# Python Program for Binary Insertion Sort

We can use binary search to reduce the number of comparisons in normal insertion sort. Binary Insertion Sort find use binary search to find the proper location to insert the selected item at each iteration.
In normal insertion, sort it takes O(i) (at ith iteration) in worst case. we can reduce it to O(logi) by using binary search.

## Python

 `# Python Program implementation   ``# of binary insertion sort `` ``def` `binary_search(arr, val, start, end): ``    ``# we need to distinugish whether we should insert ``    ``# before or after the left boundary. ``    ``# imagine [0] is the last step of the binary search ``    ``# and we need to decide where to insert -1 ``    ``if` `start ``=``=` `end: ``        ``if` `arr[start] > val: ``            ``return` `start ``        ``else``: ``            ``return` `start``+``1`` ``    ``# this occurs if we are moving beyond left\'s boundary ``    ``# meaning the left boundary is the least position to ``    ``# find a number greater than val ``    ``if` `start > end: ``        ``return` `start `` ``    ``mid ``=` `(start``+``end)``/``2``    ``if` `arr[mid] < val: ``        ``return` `binary_search(arr, val, mid``+``1``, end) ``    ``elif` `arr[mid] > val: ``        ``return` `binary_search(arr, val, start, mid``-``1``) ``    ``else``: ``        ``return` `mid `` ``def` `insertion_sort(arr): ``    ``for` `i ``in` `xrange``(``1``, ``len``(arr)): ``        ``val ``=` `arr[i] ``        ``j ``=` `binary_search(arr, val, ``0``, i``-``1``) ``        ``arr ``=` `arr[:j] ``+` `[val] ``+` `arr[j:i] ``+` `arr[i``+``1``:] ``    ``return` `arr `` ``print``(``"Sorted array:"``) ``print` `insertion_sort([``37``, ``23``, ``0``, ``17``, ``12``, ``72``, ``31``, ``                        ``46``, ``100``, ``88``, ``54``]) `` ``# `