Python question Analysis: Invariants (Q16-17) For each of the following functions, identify the loop invariant, exit condition and post condition. Question 16 (Invariant 1) This function returns the list of integers that are multiples of both 3 and 7 that occurs within a given list. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of the loop, which shows the algorithm’s correctness. def multiples_count(lst): """ Input: a list of integers, lst Output: the list of integers in lst that are multiples of both 3 and 7 """ res = [] for i in range(len(lst)): if lst[i]%3 == 0 and lst[i]%7 == 0: res.append(lst[i]) # Identify the loop invariant here return res Question 17 (Invariant 2) This function checks if a given list (of comparable elements) is sorted in ascending order. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of each iteration of the loop, which shows the algorithm’s correctness. def is_sorted(lst): """ Input: a list of comparable elements Output: True if the given list is sorted in ascending order, False otherwise """ i = 0 flag = True while i < len(lst)-1: if lst[i] > lst[i+1]: flag = False break i += 1 # Identify the loop invariant here return flag

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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def multiples_count(lst):
"""
Input: a list of integers, lst
Output: the list of integers in lst that are multiples of both 3 and 7
"""
res = []
for i in range(len(lst)):
if lst[i]%3 == 0 and lst[i]%7 == 0:
res.append(lst[i])
# Identify the loop invariant here
return res

Question 17 (Invariant 2)

This function checks if a given list (of comparable elements) is sorted in ascending order. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of each iteration of the loop, which shows the algorithm’s correctness.

def is_sorted(lst):
"""
Input: a list of comparable elements
Output: True if the given list is sorted in ascending order, False otherwise
"""
i = 0
flag = True
while i < len(lst)-1:
if lst[i] > lst[i+1]:
flag = False
break
i += 1
# Identify the loop invariant here
return flag

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