#7 Medium Time O(n) Space O(1) Animated

Product of Array Except Self

Return an array where each element is the product of all other elements.

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1 Predict
2 Trace
3 Explain
4 Implement

Pattern Hashing for constant-time memory

Trade one linear scan for a small lookup structure so each value is handled once.

Approach: Prefix and Suffix Products (O(1) Space)

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Core Insight

Trade one linear scan for a small lookup structure so each value is handled once.

Common Pitfall

Do not overwrite information you still need before checking the current value.

Description

Return an array where each element is the product of all other elements.

Constraints

Time Complexity: O(n)
Space Complexity: O(1)

Solution — Prefix and Suffix Products (O(1) Space)

TimeO(n) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Create the lookup structure.
Scan each value once.
Check the needed relationship before updating state.
Return as soon as the answer is determined.

def productExceptSelf(nums):
    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

Encode and Decode Strings

Valid Sudoku

Product of Array Except Self

Steps

Description

Constraints

Tags

Solution — Prefix and Suffix Products (O(1) Space)