How to Solve Product of Array Except Self on LeetCode
The Product of Array Except Self problem tests your skills in array manipulation without division.
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 solution must run in O(n) time and without using division.
Example:
Input: nums = [1,2,3,4]
Output: [24,12,8,6]
Why This Problem Matters for Interviews
- Checks understanding of prefix/suffix patterns
- Forces you to avoid using division
- Appears in many top coding interviews
Approach to Product of Array Except Self
Prefix and Suffix Product (Optimal)
Compute prefix products, then suffix products in two passes.
Time Complexity: O(n)
Space Complexity: O(1) (output array not counting as extra space)
def productExceptSelf(nums):
n = len(nums)
answer = [1] * n
prefix = 1
for i in range(n):
answer[i] = prefix
prefix *= nums[i]
suffix = 1
for i in reversed(range(n)):
answer[i] *= suffix
suffix *= nums[i]
return answer
Key Interview Talking Points
- Why division isn’t allowed (zeroes in array)
- How prefix and suffix products cover all elements except current
- In-place space optimization
Big O Complexity Recap
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Prefix/Suffix Products | O(n) | O(1) |
Pro Interview Tips
- Draw prefix/suffix tables
- Explain the effect of zeros in the array
- Practice with edge cases (multiple zeros)