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Two Sum at Amazon — Interview Guide

The problem at Amazon

Given an array of integers and a target value, return the indices of the two numbers that add up to the target. You may assume exactly one solution exists, and you cannot use the same element twice.

Two Sum is the canonical warm-up question. It looks trivial, but interviewers use it to check whether you reach for the O(n) hash-map solution immediately or get stuck in the O(n²) nested-loop trap.

Amazon uses this problem to assess customer-obsessed, data-driven, bar-raising. Expect Amazon-specific follow-ups that tie the solution back to production reasoning and the company's engineering bar.

Key concepts

Complement lookup: for each x, you need target - x; store seen values in a hash map.
Single-pass vs two-pass: a single pass that checks the map before inserting avoids double-counting an element.
Hash maps give O(1) average lookup, which is what makes the optimal solution O(n).

Approach

Create an empty hash map from value to index.
Iterate the array; for each element compute its complement.
If the complement is already in the map, return both indices.
Otherwise store the current value and its index and continue.

def two_sum(nums, target):
    seen = {}
    for i, x in enumerate(nums):
        need = target - x
        if need in seen:
            return [seen[need], i]
        seen[x] = i

Complexity

Metric	Value	Why
Time	O(n)	One pass, O(1) average map lookup
Space	O(n)	Map stores up to n entries

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