Lecture Notes in Computer Science- P59 pptx

Learning Kruskal's Algorithm, Prim's Algorithm and Dijkstra's Algorithm by Board Game 279 (4) All the players have to learn the related knowledge about the shortest path algo- rithm and minimum spanning tree. 5.3 Game Progress In the new edition of Ticket to Ride, we fixed some rules based on original rules be- cause of our ideal – combining the board game and three minimum spanning tree theories. The progress is likely the original game. The difference between new and old edition games is that we gave the new game an additional element. The element is the concept of start location and minimum spanning tree theories cards. First, players should cast a start point and knowledge card. Then, they should choose if they want them. After casting start point and knowledge cards, players begin to a single turn. In the single turn, players can do three actions: (1) Draw two of the railway cards or choose one which is opened directly. (2) Draw three of the 3 ticket cards, and reserve the selected ticket. (3) Re-cast new start point card and knowledge cards. (4) Put the railway carriages on the map to establish the route. Players also can skip the step if there is no available condition. In principle, the game will repeat these four steps until a player rich the end condi- tions of single round game. The game progress graph is shown in Fig.2. 5.4 Game Regulations There are the descriptions of the game regulations. (1) The station recorded in the starting point card has to match the stations in the knowledge card else the player cannot play the game (example is shown in Table 1). (2) Regulations of drawing the railway card: a. Railway card color: white black red yellow orange blue purple green full-color. b. In the beginning of each round, the railway cards are divided into two piles. One is composed of five opened cards and the other one is covered pile of cards. c. When drawing the cards, each player can select two cards from the covered pile of cards else select the card from five opened cards. It means player can get the wanted card which is opened. (3) Players can give up the knowledge card in hands, and player’s score will be detected according to the card. Then the player proceeds game from pick up the starting point. (4) After the player completed one knowledge card, player can decide if he/she will continue draw next knowledge card or not. (5) Establish the player’s railway routes: a. The color of the railway card and spaces of the map routes are matched, then the railway cards can occupy the routes of the railway map. The full-color card can occupy any color routes on the map. For example, there are three white 280 W C. Chang, Y D. Chiu, and M F. Li spaces on the route [BRAGANCA-BENAVENTE], the player can occupy the route with three railway cards combination. First one is three white railway cards; Second is two white and one full-color railway cards; Third is one white and two full-color railway cards; Fourth, three full-color railway cards. The other card combinations are useless. b. Grey route is available for all the colors. For example, there are three grey spaces on the route [BRAGANCA-SALAMANCA], any kinds color of rail- way cards are acceptable, such as two orange and one red railway cards. c. The quantity of the railway cards and spaces of the map routes are matched, then the railway cards can occupy the routes of the railway map. d. If the route of the map is occupied by other players, this route cannot be used by others. 5.5 Score Rules The score rules of this game are listed in the following: (1) The player will gain 10 score if the player used the most railway carriages. (2) If the ticket card is completed, the player will get the score on the card. On the country, the player did not complete the ticket card will deduct the score. (3) The score of ticket card is calculated by the shortest path from starting point to destination. For instance, the route. For instance, the route, [VALENCA-VERIN] shortest path is 3 and the route [VALENCA-BRAGA] shortest path is 2, others are following the rules. (4) Knowledge card score consists of two parts; first one is partial score when the player completed part of the answer route, second is completed score when the player completed all the answer routes. (example is shown in Table 2) In order to encourage the player follow the correct algorithm, we give high scores for players. We give a sample of Dijkstra’s algorithm in Table 2. When the player com- pleted one edge of the answer route and the railway carriages establish order is exactly the same as the Dijkstra’s algorithm, the player will get the score with three times of the spaces number of the edge. The edge from VALENCA to VERIN has 3 spaces of railway carriage; the gaining score is 3*3=9. The completed score is based on the railway stations in the knowledge card. After players completed the correct order of the algorithm, then players get the completed score. Table 1. Example of choosing start point card and knowledge card The starting point card