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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Among Selection Sort, Insertion Sort, Mergesort, Quicksort, and Heapsort, which algorithm would you choose for the situation below? Only pick one algorithm.The  simplicity of implementation should also be considered AFTER the consideration of speed, the number of assignment operation and the extra space requirement. Use the chart below for your considerations.

 

A) The list has several hundred records. The records are quite long, but the keys are very short.

 

B) The list has about 25,000 records. It is desirable to complete the sort as quickly as possible on the average, but it is also critical that the sort be completed quickly in every single case.

 

C) The list has about 45,000 records, but it starts off only slightly out of order.

 

**Table 7.1: Analysis Summary for Exchange Sort, Insertion Sort, and Selection Sort**

**Algorithm Analysis:**

1. **Exchange Sort:**
   - Comparisons of Keys: \( T(n) = \frac{n^2}{2} \)
   - Assignments of Records: 
     - Worst Case, \( W(n) = \frac{3n^2}{2} \)
     - Average Case, \( A(n) = \frac{3n^2}{4} \)
   - Extra Space Usage: In-place

2. **Insertion Sort:**
   - Comparisons of Keys: \( W(n) = \frac{n^2}{2} \)
   - Assignments of Records:
     - Worst Case, \( W(n) = \frac{n^2}{2} \)
     - Average Case, \( A(n) = \frac{n^2}{4} \)
   - Extra Space Usage: In-place

3. **Selection Sort:**
   - Comparisons of Keys: \( T(n) = \frac{n^2}{2} \)
   - Assignments of Records: \( T(n) = 3n \)
   - Extra Space Usage: In-place

*Entries are approximate.*

**Algorithm Comparison:**

1. **Mergesort (Algorithm 2.4):**
   - Comparison of Keys: 
     - Worst Case, \( W(n) = n \log n \)
     - Average Case, \( A(n) = n \log n \)
   - Assignments of Records: \( T(n) = 2n \log n \)
   - Extra Space Usage: \(\Theta(n)\) records

2. **Mergesort (Algorithm 7.4):**
   - Comparison of Keys:
     - Worst Case, \( W(n) = n \log n \)
     - Average Case, \( A(n) = n \log n \)
   - Assignments of Records: \( T(n) = 0\ \dagger \)
   - Extra Space Usage: \(\Theta(n)\) links

3. **Quicksort (with improvements):**
   - Comparison of Keys:
     - Worst Case, \( W(n) = \frac{n^2}{2} \)
     - Average Case, \( A(n) = 1.38n \log n
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Transcribed Image Text:**Table 7.1: Analysis Summary for Exchange Sort, Insertion Sort, and Selection Sort** **Algorithm Analysis:** 1. **Exchange Sort:** - Comparisons of Keys: \( T(n) = \frac{n^2}{2} \) - Assignments of Records: - Worst Case, \( W(n) = \frac{3n^2}{2} \) - Average Case, \( A(n) = \frac{3n^2}{4} \) - Extra Space Usage: In-place 2. **Insertion Sort:** - Comparisons of Keys: \( W(n) = \frac{n^2}{2} \) - Assignments of Records: - Worst Case, \( W(n) = \frac{n^2}{2} \) - Average Case, \( A(n) = \frac{n^2}{4} \) - Extra Space Usage: In-place 3. **Selection Sort:** - Comparisons of Keys: \( T(n) = \frac{n^2}{2} \) - Assignments of Records: \( T(n) = 3n \) - Extra Space Usage: In-place *Entries are approximate.* **Algorithm Comparison:** 1. **Mergesort (Algorithm 2.4):** - Comparison of Keys: - Worst Case, \( W(n) = n \log n \) - Average Case, \( A(n) = n \log n \) - Assignments of Records: \( T(n) = 2n \log n \) - Extra Space Usage: \(\Theta(n)\) records 2. **Mergesort (Algorithm 7.4):** - Comparison of Keys: - Worst Case, \( W(n) = n \log n \) - Average Case, \( A(n) = n \log n \) - Assignments of Records: \( T(n) = 0\ \dagger \) - Extra Space Usage: \(\Theta(n)\) links 3. **Quicksort (with improvements):** - Comparison of Keys: - Worst Case, \( W(n) = \frac{n^2}{2} \) - Average Case, \( A(n) = 1.38n \log n
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