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
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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]
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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