2. For this problem consider the Average problem stated below. Average Input: A sequence of n integers A= (a), a2 . am). Output: meQ such that m=- a, a) Using pseudocode state an algorithm that solves the Average problem using a loop. b) Identify the loop invariant for the loop in your algorithm that will help you prove your algorithm is correct. That is, state the loop invariant as a proposition of the kind "After iteration i of the loop.". c) Using induction prove that your loop invariant holds for each iteration i. d) Using the loop invariant show that your algorithm is correct.
2. For this problem consider the Average problem stated below. Average Input: A sequence of n integers A= (a), a2 . am). Output: meQ such that m=- a, a) Using pseudocode state an algorithm that solves the Average problem using a loop. b) Identify the loop invariant for the loop in your algorithm that will help you prove your algorithm is correct. That is, state the loop invariant as a proposition of the kind "After iteration i of the loop.". c) Using induction prove that your loop invariant holds for each iteration i. d) Using the loop invariant show that your algorithm is correct.
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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Transcribed Image Text:2. For this problem consider the Average problem stated below.
Average
Input: A sequence of n integers A = (a1, a2, .., an).
Output: meQ such that
m = -L ai
a) Using pseudocode state an algorithm that solves the Average problem using a
loop.
b) Identify the loop invariant for the loop in your algorithm that will help you prove
your algorithm is correct. That is, state the loop invariant as a proposition of the
kind "After iteration i of the loop.".
c) Using induction prove that your loop invariant holds for each iteration i.
d) Using the loop invariant show that your algorithm is correct.
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