Product of Array Except Self

Prefix/Postfix

20 min

Problem Statement

Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i]. The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer. You must write an algorithm that runs in O(n) time and without using the division operation.

Example

Example 1:

Input: nums = [1,2,3,4]

nums: [1, 2, 3, 4]

Output: [24, 12, 8, 6]

Output: [24,12,8,6]

Solution

The problem can be solved in O(n) time and O(1) extra space (the output array does not count as extra space) by first calculating the prefix products, and then multiplying by the postfix products in a second pass.

Algorithm Steps

Initialize an answer array of the same size as `nums` with all 1s.
Calculate the prefix products and store them in the answer array.
Initialize a `postfix` variable to 1.
Iterate through the array from right to left.
Multiply the current element in the answer array by `postfix`.
Update `postfix` by multiplying it with the current element in `nums`.
Return the answer array.

Product of Array Except Self

Prefix/Postfix Product Approach

Input: nums = [1, 2, 3, 4]

Output: []

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Nums

Result Array

Product of Array Except Self Solution


class Solution:
    def productExceptSelf(self, nums: list[int]) -> list[int]:
        res = [1] * (len(nums))
        
        prefix = 1
        for i in range(len(nums)):
            res[i] = prefix
            prefix *= nums[i]
        
        postfix = 1
        for i in range(len(nums) - 1, -1, -1):
            res[i] *= postfix
            postfix *= nums[i]
        return res