Please solve both parts of the question(the entire problem). Thank you! Part IWrite a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Implement and use the helper function_merge , which merges two sorted arrays.Sample Output> merge_sort([10, 32, 83, 2, 72, 100, 32])[2, 10, 32, 32, ]> merge_sort ( ['a','g','a', 't','e'])['a','a','g','e', 't']In [ ]: def _merge(P, Q):""merges two sorted arraysINPUT:* P, Q - the two sorted arraysOUTPUT: a sorted list consisting of elements in P and QpassIn [ ]: def merge_sort(array):""sorts a given listINPUT:* array - the listOUTPUT: a sorted copy of the list.passPart IIUse a proof by induction to show that the function merge_sort will correctly sort any array of size n.ProofType your answer here. Use to type LaTeX math expressions, e.g. p A q

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Write a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Implement and use the helper function _merge , which merges two sorted arrays. Sample Output > merge_sort([10, 32, 83, 2, 72, 100, 32]) [2, 10, 32, 32, ] > merge_sort(['a','g','a','t','e']) ['a','a','g','e', 't'] In [ ]: def _merge(P, Q): ""merges two sorted arrays INPUT: * P. 0 - the two sorted arrays OUTPUT: a sorted list consisting of elements in P and Q pass In [ ]: def merge_sort(array): ""sorts a given list INPUT: * array - the list OUTPUT: a sorted copy of the list. pass

Write a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Implement and use the helper function _merge , which merges two sorted arrays. Sample Output > merge_sort([10, 32, 83, 2, 72, 100, 32]) [2, 10, 32, 32, ] > merge_sort(['a','g','a','t','e']) ['a','a','g','e', 't'] In [ ]: def _merge(P, Q): ""merges two sorted arrays INPUT: * P. 0 - the two sorted arrays OUTPUT: a sorted list consisting of elements in P and Q pass In [ ]: def merge_sort(array): ""sorts a given list INPUT: * array - the list OUTPUT: a sorted copy of the list. pass

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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Question

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Please solve both parts of the question(the entire problem). Thank you!

Part I
Write a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Implement and use the helper function
_merge , which merges two sorted arrays.
Sample Output
> merge_sort([10, 32, 83, 2, 72, 100, 32])
[2, 10, 32, 32, ]
> merge_sort ( ['a','g','a', 't','e'])
['a','a','g','e', 't']
In [ ]: def _merge(P, Q):
""merges two sorted arrays
INPUT:
* P, Q - the two sorted arrays
OUTPUT: a sorted list consisting of elements in P and Q
pass
In [ ]: def merge_sort(array):
""sorts a given list
INPUT:
* array - the list
OUTPUT: a sorted copy of the list.
pass
Part II
Use a proof by induction to show that the function merge_sort will correctly sort any array of size n.
Proof
Type your answer here. Use to type LaTeX math expressions, e.g. p A q

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