T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.
T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.
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
Related questions
Question
T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.
![146
4 Searching and Sorting
Jill's number
number 6?" or "Is your number even and greater than 543?" How should Jack
formulate his sequence of questions to find Jill's number most quickly; that is, with
fewest questions (in the worst case)?
Binary Search as given in Algorithm 4.1.2 makes three comparisons with each
probe (i.e., asks 3 questions about each number it investigates). If we wanted to
reduce the number of comparisons, we could modify it to search for the target value
T by making exactly one comparison per probe until the sublist we're searching has
only one entry and then testing to see if that single entry equals T.
- Jack may not ask "What is your number?" but may ask "Is your
Algorithm 4.2.1: Binary Search #2
// version #2.O
Begin
р+ 1;
q + n;
While (p < q) Do
j- [(p+g)/2];
If (A[j]< T) Then
p +j+1;
Else
j;
// the if
// the while
End;
End;
// Now, p = q
If (A[p]= T) Then
Output ("T is A[", p, "]");
Else
Output("T is not in A");
End;
// the if
End.
Walkthrough with n = 12 and A = (3, 5, 8, 8, 9, 16, 29, 41, 50, 63, 64, 67)
// A[1] = 3, A[2] = 5,
A[3] = 8, A[4] = 8,
I АП %3 29, А 8] — 41, А9] —50, А[10] — 63, Al1] — 64, &
A[5] = 9,
A[6] = 16,
A[12] =
= 67
If T = 9, then (using t for True and f for False)
// and T for target
p<q
A[j]
A[j] <T
A[p] = T
output
1
6.
12
t
16
f
1
3
6
8.
t
4
6
t
9.
f
4
5
t
8
t
5
f
t
T is A[5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4792360-22b4-40c0-a48a-02ce03c9f6f7%2F0949ecd7-378e-48b9-b226-d8518ed519fd%2F86jxhan_processed.png&w=3840&q=75)
Transcribed Image Text:146
4 Searching and Sorting
Jill's number
number 6?" or "Is your number even and greater than 543?" How should Jack
formulate his sequence of questions to find Jill's number most quickly; that is, with
fewest questions (in the worst case)?
Binary Search as given in Algorithm 4.1.2 makes three comparisons with each
probe (i.e., asks 3 questions about each number it investigates). If we wanted to
reduce the number of comparisons, we could modify it to search for the target value
T by making exactly one comparison per probe until the sublist we're searching has
only one entry and then testing to see if that single entry equals T.
- Jack may not ask "What is your number?" but may ask "Is your
Algorithm 4.2.1: Binary Search #2
// version #2.O
Begin
р+ 1;
q + n;
While (p < q) Do
j- [(p+g)/2];
If (A[j]< T) Then
p +j+1;
Else
j;
// the if
// the while
End;
End;
// Now, p = q
If (A[p]= T) Then
Output ("T is A[", p, "]");
Else
Output("T is not in A");
End;
// the if
End.
Walkthrough with n = 12 and A = (3, 5, 8, 8, 9, 16, 29, 41, 50, 63, 64, 67)
// A[1] = 3, A[2] = 5,
A[3] = 8, A[4] = 8,
I АП %3 29, А 8] — 41, А9] —50, А[10] — 63, Al1] — 64, &
A[5] = 9,
A[6] = 16,
A[12] =
= 67
If T = 9, then (using t for True and f for False)
// and T for target
p<q
A[j]
A[j] <T
A[p] = T
output
1
6.
12
t
16
f
1
3
6
8.
t
4
6
t
9.
f
4
5
t
8
t
5
f
t
T is A[5]
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