The Secret to Solving Two Sum Efficiently

To optimize this problem, we need an important observation. If the current number

is X, then to reach the target, we need another number equal to

target minus X, and this value is called the compliment. We can use a HashMap to solve this efficiently.

The idea is simple. We traverse the array once. For each number, we compute its compli-

compliment. We check if the compliment already exists in the map. If it exists,

we have found our answer. If it doesn't, we store the current number and its index

in the map. This approach works because we only look at previous elements.

We never use the same element twice. We find the solution in a single pass. This reduces the