C++Alpha-Beta剪枝函数
时间: 2024-06-12 08:04:27 浏览: 19
Alpha-Beta剪枝函数是一种用于搜索算法中的优化技术,它可以帮助减少搜索空间,从而提高搜索效率。该算法是在Minimax算法的基础上进行的改进,Minimax算法是一种用于博弈论中的搜索算法。
在Alpha-Beta剪枝函数中,我们将搜索树中的节点分为两类:Alpha节点和Beta节点。Alpha节点表示当前玩家可以取得的最大分数,Beta节点表示对手可以取得的最小分数。在搜索树的遍历过程中,我们维护两个变量:alpha和beta,它们分别表示当前玩家可以取得的最大分数和对手可以取得的最小分数。
当搜索到一个节点时,如果当前节点是Alpha节点,则更新alpha的值,如果当前节点是Beta节点,则更新beta的值。在搜索过程中,如果发现某个节点的alpha值大于等于beta值,则说明当前节点的子树已经搜索完毕,可以直接剪枝。
Alpha-Beta剪枝函数可以大大减少搜索空间,从而提高搜索效率。它在许多博弈论和人工智能领域中得到广泛应用。
相关问题
用c++实现alphabeta剪枝五子棋
好的,下面是一个简单的五子棋AlphaBeta剪枝的C++实现。假设我们已经定义了一个棋盘类Board,其中包含了如下方法:
- `int getWinner()`:返回当前棋局的胜者,如果没有胜者则返回0;
- `vector<pair<int, int>> getPossibleMoves()`:返回当前可行的落子位置;
- `void makeMove(int x, int y, int player)`:在棋盘上落子,player为落子玩家的编号(1或2);
- `void unmakeMove(int x, int y)`:撤销上一次落子。
接下来是AlphaBeta剪枝的实现:
```c++
const int INF = 1e9;
int AlphaBeta(Board& board, int depth, int alpha, int beta, int player) {
// 到达搜索深度或者棋局结束,返回当前局面的得分
if (depth == 0 || board.getWinner() != 0) {
int score = board.evaluate(player); // 这里需要自己实现一个评估函数
return (player == 1) ? score : -score;
}
vector<pair<int, int>> moves = board.getPossibleMoves();
// 对可行的落子位置进行排序,以加速剪枝
sort(moves.begin(), moves.end(), [&](const pair<int, int>& a, const pair<int, int>& b) {
int sa = board.evaluateMove(a.first, a.second, player);
int sb = board.evaluateMove(b.first, b.second, player);
return sa > sb;
});
if (player == 1) {
for (auto [x, y] : moves) {
board.makeMove(x, y, player);
int val = AlphaBeta(board, depth - 1, alpha, beta, 3 - player);
board.unmakeMove(x, y);
alpha = max(alpha, val);
if (alpha >= beta) break; // beta剪枝
}
return alpha;
} else {
for (auto [x, y] : moves) {
board.makeMove(x, y, player);
int val = AlphaBeta(board, depth - 1, alpha, beta, 3 - player);
board.unmakeMove(x, y);
beta = min(beta, val);
if (alpha >= beta) break; // alpha剪枝
}
return beta;
}
}
pair<int, int> findBestMove(Board& board, int depth, int player) {
vector<pair<int, int>> moves = board.getPossibleMoves();
pair<int, int> bestMove = moves[0];
int bestScore = -INF;
for (auto [x, y] : moves) {
board.makeMove(x, y, player);
int score = AlphaBeta(board, depth - 1, -INF, INF, 3 - player);
board.unmakeMove(x, y);
if (score > bestScore) {
bestScore = score;
bestMove = {x, y};
}
}
return bestMove;
}
```
其中,`AlphaBeta()`函数实现了AlphaBeta搜索,`findBestMove()`函数则是对所有可行的落子位置进行搜索,返回最优的落子位置。在搜索时,我们需要定义一个评估函数`evaluate()`和一个落子评估函数`evaluateMove()`,用于评估当前局面和每个落子位置的得分。这些函数需要根据具体问题进行实现。
C++alphabeta剪枝算法五子棋
C++实现Alpha-Beta剪枝算法的五子棋代码:
```c++
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const int N = 15; // 棋盘大小
const int INF = 9999999; // 无穷大
int board[N][N]; // 棋盘
int player; // 玩家
int computer; // AI
int depth = 3; // 搜索深度
// 初始化棋盘
void init_board() {
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
board[i][j] = 0;
}
}
}
// 打印棋盘
void print_board() {
cout << " ";
for (int i = 0; i < N; i++) {
cout << " " << i + 1;
}
cout << endl;
for (int i = 0; i < N; i++) {
cout << i + 1 << " ";
for (int j = 0; j < N; j++) {
if (board[i][j] == player) {
cout << "O ";
} else if (board[i][j] == computer) {
cout << "X ";
} else {
cout << "+ ";
}
}
cout << endl;
}
}
// 判断游戏是否结束
bool game_over(int p) {
// 横向判断
for (int i = 0; i < N; i++) {
for (int j = 0; j <= N - 5; j++) {
if (board[i][j] == p && board[i][j + 1] == p && board[i][j + 2] == p && board[i][j + 3] == p && board[i][j + 4] == p) {
return true;
}
}
}
// 纵向判断
for (int i = 0; i <= N - 5; i++) {
for (int j = 0; j < N; j++) {
if (board[i][j] == p && board[i + 1][j] == p && board[i + 2][j] == p && board[i + 3][j] == p && board[i + 4][j] == p) {
return true;
}
}
}
// 斜向判断
for (int i = 0; i <= N - 5; i++) {
for (int j = 0; j <= N - 5; j++) {
