An alternative visual analysis of the build heap algorithm

Abstract

This article presents an alternative visual analysis of the BUILDHEAP algorithm provided by Goodrich and Tamassia [4]. The analysis is based only on elementary properties of complete binary trees and a simple comparison of the areas of rectangles. As such, it should be accessible to a wide cross-section of students taking a typical algorithm design and analysis course.

Evaluating the Effectiveness of Algorithm Analysis Visualizations

“…Goodrich and Tamassia [7] present simple visual proofs for several core topics in DSA courses (summing linear terms, counting nodes in a binary tree, analyzing binary tree traversal, analyzing bottom-up heap construction, rebalancing AVL trees via rotations) in an attempt to justify the potential of using visual alternatives for teaching algorithm analysis concepts. 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.…”

“…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].…”

“…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]. On the other hand, the binary tree traversal, the bottom-up heap construction description, and the analysis of AVL trees proofs presented in [7] apply what we refer to as the "Visual Description Principle".…”