Teaching the analysis of algorithms with visual proofs

摘要

We describe an approach for visually teaching important proofs in the Junior-Senior level course on the design and analysis of data structures and algorithms (CS7/DS&A). The main idea of this educational paradigm is to justify important claims about data structures and algorithms by using pictures that visualize proofs so clearly that the pictures can qualify as proofs themselves. The advantage of using this approach for DS&A is that it augments or even replaces inductive arguments that many students find difficult. Moreover, this paradigm communicates important algorithmic facts in a compelling way for students who are more visually-oriented. We illustrate this technique by giving examples of visual proofs of several key concepts in DS&A.