if (board[i][j] == p && board[i + 1][j + 1] == p && board[i + 2][j + 2] == p && board[i + 3][j + 3] == p && board[i + 4][j + 4] == p) {
return true;
}
}
}
// 反斜向判断
for (int i = 0; i <= N - 5; i++) {
for (int j = 4; j < N; j++) {
if (board[i][j] == p && board[i + 1][j - 1] == p && board[i + 2][j - 2] == p && board[i + 3][j - 3] == p && board[i + 4][j - 4] == p) {
return true;
}
}
}
return false;
}
// 评估函数
int evaluate(int p) {
int score = 0;
// 横向评估
for (int i = 0; i < N; i++) {
for (int j = 0; j <= N - 5; j++) {
int cnt = 0;
for (int k = 0; k < 5; k++) {
if (board[i][j + k] == p) {
cnt++;
} else if (board[i][j + k] != 0) {
cnt = 0;
break;
}
}
score += cnt * cnt;
}
}
// 纵向评估
for (int i = 0; i <= N - 5; i++) {
for (int j = 0; j < N; j++) {
int cnt = 0;
for (int k = 0; k < 5; k++) {
if (board[i + k][j] == p) {
cnt++;
} else if (board[i + k][j] != 0) {
cnt = 0;
break;
}
}
score += cnt * cnt;
}
}
// 斜向评估
for (int i = 0; i <= N - 5; i++) {
for (int j = 0; j <= N - 5; j++) {
int cnt = 0;
for (int k = 0; k < 5; k++) {
if (board[i + k][j + k] == p) {
cnt++;
} else if (board[i + k][j + k] != 0) {
cnt = 0;
break;
}
}
score += cnt * cnt;
}
}
// 反斜向评估
for (int i = 0; i <= N - 5; i++) {
for (int j = 4; j < N; j++) {
int cnt = 0;
for (int k = 0; k < 5; k++) {
if (board[i + k][j - k] == p) {
cnt++;
} else if (board[i + k][j - k] != 0) {
cnt = 0;
break;
}
}
score += cnt * cnt;
}
}
return score;
}
// Alpha-Beta剪枝搜索
int alphabeta_search(int depth, int alpha, int beta, int p) {
if (depth == 0 || game_over(player) || game_over(computer)) {
return evaluate(computer) - evaluate(player);
}
vector<pair<int, int>> moves;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (board[i][j] == 0) {
moves.push_back(make_pair(i, j));
}
}
}
if (p == computer) {
int value = -INF;
for (auto move : moves) {
int i = move.first, j = move.second;
board[i][j] = p;
value = max(value, alphabeta_search(depth - 1, alpha, beta, player));
board[i][j] = 0;
alpha = max(alpha, value);
if (beta <= alpha) {
break;
}
}
return value;
} else {
int value = INF;
for (auto move : moves) {
int i = move.first, j = move.second;
board[i][j] = p;
value = min(value, alphabeta_search(depth - 1, alpha, beta, computer));
board[i][j] = 0;
beta = min(beta, value);
if (beta <= alpha) {
break;
}
}
return value;
}
}
// AI下棋
void computer_move() {
int value = -INF;
vector<pair<int, int>> moves;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (board[i][j] == 0) {
board[i][j] = computer;
int tmp = alphabeta_search(depth - 1, -INF, INF, player);
board[i][j] = 0;
if (tmp > value) {
value = tmp;
moves.clear();
moves.push_back(make_pair(i, j));
} else if (tmp == value) {
moves.push_back(make_pair(i, j));
}
}
}
}
int idx = rand() % moves.size();
int i = moves[idx].first, j = moves[idx].second;
board[i][j] = computer;
cout << "AI下棋: (" << i + 1 << "," << j + 1 << ")" << endl;
}
int main() {
init_board();
cout << "请选择先手(1:玩家 2:AI): ";
cin >> player;
if (player == 1) {
computer = 2;
} else {
computer = 1;
computer_move();
print_board();
}
while (true) {
int x, y;
cout << "请输入落子位置(x,y): ";
cin >> x >> y;
if (x < 1 || x > N || y < 1 || y > N || board[x - 1][y - 1] != 0) {
cout << "无效落子,请重新输入!" << endl;
continue;
}
board[x - 1][y - 1] = player;
if (game_over(player)) {
cout << "你赢了!" << endl;
break;
}
if (game_over(computer)) {
cout << "AI赢了!" << endl;
break;
}
computer_move();
print_board();
if (game_over(player)) {
cout << "你赢了!" << endl;
break;
}
if (game_over(computer)) {
cout << "AI赢了!" << endl;
break;
}
}
return 0;
}
```
这里使用了Alpha-Beta剪枝算法进行搜索,评估函数使用了一种简单的方式,即计算连续的空位个数的平方。可以根据需要进行更改。
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