# Python Program for Merge Sort

Merge Sort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves. The merge() function is used for merging two halves. The merge(arr, l, m, r) is key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.

## Python Program for Merge Sort

The provided Python code implements the Merge Sort algorithm, a divide-and-conquer sorting technique. It breaks down an array into smaller subarrays, sorts them individually, and then merges them back together to create a sorted array. The code includes two main functions: merge, responsible for merging two subarrays, and mergeSort, which recursively divides and sorts the array. The merge function combines two sorted subarrays into a single sorted array. The mergeSort function recursively splits the array in half until each subarray has a single element, then merges them to achieve the final sorted result. The example sorts an array using Merge Sort and prints both the initial and sorted arrays.

## Python3

 `# Python program for implementation of MergeSort` `# Merges two subarrays of arr[].``# First subarray is arr[l..m]``# Second subarray is arr[m+1..r]`  `def` `merge(arr, l, m, r):``    ``n1 ``=` `m ``-` `l ``+` `1``    ``n2 ``=` `r ``-` `m` `    ``# create temp arrays``    ``L ``=` `[``0``] ``*` `(n1)``    ``R ``=` `[``0``] ``*` `(n2)` `    ``# Copy data to temp arrays L[] and R[]``    ``for` `i ``in` `range``(``0``, n1):``        ``L[i] ``=` `arr[l ``+` `i]` `    ``for` `j ``in` `range``(``0``, n2):``        ``R[j] ``=` `arr[m ``+` `1` `+` `j]` `    ``# Merge the temp arrays back into arr[l..r]``    ``i ``=` `0`     `# Initial index of first subarray``    ``j ``=` `0`     `# Initial index of second subarray``    ``k ``=` `l     ``# Initial index of merged subarray` `    ``while` `i < n1 ``and` `j < n2:``        ``if` `L[i] <``=` `R[j]:``            ``arr[k] ``=` `L[i]``            ``i ``+``=` `1``        ``else``:``            ``arr[k] ``=` `R[j]``            ``j ``+``=` `1``        ``k ``+``=` `1` `    ``# Copy the remaining elements of L[], if there``    ``# are any``    ``while` `i < n1:``        ``arr[k] ``=` `L[i]``        ``i ``+``=` `1``        ``k ``+``=` `1` `    ``# Copy the remaining elements of R[], if there``    ``# are any``    ``while` `j < n2:``        ``arr[k] ``=` `R[j]``        ``j ``+``=` `1``        ``k ``+``=` `1` `# l is for left index and r is right index of the``# sub-array of arr to be sorted`  `def` `mergeSort(arr, l, r):``    ``if` `l < r:` `        ``# Same as (l+r)//2, but avoids overflow for``        ``# large l and h``        ``m ``=` `l``+``(r``-``l)``/``/``2` `        ``# Sort first and second halves``        ``mergeSort(arr, l, m)``        ``mergeSort(arr, m``+``1``, r)``        ``merge(arr, l, m, r)`  `# Driver code to test above``arr ``=` `[``12``, ``11``, ``13``, ``5``, ``6``, ``7``]``n ``=` `len``(arr)``print``(``"Given array is"``)``for` `i ``in` `range``(n):``    ``print``(``"%d"` `%` `arr[i],end``=``" "``)` `mergeSort(arr, ``0``, n``-``1``)``print``(``"\n\nSorted array is"``)``for` `i ``in` `range``(n):``    ``print``(``"%d"` `%` `arr[i],end``=``" "``)` `# This code is contributed by Mohit Kumra`

Output
```Given array is
12 11 13 5 6 7

Sorted array is
5 6 7 11 12 13 ```

Time Complexity: O(n*log(n))

Auxiliary Space: O(n)

Please refer complete article on Merge Sort for more details!

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