A visual proof of amortised-linear resizable arrays

Abstract

We demonstrate visually why doubling capacity is the better strategy when resizing arrays. The visual proof makes simple amortised analysis more accessible to a CS2 audience.

Evaluating the Effectiveness of Algorithm Analysis Visualizations

“…Thompson and Chadhuri [18] present an alternative visual analysis of the Build-heap algorithm (as previously presented in [7]). Blaheta [1] presents a visual proof for amortized-linear resizable arrays by proving that doubling the capacity is the best strategy when resizing linear arrays. Sher [17] presents a visual proof of the average case running time of a list-searching algorithm.…”

“…The "Area-to-Cost Principle" uses graphical primitives to represent the amount of work required for each algorithm step, and then the total running time for the algorithm can be viewed as the total surface area of the resulting shape. This approach was applied in the Build-heap visual proof [18], the visual proof to find the closed form solution of the summation n i=1 i presented in [7], the amortizedlinear resizable array proof [1], and the alternating series convergence proof [9]. Figure 1 shows the Build-heap visual proof as presented in [18].…”

“…The addressed concepts are (1) relative growth rates, (2) algorithm upper, lower, and tight bounds, (3) problem upper and lower bounds, (4) best, average and worst cases, and (5) analyzing loop constructs. For concepts (1) and 5, we did not provide any AAV in OpenDSA. This gives us an opportunity to see the difference in performance on those concepts for which AAVs were provided versus those concepts where AAVs were not provided.…”