Product of Array Except Self
Return an array where each value is the product of all other elements.
Pattern fit
This is not sum but the same prefix-suffix decomposition idea: each answer is left product times right product.
Key observation
You never need division if you build left products and then sweep from the right.
Target complexity
O(n) / O(1) extra
How to break down the solution cleanly
This is not sum but the same prefix-suffix decomposition idea: each answer is left product times right product.
You never need division if you build left products and then sweep from the right.
Define what the cumulative state means.
Build the prefix in one forward pass.
Reference implementation
Python# Generic pattern template
prefix = [0] * (len(nums) + 1)
for i, value in enumerate(nums):
prefix[i + 1] = prefix[i] + value
range_sum = prefix[r + 1] - prefix[l]
Common pitfalls
Reaching for division and breaking on zeros.
Allocating separate full left and right arrays unnecessarily.
Common follow-ups
How does the right-to-left sweep remove one array?
What changes if there are many zeros?
Continue with related problems
Build repeatable depth inside the Prefix Sum cluster before moving on.