Find the Earliest Pair with a Target Sum

Problem Statement

Given an array of integers nums and an integer target, find a pair of elements at distinct indices (i, j) with i < j such that nums[i] + nums[j] == target.

Among all valid pairs (i, j):

1. Choose the pair that minimizes the second index j.
2. If there is a tie for the smallest j, choose the pair that minimizes the first index i.

Return the values as a list [nums[i], nums[j]]. If no such pair exists, return an empty list [].

Function Signature

def earliest_pair_sum(nums: list[int], target: int) -> list[int]:
    pass

Examples

Example 1

Input: nums = [10, 5, 2, 3, 7, 5], target = 10
Output: [3, 7]
Explanation:
- Pair at indices (1, 5): nums[1] + nums[5] = 5 + 5 = 10 (j = 5)
- Pair at indices (3, 4): nums[3] + nums[4] = 3 + 7 = 10 (j = 4)
Since index 4 < 5, the pair [3, 7] has the earlier second index.

Example 2

Input: nums = [4, 3, 2, 3, 4], target = 6
Output: [4, 2]
Explanation:
Valid pairs summing to 6 are:
- (0, 2): 4 + 2 = 6 (j = 2)
- (1, 3): 3 + 3 = 6 (j = 3)
- (2, 4): 2 + 4 = 6 (j = 4)
The pair with the smallest second index is at (0, 2), so the output is [4, 2].

Example 3

Input: nums = [1, 2, 3], target = 10
Output: []
Explanation: No two elements sum to 10.

Constraints

• 0 <= len(nums) <= 10^5
• -10^9 <= nums[i] <= 10^9
• -10^9 <= target <= 10^9