player owned The recorded linked stations on the knowledge card Result VERIN VALENCA, BRAGA, CHAVES, VILA REAL, BRAGANCA Useless knowledge card VERIN VALENCA,BRAGA, CHAVES, VERIN, BRAGANCA Usable knowledge card Learning Kruskal's Algorithm, Prim's Algorithm and Dijkstra's Algorithm by Board Game 281 Fig. 2. Single round for each player 282 W C. Chang, Y D. Chiu, and M F. Li Table 2. Example of accomplish Knowledge cards and ticket cards Connected Railway Stations Knowledge Partial Score Completed Score VALENCA,VERIN,BENAV ENTE,BRAGANCA,CHAV ES,BRAGA, PORTO Dijkstra’s algorithm spaces number of the route*3 14 VALENCA,VERIN,BENAV ENTE,BRAGANCA,CHAV ES,BRAGA, PORTO Prim’s algorithm spaces number of the route *2 14 VALENCA,VERIN,BENAV ENTE,BRAGANCA,CHAV ES,BRAGA Prim’s algorithm spaces number of the route *2 12 Table 3. Comparison with traditional Education and Teaching combining board game Traditional Education Teaching minimum spanning tree theories combining board game Darren Lim ’s theory Efficiency in learning Teachers’ ability effect the level of efficiency in learning. Students can clarify their learning problem with game. Students can clarify their learning problem with game. Interest in learning Hard to let student interested in learning. Easier to make students interested in learning. Easier to make students interested in learning. Students’ feeling in learning spanning three theories. Abstract Easier to catch the theories Easier to catch the theories Prepare before learning None Students have to contact this kind of knowledge before. Students have to contact this kind of knowledge before. Usable computer science All computer sciences Graph theory Programming, Data Structure, Graph Theory 6 Comparison In this section, we compare this kind of teaching combining board game with tradi- tional education and Darren Lim’s theory [1] in several points of view in Table 3. After the comparison, we can clearly find the advantage in teaching minimum spanning tree theories combining board game. These advantages are: (1) Efficiently in learning: Students can use an existence to help them to learn, the minimum spanning tree theories are not abstracts, again. Learning Kruskal's Algorithm, Prim's Algorithm and Dijkstra's Algorithm by Board Game 283 (2) Interest in learning: Because of this tool is game, so students can learn knowledge with playing game. Anyway, playing is always funnier than sitting in the class- room. On the other hand, teaching minimum spanning tree theories combining board game also have a weak point. Students have to know this kind knowledge first, then, they can use the game help learning, and Darren Lim’s theory is, too. Compare with Darren Lim’s theory, we can find Darren Lim’s theory can use in more computer science, but depth of implement, we have concreteness ideas. We made an additional comparison table shown in Table 4. In Table 4, we compare our ideal with Darren Lim’s theory in the points of view “how to implement”, “usable range”, and “if the ideal be computerized”. We can dig out a characteristic in Darren Lim’s theory. The characteristic is the theory can be use in widen range. In the other hand, our ideal is better in having a clear and definite way to implement it. Table 4. Comparison with Darren Lim’s theory Teaching minimum spanning tree theories combining board game Darren Lim’s theory If the ideal be computerized? On cybernation No mention How to teach these concepts? Have clear and definite rules to express concepts Abstract ideal and no de- tailed description Usable range in computer science Only in graph theory Not only in graph theory, but also in data structure and programming 7 Conclusion How to teach and learn the theories of graph is an important to teachers and students. And, how to express some abstract knowledge concepts is difficult. But there, we use game to express and help students to learn minimum spanning tree theories. By this way, we believe that these minimum spanning tree concepts can be learned much more efficiently. If the idea – combining board game Ticket to Ride with minimum spanning tree theories can be cybernated, the speed of learning must be shorter and the efficiency would be higher. Acknowledgements We would like to thank National Science Council and Chung Hua University. This research was supported in part by a grant from NSC 96-2520-S-216-001 and CHU 96-2520-S-216-001, Taiwan, Republic of China. This paper owes much to the thoughtful and helpful comments of the reviewers. . learning problem with game. Students can clarify their learning problem with game. Interest in learning Hard to let student interested in learning. Easier to make students interested in. points of view in Table 3. After the comparison, we can clearly find the advantage in teaching minimum spanning tree theories combining board game. These advantages are: (1) Efficiently in. Traditional Education Teaching minimum spanning tree theories combining board game Darren Lim ’s theory Efficiency in learning Teachers’ ability effect the level of efficiency in learning. Students