
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question
![The Java code below was written to find the last index that x appears in the array A. If x doesn't
appear in A, then the function returns -1.
int find(int[] A, int x) {
int n A.length, i = n -1;
while (i = 0) {
}
}
if (A[i] = x)
return i;
i = 1;
==
return -1;
Homework 3
6
Data Struct.
Your task is as follows:
1. Write a precondition and a post-condition for find. Your conditions should be in sync with the
invariants and other justification steps you will also make about the code. At the very least, the
post-condition should allow us to say that find does find the last index of x as specified above.
2. Specify a loop invariant for the loop that find uses.
3. Fill in the missing Hoare logic justifications so that we have a complete proof that given the
precondition, the post-condition holds, thereby find meets the specification.](https://content.bartleby.com/qna-images/question/f97c0725-689e-40d7-87a0-46553d65cfc3/40b0a9d2-a4ec-4230-8503-0600ddb39834/n5z6x7_thumbnail.png)
Transcribed Image Text:The Java code below was written to find the last index that x appears in the array A. If x doesn't
appear in A, then the function returns -1.
int find(int[] A, int x) {
int n A.length, i = n -1;
while (i = 0) {
}
}
if (A[i] = x)
return i;
i = 1;
==
return -1;
Homework 3
6
Data Struct.
Your task is as follows:
1. Write a precondition and a post-condition for find. Your conditions should be in sync with the
invariants and other justification steps you will also make about the code. At the very least, the
post-condition should allow us to say that find does find the last index of x as specified above.
2. Specify a loop invariant for the loop that find uses.
3. Fill in the missing Hoare logic justifications so that we have a complete proof that given the
precondition, the post-condition holds, thereby find meets the specification.
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