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Binary Search Applications in Fractional Programming Consider an optimization problem where we seek the maximum average value over subarrays of minimum length. Given array elements $a_1, a_2, ..., a_n$ and minimum length constraint $L$, we want to find: $$\max_{\substack{1 \leq i \leq j \leq n \ j - i + 1 \geq L}} \frac{\sum_{k=i}^{j} a_k}{j - ...

Binary search extends far beyond locating values in sorted arrays. The core requirement for applying this technique is identifying a monotonic relationship between an independent variable and a computed result. When a problem can be modeled as finding an input x such that a monotonic function f(x) equals a specific target, binary search becomes ...