Binary Search Using a Recursive Function

Question

taking an intro CS class on python and was met by this lab on my textbook. It calls for binary search using recursive functions. I have the rest of the program, I simply need to define the Binary Search function. Any help on this would be greatly appreciated.

Here is the problem:

Binary search can be implemented as a recursive algorithm. Each call makes a recursive call on one-half of the list the call received as an argument.

Complete the recursive function binary_search() with the following specifications:

Parameters: a list of integers a target integer lower and upper bounds within which the recursive call will search Return value: if found, the index within the list where the target is located -1 if target is not found The algorithm begins by choosing an index midway between the lower and upper bounds.

If target == nums[index] return index If lower == upper, return lower if target == nums[lower] else -1 to indicate not found Otherwise call the function recursively with half the list as an argument: If nums[index] < target, search the list from index to upper If nums[index] > target, search the list from lower to index The list must be ordered, but duplicates are allowed.

Once the search algorithm works correctly, add the following to binary_search():

Count the number of calls to binary_search(). Count the number of times when the target is compared to an element of the list. Note: lower == upper should not be counted. Hint: Use a global variable to count calls and comparisons.

The input of the program consists of integers on one line followed by a target integer on the second.

The template provides the main program and a helper function that reads a list from input.

Ex: If the input is: 1 2 3 4 5 6 7 8 9 2 the output is:

index: 1, recursions: 2, comparisons: 3

Here is my code:

# TODO: Declare global variables here.
recursions = 0
comparisons = 0

def binary_search(nums, target, lower, upper):
    global recursions
    global comparisons
    if target == nums[(lower+upper)/2]:
        if lower == upper:
            if target == nums[lower]:
                return lower
            else:
                target == -1
    elif nums[(lower+upper)/2] < target:
        recursions =+1
        comparisons =+1
        binary_search(upper)
    elif nums[(lower+upper)/2] > target:
        recursions =+1
        comparisons =+1
        binary_search(lower)
    
        


if __name__ == '__main__':
    # Input a list of nums from the first line of input
    nums = [int(n) for n in input().split()]
    
    # Input a target value
    target = int(input())

    # Start off with default values: full range of list indices
    index = binary_search(nums, target, 0, len(nums) - 1)

    # Output the index where target was found in nums, and the
    # number of recursions and comparisons performed
    print(f'index: {index}, recursions: {recursions}, comparisons: {comparisons}')

Error output:

Traceback (most recent call last):
  File "main.py", line 34, in <module>
    index = binary_search(nums, target, 0, len(nums) - 1)
  File "main.py", line 8, in binary_search
    if target == nums[(lower+upper)/2]:
TypeError: list indices must be integers or slices, not float

If you divide an odd integer by two, you'll get a non-integer value. You probably want to be using integer division instead (//). — Toby Speight
– Toby Speight, Commented Dec 2, 2022 at 16:14

Samathingamajig · Accepted Answer · 2022-12-02 16:14:39Z

1

Your error means that lower + upper is an odd number, which when you divide by 2 results in something like 3.5, 8.5, etc., which is an invalid index for a list.

To solve this, use floored division (rounding down) with the double slash // operator

if target == nums[(lower+upper)//2]:

answered Dec 2, 2022 at 16:14

Samathingamajig

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Comments

jackal · Accepted Answer · 2022-12-02 16:42:37Z

Once you've fixed the integer division you'll have a problem when you try to make the recursive call because you're not providing enough parameters.

You may find this helpful:

recursions = 0
comparisons = 0

def binary_search(lst, t):
    def _binary_search(lst, lo, hi, t):
        global recursions, comparisons
        recursions += 1
        if hi >= lo:
            mid = (hi + lo) // 2
            comparisons += 1
            if lst[mid] == t:
                return mid

            comparisons += 1

            if lst[mid] > t:
                return _binary_search(lst, lo, mid - 1, t)
            else:
                return _binary_search(lst, mid + 1, hi, t)
        else:
            return -1
    return _binary_search(lst, 0, len(lst)-1, t)
    
index = binary_search([1, 2, 3, 4, 5, 6, 7, 8, 9], 2)

print(f'{index=} {recursions=} {comparisons=}')

Output:

index=1 recursions=2 comparisons=3

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