QuestionsQuestions are asked periodically throughout the visualizations in order to:•Direct the learner’s attention to key points•Give them the opportunity to exercise their understanding of the algorithm•Encourage them to more fully grasp the algorithm

PseudocodeBecause of the nature and complexity of the algorithms, pseudocode is presented to the student alongside the graphical visualizations.

Advantages to displaying a pseudocode pane:• Pertinent line (or lines) are highlighted at each step• Method scope changes are show along with the visualization.• A call stack is presented to the user, indicating the recursive nature of the algorithm.

The Minimax and alpha-beta pruning algorithms are both highly recursive algorithms; therefore, displaying the call stack to the student is very helpful for keeping track of method calls.

Call Stack

Variables

A list of variables and their values are kept updated for each step of the algorithm.

Visualizing Minimax

Color CodingSince Minimax explores game states of a tree, it is essential that the student be shown the progress of recursion, and additionally which nodes have been visited and which node is currently being explored.

The temporary utility value for a node is displayed to the left of a node and is updated if a better child is explored. The final utility value of the node is placed in the node after all candidate children have been explored.

Nodes in the visualization are color coded and updated over the course of the visualization:

White – node unvisitedYellow – node visitedOrange – current nodeGreen – node selected

Node UtilitiesIt is important that the student see how the algorithm keeps track of a given node’s utility.

Explanatory CaptionsTo assist the user in easily following the

current state of the visualization, a caption describing the current step of the algorithm is displayed above the tree.

Since no children have been explored yet, a temporary value is set to infinity.

The final selected action is shownIn green with an arrow pointingfrom the root to the selected node

IntroductionResearch Problem

Students enrolled in Artificial Intelligence classes often struggle with concepts relating to adversarial search, specifically the Minimax algorithm and alpha-beta pruning.

SolutionAn interactive algorithm visualization could engage students and deepen their understanding of the Minimax algorithm and its role in adversarial search.

Algorithm VisualizationA considerable amount of research has focused on the development of students’ understanding of advanced computer science algorithms.

It has been proposed that when engaged in the visualization. However, many algorithm visualizations are limited in their functionality.

Students learn at different speeds. The JHAVÉ visualization environment allows students to step forward and backward through the visualization at his or her own pace.

Visualizing Alpha-Beta Pruning

Alpha and BetaOne of the greatest difficulties students have in learning Minimax with Alpha-Beta Pruning is with keeping track of the Alpha and Beta values which are displayed to the left of the nodes which don’t represent an end state.

Pruning

To indicate when alpha beta pruning takes place a slash is placed across the edge connecting the pruned subtree to its parent, and, keeping with the proposed coloring scheme, the pruned (unexplored) nodes are left white.

One main difference, is that MAX nodes are labeled with their respective alpha values and MIN nodes are labeled with their respective beta values.

Since alpha-beta pruning is a subtle extension to the Minimax algorithm, many of the components of the alpha-beta pruning visualization are similar to the Minimax visualization.

Related WorksMany previous Minimax algorithm visualizations provide the following functionality to learners: • Random tree generation• Node and utility tracking• alpha and beta tracking when applying pruning

Our visualizations adds to these features by providing the learner with the following:• Modularized learning for Minimax and Minimax with alpha-beta pruning• Pseudocode highlighting• Explanatory captions and progressive utility tracking• Question generation and learner assessment Input Generator

Students are permitted to set bounds on the size of a randomly generated trees, or input a tree of their own design using a proprietary string to tree input scheme. This is recommended especially for users who wish to sample both algorithms and observer the nuances given the same tree.

ACKNOWLEDGEMENTSSpecial thanks to Professors George Thomas and Tom

Naps, the University of Wisconsin Oshkosh, the National Science Foundation, and the

support of our fellow researchers.

This project was funded under the NSF REU site award 0851569 at the University of Wisconsin Oshkosh.

Department of Computer ScienceUniversity of Wisconsin - Oshkosh

June 20 11 -July 2011

J.T. GralkaWashington & Jefferson Collegegralkajt@jay.washjeff.edu

Christopher WittUniversity of Wisconsin - Whitewaterwittcm19@uww.edu

Future WorkBecause these two algorithms have ‘real world’ applications in the field of Artificial Intelligence and game theory, a natural extension of this project would be to create a visualization for simple games, e.g., tic-tac-toe.

Source: Hofstadter, Douglas (1979). Gödel, Escher, Bach:

An Eternal Golden Braid

A visualization of a practical example might provide learners with a better grasp of Minimax and alpha-beta pruning.

A hypertext book is under development. This online textbook will include explanations of the algorithms and pseudocode as well as provide information on the java implementation. Students will be able to interact with various examples and practice exercises to help hone their understanding of the Minimax algorithm as well as it’s applications to the real world.