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Product of Array Except Self LC #238 Medium Array
Problem

Given an integer array nums, return an array answer such that answer[i] is equal to the product of all elements of nums except nums[i]. You must write an algorithm that runs in O(n) time and without using the division operation.

Example 1
Input: nums = [1,2,3,4]
Output: [24,12,8,6]
Explanation: 24=2×3×4, 12=1×3×4, 8=1×2×4, 6=1×2×3
Example 2
Input: nums = [-1,1,0,-3,3]
Output: [0,0,9,0,0]
Constraints: 2 ≤ nums.length ≤ 105; -30 ≤ nums[i] ≤ 30; The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer. O(1) extra space (output array does not count).
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Approach
Prefix × Suffix Products
Four views: original nums, prefix (left products), suffix (right products), then final = prefix × suffix. Same O(n) two-pass idea — no division.
Four Arrays
original
prefix
suffix
final
nums (input) prefix = product left of i suffix = product right of i final = prefix × suffix
Variables
Phase
—
i
—
running
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at i
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Step Logic
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Algorithm
1
Build prefix[]: prefix[0]=1, then prefix[i]=prefix[i−1]×nums[i−1] (L→R)
2
Build suffix[] with running product (R→L); set final[i]=prefix[i]×suffix[i]
3
Return final[] — same as in-place ans[] trick, shown as 4 arrays for clarity
Time
O(n)
Space
O(1) extra
Why It Works

At index i, exclude nums[i] and multiply everything else: left part × right part. prefix[i] stores the left product, suffix[i] the right product, and final[i] is their product. The code reuses one array instead of three — we show all four rows so each piece is visible.