The Blind Multiplier

A medium Python interview practice problem on DataDriven. Write the Python and run it against test cases, with instant feedback.

Domain
Python
Difficulty
medium
Seniority
L4

Problem

Given a list of integers, return a list of the same length where position i is the product of all input elements except nums[i]. Do not use division. Runtime should be O(n).

Compute the result of everything around you - without seeing yourself.

Example 1

Input:

nums = [1,2,3,4]

Output:

[24,12,8,6]

Example 2

Input:

nums = [-1,1,0,-3,3]

Output:

[0,0,9,0,0]

Worked solution and explanation

Why this problem exists in real interviews

Product of array except self without division tests prefix and suffix product computation. It is a classic array problem that checks whether you can decompose the problem into two passes.

Break down the requirements

Step 1: Compute prefix products

For each index i, prefix[i] is the product of all elements before i.

Step 2: Compute suffix products

For each index i, suffix[i] is the product of all elements after i.

Step 3: Multiply prefix and suffix at each position

The product of everything except nums[i] is prefix[i] * suffix[i].

The solution

Prefix-suffix product decomposition
def product_except_self(nums):
    n = len(nums)
    result = [1] * n
    prefix = 1
    for i in range(n):
        result[i] = prefix
        prefix *= nums[i]
    suffix = 1
    for i in range(n - 1, -1, -1):
        result[i] *= suffix
        suffix *= nums[i]
    return result

Common follow-up questions