highschool/Grade 10/Computer Science/ICS4U1/Sorting Methods/Merge Sort.md

Introduction

Merge sort is a comparison type sort that has an effective use of recursion and the divide and conquer algorithm.
Merge sort sorts in \(`O(N \log N)`\) time and uses \(`O(N \log N)`\) space.
We will explore the pros and cons of this sort the proofs on its time and space complexity and the implementation and algorithm of this sorting method.

Abstract: Given two sorted arrays \(`a_{lo}`\) to \(`a_{mid}`\) and \(`a_{mid+1}`\) to \(`a_{hi}`\), replace with sorted subarray \(`a_{lo}`\) to \(`a_{hi}`\).

Basic Algorithm

• Divide array into 2 halves
• Recursively sort each half
• Merge the two halfs.

def mergesort(left, right, array[]):
    if left <= right:
        mid = (left + right) / 2
        mergesort(left, mid, array[])
        mergesort(mid+1, right, array[])
        mergehalves(left, mid, right, array[])

Running Time Analysis

• Latop computer can run close to \(`10^8`\) per second.
• Supercomputer can execute \(`10^{12}`\) compares per second.