Binary Search in a Rotated Sorted Array

Binary search is one of the most efficient search algorithms, reducing the search space by half with each iteration to achieve O(log n) time complexity. The key to applying binary search successfully is identifying that the search space has a monotonic property where one half always satisfies a condition while the other half does not. For this problem, we need to carefully define our search boundaries and the condition that determines which half to eliminate. Initialize the left boundary at the minimum possible answer and the right boundary at the maximum possible answer. In each iteration, compute the midpoint and evaluate whether the condition is satisfied. Based on the result, eliminate either the left or right half of the search space. The most common mistake in binary search is getting the boundary conditions wrong, which can lead to infinite loops or off-by-one errors. Always verify your implementation with edge cases: arrays of length 0, 1, and 2. Binary search can be applied beyond sorted arrays to any problem where you can binary search on the answer space, such as minimizing the maximum value, finding the smallest value that satisfies a condition, or optimizing a parameter with a monotonic feasibility function. This powerful technique transforms many brute-force O(n) or O(n^2) solutions into elegant O(log n) solutions.