AlphaBetaSearch.java

package aima.core.search.adversarial;

import aima.core.search.framework.Metrics;

/**
 * Artificial Intelligence A Modern Approach (3rd Ed.): Page 173.<br>
 * 
 * <pre>
 * <code>
 * function ALPHA-BETA-SEARCH(state) returns an action
 *   v = MAX-VALUE(state, -infinity, +infinity)
 *   return the action in ACTIONS(state) with value v
 *   
 * function MAX-VALUE(state, alpha, beta) returns a utility value
 *   if TERMINAL-TEST(state) then return UTILITY(state)
 *   v = -infinity
 *   for each a in ACTIONS(state) do
 *     v = MAX(v, MIN-VALUE(RESULT(s, a), alpha, beta))
 *     if v >= beta then return v
 *     alpha = MAX(alpha, v)
 *   return v
 *   
 * function MIN-VALUE(state, alpha, beta) returns a utility value
 *   if TERMINAL-TEST(state) then return UTILITY(state)
 *   v = infinity
 *   for each a in ACTIONS(state) do
 *     v = MIN(v, MAX-VALUE(RESULT(s,a), alpha, beta))
 *     if v <= alpha then return v
 *     beta = MIN(beta, v)
 *   return v
 * </code>
 * </pre>
 * 
 * Figure 5.7 The alpha-beta search algorithm. Notice that these routines are
 * the same as the MINIMAX functions in Figure 5.3, except for the two lines in
 * each of MIN-VALUE and MAX-VALUE that maintain alpha and beta (and the
 * bookkeeping to pass these parameters along).
 * 
 * @author Ruediger Lunde
 * 
 * @param <STATE>
 *            Type which is used for states in the game.
 * @param <ACTION>
 *            Type which is used for actions in the game.
 * @param <PLAYER>
 *            Type which is used for players in the game.
 */
public class AlphaBetaSearch<STATE, ACTION, PLAYER> implements
		AdversarialSearch<STATE, ACTION> {

	Game<STATE, ACTION, PLAYER> game;
	private int expandedNodes;

	/** Creates a new search object for a given game. */
	public static <STATE, ACTION, PLAYER> AlphaBetaSearch<STATE, ACTION, PLAYER> createFor(
			Game<STATE, ACTION, PLAYER> game) {
		return new AlphaBetaSearch<STATE, ACTION, PLAYER>(game);
	}

	public AlphaBetaSearch(Game<STATE, ACTION, PLAYER> game) {
		this.game = game;
	}

	@Override
	public ACTION makeDecision(STATE state) {
		expandedNodes = 0;
		ACTION result = null;
		double resultValue = Double.NEGATIVE_INFINITY;
		PLAYER player = game.getPlayer(state);
		for (ACTION action : game.getActions(state)) {
			double value = minValue(game.getResult(state, action), player,
					Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
			if (value > resultValue) {
				result = action;
				resultValue = value;
			}
		}
		return result;
	}

	public double maxValue(STATE state, PLAYER player, double alpha, double beta) {
		expandedNodes++;
		if (game.isTerminal(state))
			return game.getUtility(state, player);
		double value = Double.NEGATIVE_INFINITY;
		for (ACTION action : game.getActions(state)) {
			value = Math.max(value, minValue( //
					game.getResult(state, action), player, alpha, beta));
			if (value >= beta)
				return value;
			alpha = Math.max(alpha, value);
		}
		return value;
	}

	public double minValue(STATE state, PLAYER player, double alpha, double beta) {
		expandedNodes++;
		if (game.isTerminal(state))
			return game.getUtility(state, player);
		double value = Double.POSITIVE_INFINITY;
		for (ACTION action : game.getActions(state)) {
			value = Math.min(value, maxValue( //
					game.getResult(state, action), player, alpha, beta));
			if (value <= alpha)
				return value;
			beta = Math.min(beta, value);
		}
		return value;
	}

	@Override
	public Metrics getMetrics() {
		Metrics result = new Metrics();
		result.set("expandedNodes", expandedNodes);
		return result;
	}
}