运用了极小化极大算法，α-β剪枝。经过最近的优化，运行速度提高了许多，在maxDepth为3的情况下（加根节点是4层），开启O2优化并且用Release版本编译，能达到两秒左右搜索完毕。这个版本把maxDepth改为4，搜索时间大概30秒左右。
关于本文使用的估价函数，可以参考这篇博客。
#pragma once
#include<iostream>
#include<vector>
#include<array>
#include<fstream>
#include<algorithm>
class GameTree
{
public:
class Node
{
public:
enum State :uint8_t/*节省内存*/ { SPACE, BLACK, WHITE };
private:
friend class GameTree;
static const uint8_t BOARDSIZE = 15;
int value;//叶节点表示估价函数的结果，MAX节点表示α值，MIN节点表示β值
int evaluateValue;//估价函数计算的结果，用于优化
unsigned short depth;//深度
uint8_t lastX, lastY;//上一次落子的xy坐标
Node* father;//父亲节点
std::vector<Node*> children;//子节点
State **board;//棋盘
int Evaluate()const//估价函数
{
static auto EvaluateSome = [](State **board, uint8_t beginX, uint8_t endX, uint8_t beginY, uint8_t endY) {
static auto EvaluateList = [](const std::array<State, 5>& v)//假定自己是白方
{
//判断颜色并记录棋子个数
State lastColor = SPACE;
uint8_t count = 0;
for (State i : v)
{
if (i != SPACE)
{
++count;
if (i != lastColor)
{
if (lastColor == SPACE)//遇到的第一个棋子
{
lastColor = i;
}
else//有不同颜色的棋子
{
return 0;
}
}
}
}
if (!count)//没有棋子
return 0;
if (count == 5)
{
return lastColor == WHITE ? INT_MAX : INT_MIN;//一定不要认为-INT_MAX就是INT_MIN！
}
const int result = static_cast<int>(std::pow(10, count - 1));
return lastColor == WHITE ? result : -3 * result;//对手返回负值，我方返回正值
};
int result = 0;
for (uint8_t i = beginX; i < endX; i++)//分别从四个方向判断
{
for (uint8_t j = beginY; j < endY; j++)
{
if (j + 4 < endY)
{
std::array<State, 5>v;
for (uint8_t k = 0; k < 5; k++)
v[k] = board[i][j + k];
const int t = EvaluateList(v);
if (t == INT_MAX || t == INT_MIN)//决出胜负直接返回
return t;
result += t;
}
if (i + 4 < endX)
{
std::array<State, 5>v;
for (uint8_t k = 0; k < 5; k++)
v[k] = board[i + k][j];
const int t = EvaluateList(v);
if (t == INT_MAX || t == INT_MIN)//决出胜负直接返回
return t;
result += t;
}
if (i + 4 < endX && j + 4 < endY)
{
std::array<State, 5>v;
for (uint8_t k = 0; k < 5; k++)
v[k] = board[i + k][j + k];
const int t = EvaluateList(v);
if (t == INT_MAX || t == INT_MIN)//决出胜负直接返回
return t;
result += t;
}
if (i + 4 < endX && j >= 4)
{
std::array<State, 5>v;
for (uint8_t k = 0; k < 5; k++)
v[k] = board[i + k][j - k];
const int t = EvaluateList(v);
if (t == INT_MAX || t == INT_MIN)//决出胜负直接返回
return t;
result += t;
}
}
}
return result;
};
uint8_t beginX, endX, beginY, endY;
if (lastX <= 5)
beginX = 0;
else
beginX = lastX - 5;
endX = lastX + 5;
if (endX > BOARDSIZE)
endX = BOARDSIZE;
if (lastY <= 5)
beginY = 0;
else
beginY = lastY - 5;
endY = lastY + 5;
if (endY > BOARDSIZE)
endY = BOARDSIZE;
const int t = EvaluateSome(board, beginX, endX, beginY, endY);
if (t == INT_MAX || t == INT_MIN)//决出胜负直接返回
return t;
return t - EvaluateSome(father->board, beginX, endX, beginY, endY) + father->evaluateValue;
}
public:
//非根节点的构造函数
Node(Node* nf, uint8_t x, uint8_t y) :father(nf), lastX(x), lastY(y), depth(nf->depth + 1), value(0), board(new State* [BOARDSIZE])
{
father->children.push_back(this);
for (int i = 0; i < BOARDSIZE; ++i)
{
