What are some algorithms to solve the two-sum problem?

What are some algorithms to solve the two-sum problem?

The two-sum problem involves finding two numbers in an array that add up to a specific target. Common algorithms include:

1. Brute Force: Check all pairs of numbers.
2. Hash Map: Store numbers in a hash map for quick lookup.
3. Sorting: Sort the array and use two pointers to find the sum.

Can you explain the hash map approach in detail?

Sure! In the hash map approach, you iterate through the array and for each number, calculate the complement (target - current number). You then check if this complement exists in the hash map. If it does, you've found your two numbers. If not, you add the current number to the hash map and continue.

What is the time complexity of the hash map approach?

The time complexity of the hash map approach is O(n), where n is the number of elements in the array. This is because you traverse the array once and each lookup in the hash map is O(1) on average.

Are there any space complexity concerns with this method?

Yes, the space complexity is O(n) as well, since in the worst case, you may need to store all n elements in the hash map.