Two Sum - Algorithm

Use a hash map from value to index:

$1.$ For each index $i$ with value $nums[i]$:

• Compute $complement = target - nums[i]$
• If $complement$ is in the map, return $[map[complement], i]$
• Otherwise, add $nums[i] \to i$ to the map

$2.$ If no pair found, return empty (but problem guarantees a solution exists). One pass through the array. Each element is checked and added once. Time: $O(n)$. Space: $O(n)$.