 1]) //Input: An array A[0..n - 1] of real numbers if n = 1 return A[0] else temp ← Riddle(A[0..n - 2]) if temp ≤ A[n 1] return temp else return A[n − 1] a. What does this algorithm compute? The given algorithm will recursively calculate the minimum of the given array or list of elements. For every value of n. It calculates the minimum of all values preceding n(ie. <= n- 1). If the value returned is less than the value[n], it returns that value else it returns value[n]. b. What is its input size? Input size: an array of size 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. e. What is the efficiency class of this algorithm?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7757f974-220a-4bcf-b905-f534f24cec51%2F6d0902e6-3a8a-41bc-84a1-856af977ffae%2F24l52f_processed.png&w=3840&q=75)
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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