Practical Applications of Binary Search and Fractional Programming

Binary search is a fundamental algorithm with applications in various computational problems. The key considerations when implementing binary search include identifying the search target, determining search boundaries, and designing the validation function. Music Notes Timing Analysis Determine the number of songs played within a given time fra ...

Posted on Wed, 13 May 2026 19:18:36 +0000 by Ghost_81st

Optimal Network Cable Segmentation for Competition Setup

Problem Description A programming competition is being organized where all participant computers must be connected to a central server using equal-length cables arranged in a star topology. Given a colleciton of network cables of various lengths, the objective is to determine the maximum possible length such that exactly K segments of equal len ...

Posted on Wed, 13 May 2026 01:38:41 +0000 by birwin

SMU Autumn 2023 Round 2 (Div.1+2) - Problem Solutions

C. Chaotic Construction When the circular track is unwrapped into a linear sequence from 1 to 2n, placing a barrier at position D corresponds to having barriers at both D and D+n on this line. For any query (x, y), we check whether any barrier falls between x and y, or between x and y+n. We maintain a booolean array to track which positions are ...

Posted on Sun, 10 May 2026 16:35:21 +0000 by Gibb Boy

Unconventional Approaches to Dynamic Programming Optimization

DP optimization often feels like an arcane art. The question arises: can anyone actually devise such solutions during a programming contest? (Perhaps I'm still learning this skill.) The core ideas I've encountered fall into these categories: When transitioning from state i to i+1, the number of states that change is small, so we can inherit val ...

Posted on Sun, 10 May 2026 08:00:30 +0000 by maxpagels

Minimum Days to Create m Bouquets Using Binary Search

Problem Overview Given an array bloomDay where bloomDay[i] represents the day on which the i-th flower blooms, determine the minimum number of days required to make m bouquets. Each bouquet requires exactly k adjacent flowers that have already bloomed. If it's impossible to create m bouquets (insufficient flowers), return -1. Constraints 1 &lt ...

Posted on Sat, 09 May 2026 21:41:34 +0000 by dujed

Abstracting Binary Search for Monotonic Function Boundaries

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 ...

Posted on Sat, 09 May 2026 17:30:22 +0000 by twister47