Binary search is an efficient algorithm used to find a target value in a sorted array. It works by repeatedly dividing the search interval in half, offering a time complexity of O(log n).

Binary search is one of the most efficient algorithms in competitive programming for searching a target value in a sorted array or determining an optimal solution in optimization problems. The algorithm works by dividing the search space in half with each iteration, reducing the time complexity to O(log n), which makes it extremely fast for large input sizes. For example, if you have an array of one million elements, binary search will find the target in about 20 iterations, which is much faster than a linear search that would require up to a million comparisons. The basic idea behind binary search is to compare the target value with the middle element of the array. If the target is smaller than the middle element, you discard the upper half of the array and continue searching in the lower half. Conversely, if the target is larger, you discard the lower half and search in the upper half. Binary search can also be applied to problems beyond searching for a specific element in an array. It's commonly used in optimization problems where you're trying to find the minimum or maximum value that satisfies a certain condition, such as in scheduling problems or finding the smallest possible value that allows a task to be completed within a given constraint. One of the key challenges in binary search is handling edge cases, such as when the target value doesn't exist in the array or when the search space is empty. Understanding how and when to apply binary search can significantly improve your problem-solving efficiency in competitive programming.