Two Sum Problem

Two Sum My Thinking and Approach Introduction In this problem, I was given an array of integers and asked to find two numbers such that their sum equals a given target. This problem is simple but important for understanding optimization techniques. Problem Statement Given an array of integers nums Given an integer target Return indices of two numbers such that: nums[i] + nums[j] = target Conditions: Only one valid solution exists Cannot use the same element twice Return indices in any order My Initial Thought At first, I considered: Using two loops Checking all possible pairs But this approach takes more time and is not efficient. Key Observation Instead of checking all pairs: For each number, I can calculate the complement Complement = target - current number If the complement already exists, I found the answer. Optimized Approach I decided to: Use a dictionary (hashmap) Store numbers and their indices Check for complement while traversing Logic: If complement exists → return indices