#1EasyHash Map

Two Sum

The most asked interview problem — find two indices that add to a target.

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Problem Statement

Given an array of integers nums and an integer target, return the indices of the two numbers that add up to target. You may assume that each input has exactly one solution, and you may not use the same element twice.

Examples

Example 1

Input:nums = [2,7,11,15], target = 9
Output:[0,1]

Explanation: nums[0] + nums[1] = 2 + 7 = 9

Example 2

Input:nums = [3,2,4], target = 6
Output:[1,2]

Explanation: nums[1] + nums[2] = 2 + 4 = 6

Constraints

  • 2 ≤ nums.length ≤ 10⁴
  • -10⁹ ≤ nums[i] ≤ 10⁹
  • -10⁹ ≤ target ≤ 10⁹
  • Only one valid answer exists.

Solutions

1
Brute Force — Nested Loops
TimeO(n²)SpaceO(1)

Try every pair of elements. For each element at index i, scan every element at index j > i and check if their sum equals the target. Simple but slow — O(n²) for large arrays.

Visual Animation
def twoSum(nums: list[int], target: int) -> list[int]:
    n = len(nums)
    for i in range(n):
        for j in range(i + 1, n):
            if nums[i] + nums[j] == target:
                return [i, j]
    return []  @@0@@

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