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How to implement an auxiliary heuristic to speed up the search in the Tic-Tac-Toe game tree?
There is a task - to implement a minimax algorithm for playing tic-tac-toe, as well as auxiliary search heuristics to eliminate the "plateau" effect and other side effects. The specific paragraph reads:
Implement an auxiliary heuristic (calculating the difference in the number of possible lines for the game to be completed by one and the other opponent in the current state) to speed up the search on the Tic-Tac-Toe game tree.
I don’t quite understand which way to go and how to introduce such a heuristic. There is such an implementation where the game itself works correctly:
// minmax2.cpp: определяет точку входа для консольного приложения.
//
#include "stdafx.h"
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <limits>
using namespace std;
class Game
{
enum class Player
{
none = '-',
human = 'X',
computer = 'O'
};
struct Move
{
unsigned int x = 0;
unsigned int y = 0;
};
Player board[3][3];
public:
int steps = 0;
Game()
{
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
board[i][j] = Player::none;
}
}
}
void printBoard()
{
std::cout << "+-----------------+";
for (unsigned int i = 0; i < 3; i++)
{
std::cout << "\n|";
for (unsigned int j = 0; j < 3; j++)
{
std::cout << std::setw(3) << static_cast<char>(board[i][j]) << std::setw(3) << " |";
}
}
std::cout << "\n+-----------------+\n";
}
bool isTie()
{
for (unsigned int i = 0; i < 3; i++)
{
if (board[i][0] == Player::none || board[i][1] == Player::none || board[i][2] == Player::none)
return false;
}
return true;
}
bool checkWin(Player player)
{
for (unsigned int i = 0; i < 3; i++)
{
// Check horizontals
if (board[i][0] == player && board[i][1] == player && board[i][2] == player)
return true;
// Check verticals
if (board[0][i] == player && board[1][i] == player && board[2][i] == player)
return true;
}
// Check diagonals
if (board[0][0] == player && board[1][1] == player && board[2][2] == player)
return true;
if (board[0][2] == player && board[1][1] == player && board[2][0] == player)
return true;
return false;
}
Move minimax()
{
int score = std::numeric_limits<int>::max();
Move move;
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
if (board[i][j] == Player::none)
{
board[i][j] = Player::computer;
int temp = maxSearch();
if (temp < score)
{
score = temp;
move.x = i;
move.y = j;
}
board[i][j] = Player::none;
}
}
}
cout << "\nsteps counted: \n" << steps;
steps = 0;
return move;
}
int maxSearch()
{
if (checkWin(Player::human)) { return 10; }
else if (checkWin(Player::computer)) { return -10; }
else if (isTie()) { return 0; }
steps++;
int score = std::numeric_limits<int>::min();
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
if (board[i][j] == Player::none)
{
board[i][j] = Player::human;
score = std::max(score, minSearch());
board[i][j] = Player::none;
}
}
}
return score;
}
int minSearch()
{
if (checkWin(Player::human)) { return 10; }
else if (checkWin(Player::computer)) { return -10; }
else if (isTie()) { return 0; }
steps++;
int score = std::numeric_limits<int>::max();
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
if (board[i][j] == Player::none)
{
board[i][j] = Player::computer;
score = std::min(score, maxSearch());
board[i][j] = Player::none;
}
}
}
return score;
}
void getHumanMove()
{
bool fail = true;
unsigned int x = -1, y = -1;
do
{
std::cout << "Your Move: ";
char c;
std::cin >> c;
x = c - '0';
std::cin >> c;
y = c - '0';
fail = board[x][y] != Player::none;
std::cin.clear();
std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
} while (fail);
board[x][y] = Player::human;
}
void play()
{
unsigned int turn = 0;
bool exit = false;
printBoard();
std::cout << "Enter your move in coordinate form[row, col]. ex: 02\n";
do
{
// human move
if (turn == 0)
{
getHumanMove();
if (checkWin(Player::human))
{
std::cout << "Human Wins\n";
exit = true;
}
}
else
{
std::cout << "\nComputer Move: ";
Move aimove = minimax();
std::cout << aimove.x << aimove.y << "\n";
board[aimove.x][aimove.y] = Player::computer;
if (checkWin(Player::computer))
{
std::cout << "Computer Wins\n";
exit = true;
}
}
if (isTie())
{
std::cout << "\n*** Tie ***\n";
exit = true;
}
turn ^= 1;
printBoard();
} while (!exit);
}
};
int main()
{
Game tictactoe;
tictactoe.play();
std::cin.ignore();
}
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