极小化极大算法
Minimax算法(亦稱 MinMax or MM[1])又名极小化极大算法,是一种找出失败的最大可能性中的最小值的算法。
概述
Minimax算法常用于棋类等由两方较量的游戏和程序。该算法是一个零总和算法,即一方要在可选的选项中选择将其优势最大化的选择,另一方则选择令对手优势最小化的方法。而开始的时候总和为0。很多棋类游戏可以采取此算法,例如井字棋(tic-tac-toe)。
伪代码
function minimax(node, depth)
if node is a terminal node or depth = 0
return the heuristic value of node
if the adversary is to play at node
let α := +∞
foreach child of node
α := min(α, minimax(child, depth-1))
else {we are to play at node}
let α := -∞
foreach child of node
α := max(α, minimax(child, depth-1))
return α
参考文献
- Provincial Healthcare Index 2013 (Bacchus Barua, Fraser Institute, January 2013 -see page 25-)
外部連結
- Hazewinkel, Michiel (编), , , Springer, 2001, ISBN 978-1-55608-010-4
- A visualization applet
- Maximin principle at Dictionary of Philosophical Terms and Names
- Play a betting-and-bluffing game against a mixed minimax strategy
- Minimax at Dictionary of Algorithms and Data Structures
- Minimax (with or without alpha-beta pruning) algorithm visualization — game tree solving (Java Applet), for balance or off-balance trees.
- Minimax Tutorial with a Numerical Solution Platform
- Java implementation used in a Checkers Game
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