I've got a question that says use the binary insertion sort in which a binary search algorithm is used to determine the index to sort a list: 

So, without thinking I tried implemented this for hours: 

```
from binsert import binsert

def binary_insertion(List,L,R):
    """uses binary searching algorithm
    to determine the position for insertion"""

    for i in range(1,len(List)):
        position = binsert(List, i, L, R)
        for k in range(0, i-position):
            #note: the position must be atleast one
            #less than j otherwise this code won't
            #run, and it gives accuracy to statement:
            List[position-k] = List[position-k-1]
            #as the list bound is never exceeded

if __name__ == '__main__':

    List = [8, 9, 16, 17, 31, 34, 35, 39, 41, 45]
    Lcopy1 = List[:]
    Lcopy2 = List[:]

    binary_insertion(Lcopy1, 0, len(List)-1)
    print("The binary is: ", Lcopy1)  

```

Where the binsert contains: 

```
#!/usr/bin/python3

def binsert(List, search, L, R):
    """binary insertion determining algorithm"""
    List.sort()

    if L > R:
        #some code here

        ''' elif L == len(List):
            return L
        else R < 0:
            return L
        else:
            return L '''

        return L

    mid = (L+R)//2

    if List[mid] == search:
        return mid
    elif search < List[mid]:
        return binsert(List, search, L, mid-1)
    elif search > List[mid]:
        return binsert(List, search, mid+1, R)

if __name__ == '__main__':

    import random

    List =  [0, 9, 18, 25, 29, 34, 39, 40, 43, 49]
    print("The length of the list is: ", len(List))
    print("The list is: \n",List)
    Listnumber = binsert(List, 26, 0, len(List)-1)
    print("The item is to be inserted in: {}".format(Listnumber))  

```

Now after I was done with these, I realized that ***This is a sorting algorithm*** but the binary search required input to be sorted, and I was trying to implement mutually exclusive things. 

Either I've done a mistake in understanding and there's another explanation to what the question was saying, Or I just wasted my time. 

So, I wanted to know what was the case.