def selection_sort(L): Pre: L is a list of numbers Post: L is sorted in non-decreasing order II III # i indicates how many items were sorted for i in range (len(L)): # To find the minimum value of the unsorted segment # We first assume that the first element is the lowest min_index = i # We then use j to loop through the remaining elements for j in range (i+1, len(L)): # Update the min_index if the element at j is lower than it if L[j] < L[min_index]: min_index j # After finding the lowest item of the unsorted regions, # swap with the first unsorted item L[i], L[min_index] L [min_index], L[i] %3D The loop invariant for the outer loop is rather simple: 0 < i < len(L) and L[0 : i] is sorted. Clearly, once the loop finishes and i = len(L), this implies the postcondi- tion, and L is sorted. State and prove the loop invariant for the inner loop that can be used to prove the loop invariant for the outer loop. However, you do not need to prove how it is connected to the outer loop (though this is good practice). Hint: You should start by fixing a value for i, and assuming the outer loop in- variant holds for that i. You should use this assumption in your proof for the inner loop invariant.

def selection_sort(L): Pre: L is a list of numbers Post: L is sorted in non-decreasing order II III # i indicates how many items were sorted for i in range (len(L)): # To find the minimum value of the unsorted segment # We first assume that the first element is the lowest min_index = i # We then use j to loop through the remaining elements for j in range (i+1, len(L)): # Update the min_index if the element at j is lower than it if L[j] < L[min_index]: min_index j # After finding the lowest item of the unsorted regions, # swap with the first unsorted item L[i], L[min_index] L [min_index], L[i] %3D The loop invariant for the outer loop is rather simple: 0 < i < len(L) and L[0 : i] is sorted. Clearly, once the loop finishes and i = len(L), this implies the postcondi- tion, and L is sorted. State and prove the loop invariant for the inner loop that can be used to prove the loop invariant for the outer loop. However, you do not need to prove how it is connected to the outer loop (though this is good practice). Hint: You should start by fixing a value for i, and assuming the outer loop in- variant holds for that i. You should use this assumption in your proof for the inner loop invariant.

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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