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Algorithm Binary Search Input: L = a₁, a2, ..., an list of distinct integers; x integer Output: p integer i = 1; j=n; found = F; p = 0; while i

Algorithm Binary Search Input: L = a₁, a2, ..., an list of distinct integers; x integer Output: p integer i = 1; j=n; found = F; p = 0; while i

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Algorithm Binary Search **Input:** - \( L = a_1, a_2, \ldots, a_n \), a list of distinct integers - \( x \), an integer **Output:** - \( p \), an integer **Procedure:** 1. Set \( i = 1 \) 2. Set \( j = n \) 3. Set \( \text{found} = F \) 4. Set \( p = 0 \) 5. While \( i \leq j \) and \( \text{found} = F \), do the following: - Calculate \( m = \left\lfloor \frac{i+j}{2} \right\rfloor \) - If \( a_m = x \) then - Set \( \text{found} = T \) and \( p = m \) - Else if \( a_m < x \) then - Set \( i = m + 1 \) - Else - Set \( j = m - 1 \) 6. Return \( p \) **Example:** When performing Algorithm Binary Search with input \( L = 1, 3, 5, 7, 9, 11, 13 \) and \( x = 9 \), how many times is \( x \) compared to an element \( a_i \) of the list \( L \)?
Transcribed Image Text:Algorithm Binary Search **Input:** - \( L = a_1, a_2, \ldots, a_n \), a list of distinct integers - \( x \), an integer **Output:** - \( p \), an integer **Procedure:** 1. Set \( i = 1 \) 2. Set \( j = n \) 3. Set \( \text{found} = F \) 4. Set \( p = 0 \) 5. While \( i \leq j \) and \( \text{found} = F \), do the following: - Calculate \( m = \left\lfloor \frac{i+j}{2} \right\rfloor \) - If \( a_m = x \) then - Set \( \text{found} = T \) and \( p = m \) - Else if \( a_m < x \) then - Set \( i = m + 1 \) - Else - Set \( j = m - 1 \) 6. Return \( p \) **Example:** When performing Algorithm Binary Search with input \( L = 1, 3, 5, 7, 9, 11, 13 \) and \( x = 9 \), how many times is \( x \) compared to an element \( a_i \) of the list \( L \)?
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