## Introduction
Merge sort is a comparison type sort that has an effective use of recursion and the divide and conquer algorithm. <br>
Merge sort sorts in $`O(N \log N)`$ time and uses $`O(N \log N)`$ space. <br>
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.

```py
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.