Three Efficient Approaches - > Two Sum Problem

The provided text outlines three distinct strategies for solving the Two Sum problem from LeetCode, which requires finding the indices of two numbers in an array that equal a specific target sum. The most basic approach is a brute force method that checks every possible pair, resulting in an inefficient $O(n^2)$ time complexity. A more optimized solution involves using a two-pointer technique on a sorted version of the data, which improves the performance to $O(n \log n)$ while requiring extra steps to preserve original indices. The most effective strategy discussed is utilizing a hash map to store previously seen values and their positions, allowing the program to identify the necessary complement in a single pass. This final method achieves an ideal $O(n)$ time complexity by leveraging constant-time lookups. The guide also highlights critical edge cases, such as preventing the reuse of a single element to reach the target sum