# Algorithmic Problem Solving

Research Group, University of Nottingham

The algorithmic problem solving group conducts research into mathematical method, in particular the problem-solving skills involved in the formulation and solution of algorithmic problems. Our goal is to articulate these skills primarily by way of concrete examples, but also by the development of appropriate mathematical theory.

## The Capacity C Torch Problem

Roland Backhouse, Mathematics of Program Construction, 2008.

The torch problem (also known as the bridge problem or the flashlight problem) is about getting a number of people across a bridge as quickly as possible under certain constraints. Although a very simply stated problem, the solution is surprisingly non-trivial. The case in which there are just four people and the capacity of the bridge is two is a well-known puzzle, widely publicised on the internet. We consider the general problem where the number of people, their individual crossing times and the capacity of the bridge are all input parameters. We present an algorithm that determines the shortest total crossing time; the number of primitive computations executed by the algorithm (i.e. the worst-case time complexity of the algorithm) is proportional to the square of the number of people.