Problem Description
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.
Key Insights
- The result for each element can be computed using the products of the elements to the left and the right of that element.
- We can iteratively compute two arrays (or use a single output array) to store the left and right products.
- No division is required, making the solution robust against zeroes in the input array.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1) (excluding the output array)
Solution
To solve the problem, we can utilize an output array to store the results. First, we will compute the products of all elements to the left of each index and store them in the output array. Then, we will iterate from the right to compute the products of all elements to the right while multiplying them with the values already in the output array. This approach ensures that we only traverse the input array a couple of times, achieving O(n) time complexity without using division.