4 Modeling and Simulation
This chapter covers
- Recognizing modeling problems in the context of USACO.
- Solving dynamic modeling problems described by a progression of steps.
- Solving static modeling problems described by a scenario and rules.
- Analyzing periodic modeling problems and using the appropriate tools for solving.
- Accelerating the solutions of modeling problems.
Modeling problems are often referred to as simulation problems or implementation problems. These problems describe a process and ask a question related to the outcome of this process.
For example, consider a modeling problem where a cyclist adapts her speed in response to the terrain. When she pedals uphill, her speed is reduced by half every minute. When she pedals downhill, her speed triples every minute. Given a specific terrain and a starting speed, you are asked to simulate her speed along the ride and determine her finish time for a race.
At the Bronze level, solving modeling problems usually boils down to brute-force implementation of the procedure described in the problem. Thus, the main goal of the problem is to assess one’s ability to understand the process, to pay attention to the fine details of implementation, and to demonstrate mastery of the programming language.