1. task: Introduction and basics. And again, Peter Puzzle has found a piece of paper with the following code: int FooBar (A, i) { n= len (A); if (i == n-1) return A; for (j= (i + 1); j
1. task: Introduction and basics. And again, Peter Puzzle has found a piece of paper with the following code: int FooBar (A, i) { n= len (A); if (i == n-1) return A; for (j= (i + 1); j
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
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![1. task: Introduction and basics. And again, Peter Puzzle has found a piece of
paper with the following code:
int FooBar (A, i) {
n= len (A);
if (i == n-1) return A;
for (j= (i + 1); j<n; j++) {
if (A[i] <A[j]) { temp= A[i]; A[i] = A[j]; A[j] = temp; }
}
return FooBar (A, i+1)
}
QUESTIONS:
A) (i.) What is the loop invariant for the for loop based on which you can
show what the function actually returns? (ii.) Show that it remains invariant
throughout the execution of the function.
B) (i.) What does the array A returned by the function FooBar (A, i) contain?
Justify your answer. (ii.) What does the array A returned by the function
FooBar (A, 0) contain? Justify your answer.
HINT: Use induction.
C) (i.) What is the time complexity of the function FooBar if we count the
number of comparisons over the elements of the array A? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45a2c93f-7502-4c22-a7b1-88698e38cece%2Fbba35f42-cb47-4933-bc56-b5b38b41eec3%2Fdakh0om_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. task: Introduction and basics. And again, Peter Puzzle has found a piece of
paper with the following code:
int FooBar (A, i) {
n= len (A);
if (i == n-1) return A;
for (j= (i + 1); j<n; j++) {
if (A[i] <A[j]) { temp= A[i]; A[i] = A[j]; A[j] = temp; }
}
return FooBar (A, i+1)
}
QUESTIONS:
A) (i.) What is the loop invariant for the for loop based on which you can
show what the function actually returns? (ii.) Show that it remains invariant
throughout the execution of the function.
B) (i.) What does the array A returned by the function FooBar (A, i) contain?
Justify your answer. (ii.) What does the array A returned by the function
FooBar (A, 0) contain? Justify your answer.
HINT: Use induction.
C) (i.) What is the time complexity of the function FooBar if we count the
number of comparisons over the elements of the array A? Justify your answer.
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