Binary search is a fundamental algorithm used to quickly find an element in a sorted array or list. It works by repeatedly dividing the search space in half until the target element is found or the search space is empty, resulting in a time complexity of O(log n). Binary search can be applied in various competitive programming scenarios beyond just finding elements in sorted lists. For example, it can be used to find the smallest or largest value that meets a certain condition in optimization problems, such as finding the minimum height of a ladder required to reach a certain point. Additionally, binary search can be applied to floating-point numbers by defining a small range tolerance, which is useful in problems involving real numbers. By mastering binary search and understanding its applications, you’ll be able to solve a wide range of problems efficiently, especially those that require searching in sorted data.