Update Merge Sort.md

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

@@ -1,4 +1,25 @@
 ## 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.
+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.
+