我为游戏Checkers编写了minimax算法alpha beta pruning,现在我正在尝试使用negamax方法重写它。我期待这两者是等价的,因为negamax只是一种编写极小极大的技巧。但由于某种原因,我的两种算法表现不同。当我在相同的输入上运行它们时,negamax版本似乎评估了更多的状态,所以我认为alpha beta修剪一定有问题。
下面的代码显示了两种算法(minimax
和negamax
函数),并在底部显示了我称之为play
的函数。 evaluate
函数是我用来评估两种算法中状态的基本启发式算法。
任何有关发现错误的帮助都会受到很多关注。
#include "player.hpp"
#include <algorithm>
#include <limits>
#include <cstdlib>
namespace checkers
{
int evaluatedStates = 0;
int evaluate(const GameState &state)
{
// FIXME: Improve heuristics.
int redScore = 0;
int whiteScore = 0;
int piece = 0;
for (int i = 1; i <= 32; ++i)
{
piece = state.at(i);
if (piece & CELL_RED) {
++redScore;
if (piece & CELL_KING)
redScore += 2; // King bonus.
} else if (piece & CELL_WHITE) {
++whiteScore;
if (piece & CELL_KING)
whiteScore += 2; // King bonus.
}
}
return state.getNextPlayer() == CELL_RED ? whiteScore - redScore : redScore - whiteScore;
}
int minimax(const GameState &state, int depth, int a, int b, bool max)
{
if (depth == 0 || state.isEOG()) {
++evaluatedStates;
return evaluate(state);
}
std::vector<GameState> possibleMoves;
state.findPossibleMoves(possibleMoves);
if (max) {
for (const GameState &move : possibleMoves) {
a = std::max(a, minimax(move, depth - 1, a, b, false));
if (b <= a)
return b; // β cutoff.
}
return a;
} else {
for (const GameState &move : possibleMoves) {
b = std::min(b, minimax(move, depth - 1, a, b, true));
if (b <= a)
return a; // α cutoff.
}
return b;
}
}
int negamax(const GameState &state, int depth, int a, int b)
{
if (depth == 0 || state.isEOG()) {
++evaluatedStates;
return evaluate(state);
}
std::vector<GameState> possibleMoves;
state.findPossibleMoves(possibleMoves);
for (const GameState &move : possibleMoves) {
a = std::max(a, -negamax(move, depth - 1, -b, -a));
if (b <= a)
return b; // β cutoff.
}
return a;
}
GameState Player::play(const GameState &pState, const Deadline &pDue)
{
GameState bestMove(pState, Move());
std::vector<GameState> possibleMoves;
pState.findPossibleMoves(possibleMoves);
int a = -std::numeric_limits<int>::max();
int b = std::numeric_limits<int>::max();
for (const GameState &move : possibleMoves) {
int v = negamax(move, 10, a, b);
//int v = minimax(move, 10, a, b, false);
if (v > a) {
a = v;
bestMove = move;
}
}
std::cerr << "Evaluated states: " << evaluatedStates << std::endl;
return bestMove;
}
/*namespace checkers*/ }
答案 0 :(得分:1)
您的minimax()
和negamax()
功能正确无误。我假设state.getNextPlayer()
返回必须下一步移动的玩家。这意味着您的evaluate()
和negamax()
函数会从该播放器的角度返回一个分数。
但是,minimax()
会从max
的角度返回分数。因此,如果您尝试在minimax()
函数中取消注释play()
,则会导致错误
//int v = negamax(move, 10, a, b);
int v = minimax(move, 10, a, b, false); // assumes perspective of min player
^^^^^
if (v > a) { // assumes perspective of max player
a = v;
bestMove = move;
}
使用minimax()
参数替换对true
的调用应解决此问题:
int v = minimax(move, 10, a, b, true); // assumes perspective of max player