Find the Unique Pair of Array Indices Whose Values Sum to a Target
Company: Meta
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
Given an array of integers `nums` and an integer `target`, return the indices of the two different elements whose values add up to `target`.
### Function Signature
```python
def two_sum(nums: list[int], target: int) -> list[int]:
```
### Rules
- Exactly one pair of indices `i < j` satisfies `nums[i] + nums[j] == target`.
- Return that pair as `[i, j]` with the smaller index first.
- An element cannot be paired with itself, although equal values at different indices may form the pair.
### Constraints
- `2 <= len(nums) <= 10000`
- `-10^9 <= nums[i] <= 10^9`
- `-10^9 <= target <= 10^9`
- Exactly one valid pair exists.
### 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: `2 + 4 = 6`; index 0 cannot be used twice to make `3 + 3`.
**Example 3**
Input: `nums = [3, 3]`, `target = 6`
Output: `[0, 1]`
Overview: Given an integer array and a target, return the indices of the only pair of different elements whose values add up to the target, smaller index first. Arrays hold up to 10,000 values of up to one billion in magnitude, and the task is a common warm-up that tests clean, efficient array reasoning.