Algorithms Study Guide

To determine the correct output of an algorithm, it's essential to follow the instructions precisely, step by step, as they would be executed by a computer. This involves tracking the values of all variables at each stage of the algorithm's execution. A trace table is a powerful tool for this purpose. It is a systematic way to record the values of variables and the output of an algorithm as it progresses through its steps with a given set of input data. Each row in the trace table typically represents a single execution step or iteration, and each column represents a variable or the output. By diligently filling out a trace table, one can accurately predict the final state of variables and the ultimate output, helping to identify logical errors or unexpected behaviour within the algorithm.

Evaluating an algorithm means logically analysing whether it effectively solves the intended problem (fitness for purpose) and how well it uses computational resources (efficiency). Fitness for purpose requires confirming that the algorithm gives correct and reliable results for all expected inputs, including edge and invalid cases. Efficiency involves assessing the use of time (such as number of comparisons or passes through loops) and memory required, especially as input sizes increase. Logical reasoning helps predict an algorithm’s behaviour, while applying varied test data assures intended performance and reveals possible weaknesses, ensuring thorough evaluation.