board[i] = new State[BOARDSIZE];
memcpy_s(board[i], BOARDSIZE * sizeof(State), father->board[i], BOARDSIZE * sizeof(State));
}
board[lastX][lastY] = IsMaxNode() ? BLACK : WHITE;
evaluateValue = Evaluate();
for (int i = 0; i < BOARDSIZE; ++i)
{
delete[] board[i];
}
delete[] board;
board = nullptr;
}
//根节点的构造函数
Node(int _depth, uint8_t x, uint8_t y) :father(nullptr), depth(_depth), lastX(x), lastY(y), value(0),evaluateValue(0),board(new State*[BOARDSIZE])
{
for (int i = 0; i < BOARDSIZE; ++i)
{
board[i] = new State[BOARDSIZE];
memset(board[i], 0, BOARDSIZE * sizeof(State));
}
board[x][y] = IsMaxNode() ? BLACK : WHITE;
}
inline int GetEvaluateValue()const
{
return evaluateValue;
}
inline bool IsMaxNode()const//默认计算机后手
{
return depth & 1u;//相当于depth%2
}
void Search(unsigned short _depth)
{
if (_depth == 0 || this->evaluateValue == INT_MAX || this->evaluateValue == INT_MIN)
{
this->value = this->evaluateValue;
return;
}
bool created = false;//记录是否new出新的Node，如果没有就不用排序了。
if (!board)//不是根节点
{
board = new State * [BOARDSIZE];
for (int i = 0; i < BOARDSIZE; ++i)
{
board[i] = new State[BOARDSIZE];
memcpy_s(board[i], BOARDSIZE * sizeof(State), father->board[i], BOARDSIZE * sizeof(State));
}
board[lastX][lastY] = IsMaxNode() ? BLACK : WHITE;
}
for (uint8_t i = 0; i < BOARDSIZE; i++)
{
for (uint8_t j = 0; j < BOARDSIZE; j++)
{
if (!board[i][j])
{
bool flag = false;
if (_depth >= 2)//若剩余深度小于2，则下一层肯定没有搜索过
{
for (Node* child : this->children)
{
if (child->lastX == i && child->lastY == j)//已经被搜索过
{
flag = true;
break;
}
}
}
if (!flag)
{
new Node(this, i, j);
created = true;
}
}
}
}
if (IsMaxNode())
{
this->value = INT_MIN;
if (created)
{
std::sort(this->children.begin(), this->children.end(), [](Node* a, Node* b) {
return a->GetEvaluateValue() > b->GetEvaluateValue();
});//按照估价从大到小排序，增加剪枝的概率
}
}
else
{
this->value = INT_MAX;
if (created)
{
std::sort(this->children.begin(), this->children.end(), [](Node* a, Node* b) {
return a->GetEvaluateValue() < b->GetEvaluateValue();
});//按照估价从小到大排序，增加剪枝的概率
}
}
auto ReleaseMemory = [this] {
if (father)//不是根节点
{
for (int i = 0; i < BOARDSIZE; ++i)
{
delete[] board[i];
}
delete[] board;
board = nullptr;
}
};
for (Node* child : this->children)
{
child->Search(_depth - 1);
//α - β 剪枝
if (IsMaxNode())
{
if (child->value > this->value)
{
this->value = child->value;
if (this->father && this->value >= this->father->value && this != this->father->children.front())
{
ReleaseMemory();
return;//剪枝
}
}
}
else//MIN节点
{
if (child->value < this->value)
{
this->value = child->value;
if (this->father && this->value <= this->father->value && this != this->father->children.front())
{
ReleaseMemory();
return;//剪枝
}
}
}
}
ReleaseMemory();
}
void DeleteAllButThis()
{
if (!father->board)//父节点不是根节点
throw std::invalid_argument("this->father必须是根节点！");
for (Node* n : father->children)
{
if (n != this)
delete n;
}
board = new State * [BOARDSIZE];
for (int i = 0; i < BOARDSIZE; ++i)
{
board[i] = new State[BOARDSIZE];
