binary tree explanation why does this work

Question

Started reading a book about basic data structures and algorithms which uses this example code,

    def binary_search(list, item):
    low = 0  
    high = len(list)-1  #sets upper range to length of provided list

    while low <= high:
        mid = (low + high) #why does (low + high) give me middle of list?
        guess = list[mid]
        if guess == item:
            return mid
        if guess > item:
            high = mid - 1
        else:
            low = mid + 1
    return None

my_list = [1,3,5,7,9]

print binary_search(my_list,3)
print binary_search(my_list,-1)

While I understand the concept of the tree I don't understand why

mid = (low + high) #why does (low + high) give me middle of list? wouldn't low + high just give me the same value as high? shouldn't i need low + high / 2 to find the midpoint? yet it works perfectly fine?

Answer 1

It works because mid is always in the right range, but this is linear search, not binary. You can check this by printing the indices that are examined:

def binary_search(list, item):
    low = 0  
    high = len(list)-1  #sets upper range to length of provided list

    while low <= high:
        mid = (low + high) #why does (low + high) give me middle of list?
        print("mid =", mid)
        guess = list[mid]
        if guess == item:
            return mid
        if guess > item:
            high = mid - 1
        else:
            low = mid + 1

Looking for -1 in your example:

>>> print (binary_search([1,3,5,7,9],-1))
mid = 4
mid = 3
mid = 2
mid = 1
mid = 0
None

So you are correct: you should divide mid by 2 (and avoid using list as a variable name).