Create merge_sort.md

Author: Mukundan314

chapters/sorting_searching/merge/merge_sort.md

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+# Merge Sort
+
+In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm.
+Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output.
+Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945.
+A detailed description and analysis of bottom-up mergesort appeared in a report by Goldstine and von Neumann as early as 1948.
+
+Conceptually, a merge sort works as follows:
+    1. Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
+    2. Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.
+
+{% method %}
+{% sample lang="py" %}
+[import:1-40, lang:"python"](code/python/merge.py)
+{% endmethod %}
+
+This algorithim can be made faster by doing the merge operations in parallel.
+
+<script>
+MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
+</script>
+$$
+\newcommand{\d}{\mathrm{d}}
+\newcommand{\bff}{\boldsymbol{f}}
+\newcommand{\bfg}{\boldsymbol{g}}
+\newcommand{\bfp}{\boldsymbol{p}}
+\newcommand{\bfq}{\boldsymbol{q}}
+\newcommand{\bfx}{\boldsymbol{x}}
+\newcommand{\bfu}{\boldsymbol{u}}
+\newcommand{\bfv}{\boldsymbol{v}}
+\newcommand{\bfA}{\boldsymbol{A}}
+\newcommand{\bfB}{\boldsymbol{B}}
+\newcommand{\bfC}{\boldsymbol{C}}
+\newcommand{\bfM}{\boldsymbol{M}}
+\newcommand{\bfJ}{\boldsymbol{J}}
+\newcommand{\bfR}{\boldsymbol{R}}
+\newcommand{\bfT}{\boldsymbol{T}}
+\newcommand{\bfomega}{\boldsymbol{\omega}}
+\newcommand{\bftau}{\boldsymbol{\tau}}
+$$