Simple two-sum
Input
nums = [2,7,11,15], target = 9
Output
(0, 1)
nums[0] + nums[1] == 9, so return indices (0,1).
Full lesson preview
Find a two-sum pair using a hash map
Find indices of two numbers that add up to a target using a hash map for O(n) time.
Python practice15 minHashing & SetsIntermediateLast updated March 26, 2026
Problem statement
Given an array of integers nums and an integer target, return a tuple (i, j) of indices such that nums[i] + nums[j] == target and i < j. If multiple valid pairs exist, return the pair corresponding to the earliest j when scanning from left to right (i.e., the first pair you find in a single pass). If no such pair exists, return None. Aim for O(n) time and O(n) extra space.
Task
Use a hash map to record seen values and their indices so you can find a complementary value in O(1) time per element.
Examples
Input format
two_sum_hash(nums, target) where nums is List[int] and target is int
Output format
A tuple (i, j) with i < j if a pair exists, otherwise None.
Constraints
2 <= len(nums) <= 10^5; integers are within 32-bit signed range. You may assume exactly one solution for some inputs, but your function should handle inputs with no solution by returning None.
Samples
Sample 1
Input
two_sum_hash([3,2,4], 6)
Output
(1, 2)
nums[1] + nums[2] == 6.