BinaryInsertionSort.py

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])