This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses two pointers to scan from both ends of a sorted list. We compare these algorithms in terms of time complexity, space complexity, and practical performance. Our findings demonstrate that while Linear Search is straightforward, it is inefficient for large datasets. Binary Search is efficient for sorted data but requires an initial sorting step. The Two Pointer Search, combining elements of both methods, offers a practical balance of simplicity and efficiency. We propose a novel implementation of the Two Pointer Search algorithm and validate its performance through comprehensive testing on various hardware configurations. The results indicate that our proposed algorithm significantly improves search efficiency, making it suitable for both sorted and unsorted datasets. Future work will extend this algorithm to more complex data structures and real-world applications.