Exercise 7.3.1: Worst-case time complexity - counting numbers in a sequence less than a target value. CountValuesLessThanT Input: a1, az.an n, the length of the sequence. T, a target value. Output: The number of values in the sequence that are less than T. count := 0 For i = 1 to n If (a < T), count := count + 1 End-for Return( count) (a) Characterize the asymptotic growth of the worst-case time complexity of the algorithm. Justify your answer.

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
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**Exercise 7.3.1: Worst-case time complexity - counting numbers in a sequence less than a target value.**

**Algorithm: CountValuesLessThanT**

- **Input:** 
  - \( a_1, a_2, \ldots, a_n \)
  - \( n \), the length of the sequence.
  - \( T \), a target value.

- **Output:** The number of values in the sequence that are less than \( T \).

1. Initialize \( count := 0 \)

2. For \( i = 1 \) to \( n \)  
   - If \( (a_i < T) \), then \( count := count + 1 \)  
   End-for

3. Return \( count \)

---

(a) **Characterize the asymptotic growth of the worst-case time complexity of the algorithm. Justify your answer.**
Transcribed Image Text:**Exercise 7.3.1: Worst-case time complexity - counting numbers in a sequence less than a target value.** **Algorithm: CountValuesLessThanT** - **Input:** - \( a_1, a_2, \ldots, a_n \) - \( n \), the length of the sequence. - \( T \), a target value. - **Output:** The number of values in the sequence that are less than \( T \). 1. Initialize \( count := 0 \) 2. For \( i = 1 \) to \( n \) - If \( (a_i < T) \), then \( count := count + 1 \) End-for 3. Return \( count \) --- (a) **Characterize the asymptotic growth of the worst-case time complexity of the algorithm. Justify your answer.**
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