memcpy_s(board[i], BOARDSIZE * sizeof(State), father->board[i], BOARDSIZE * sizeof(State));
delete[] father->board[i];
}
delete[] father->board;
board[lastX][lastY] = IsMaxNode() ? BLACK : WHITE;
free(father);//避免调用析构函数
father = nullptr;
}
inline bool IsFull()const
{
return depth == BOARDSIZE * BOARDSIZE;
}
inline State GetWinner()const
{
if (this->value == INT_MAX)
{
return Node::WHITE;
}
else if (this->value == INT_MIN)
{
return Node::BLACK;
}
return Node::SPACE;
}
~Node()
{
if (board)
{
for (int i = 0; i < BOARDSIZE; ++i)
{
delete[] board[i];
}
delete[] board;
}
for (Node* n : children)
{
delete n;
}
}
};
private:
Node* root;
const unsigned short maxDepth;
public:
GameTree(unsigned short _maxDepth) : root(nullptr), maxDepth(_maxDepth)
{
if (_maxDepth < 2)
throw std::invalid_argument("最大层数必须大于等于2！");
}
std::pair<uint8_t, uint8_t>AIGetNextPos(uint8_t x, uint8_t y)
{
if (root)
{
for (Node* node : root->children)//进入用户选择的分支
{
if (node->lastX == x && node->lastY == y)
{
node->DeleteAllButThis();
root = node;
break;
}
}
}
else//第一次开局
{
root = new Node(1, x, y);
}
root->Search(maxDepth);
if (root->IsFull())
return std::make_pair(Node::BOARDSIZE, Node::BOARDSIZE);
for (Node* node : root->children)//选择分值最大的
{
if (node->value == root->value)
{
node->DeleteAllButThis();
root = node;
break;
}
}
return std::make_pair(root->lastX, root->lastY);
}
Node::State GetWinner()const
{
return root->GetWinner();
}
void Run()
{
while (1)
{
int x, y;
do
{
std::cout << "输入x,y坐标";
std::cin >> x >> y;
} while (x < 0 || y < 0 || x >= 15 || y >= 15 || (root && root->board[x][y] != Node::SPACE));
if (root)
{
for (Node* node : root->children)//进入用户选择的分支
{
if (node->lastX == x && node->lastY == y)
{
node->DeleteAllButThis();
root = node;
break;
}
}
}
else//第一次开局
{
root = new Node(1, x, y);
}
system("cls");
for (int i = 0; i < Node::BOARDSIZE; i++)
{
for (int j = 0; j < Node::BOARDSIZE; j++)
{
if (root->board[i][j] == Node::SPACE)
std::cout << "十 ";
else if (root->board[i][j] == Node::BLACK)
std::cout << "黑 ";
else
std::cout << "白 ";
}
std::cout << '\n';
}
root->Search(maxDepth);
if (root->value == INT_MAX)
{
std::cout << "电脑胜利！";
break;
}
else if (root->value == INT_MIN)
{
std::cout << "玩家胜利！";
break;
}
else if (root->IsFull())//不能用root->value==0判断平局，因为平局一定为0，但为0不一定平局
{
std::cout << "平局！";
break;
}
for (Node* node : root->children)//选择分值最大的
{
if (node->value == root->value)
{
node->DeleteAllButThis();
root = node;
break;
}
}
system("cls");
for (int i = 0; i < Node::BOARDSIZE; i++)
{
for (int j = 0; j < Node::BOARDSIZE; j++)
{
if (root->board[i][j] == Node::SPACE)
std::cout << "十 ";
else if (root->board[i][j] == Node::BLACK)
std::cout << "黑 ";
else
std::cout << "白 ";
}
std::cout << '\n';
}
if (root->value == INT_MAX)
{
std::cout << "电脑胜利！";
break;
}
else if (root->value == INT_MIN)
{
std::cout << "玩家胜利！";
break;
}
else if (root->IsFull())//不能用root->value==0判断平局，因为平局一定为0，但为0不一定平局
{
std::cout << "平局！";
break;
}
}
}
~GameTree()
{
delete root;
}
};
