c++ - N 皇后解决方案 C++

Question

所以我需要帮助解决经典的 N-Queens 问题。

运行程序的命令是:nqueens N k - 其中 N 是表的大小 (N x N)，k 是解决方案的数量

因此，例如，如果我通过键入 nqueens 4 1 运行该程序，将打印出以下内容。

_ 问 _ _

_ _ _ 问

问 _ _ _

_ _ 问 _

但是，我不知道如何处理超过 1 个解决方案？我如何才能确定此问题的不止一种解决方案？

目前我所拥有的如下:

#include <cstdlib>
#include <iomanip>
#include <cmath>
#include <vector>


using namespace std;

class Board
{
private:
    bool** spaces;
    int size;

public:
    Board(int size)
    {
        this->size = size;
        spaces = new bool*[size];
        for (int i = 0; i < size; ++i)
        {
            spaces[i] = new bool[size];
        }
    }

    bool isSafe(int row, int column, vector<int>& state)
    {
       //check row conflict
       //no need to check for column conflicts
       //because the board is beimg filled column
       //by column
       for(int i = 0; i < column; ++i)
       {
          if(state[i] == row)
             return false;
       }

       //check for diagonal conflicts
       int columnDiff = 0;
       int rowDiff = 0;
       for(int i = 0; i < column; ++i)
       {
          columnDiff = abs(column - i);
          rowDiff = abs(row - state[i]);
          if(columnDiff == rowDiff)
             return false;
       }

       return true;

    }

    int getSize()
    {
        return size;
    }

    bool getSpace(int x, int y)
    {
        return spaces[y][x];
    }

    void setSpace(int x, int y, bool value)
    {
        spaces[y][x] = value;
    }

    Board(Board& other)
    {
        this->size = other.getSize();
        spaces = new bool*[size];
        for (int i = 0; i < size; ++i)
        {
            spaces[i] = new bool[size];
            for (int j = 0; j < size; ++j)
            {
                spaces[i][j] = other.getSpace(j, i);
            }
        }
    }

    void backtrack(vector<int>& state, int board_size)
  {
     int row = 0;
     int column = 0;
     bool backtrack = false;

     while(column < board_size)
     {
        while(row < board_size)
        {
           if(backtrack)
           {
              row = state[column] + 1;
              if(row == board_size)
              {
                 column--; //backtrack more
                 backtrack = true;
                 row = 0;
                 break;
              }

              backtrack = false;
           }

           if(isSafe(row, column, state))
           {
              state[column] = row;
              row = 0;
              column++; //advance
              backtrack = false;
              break;
           }

           else
           {
              if(row == (board_size - 1))
              {
                 column--; //backtrack
                 backtrack = true;
                 row = 0;
              }
              else
              {
                 row++;
              }
           }
        }
     }
  }
};

int print_solutions(Board *board, vector<int>& state, int board_size)
{
   for(int i=0; i < board_size; ++i)
   {
      for(int j=0; j < board_size; ++j)
      {
         if(state[i] == j)
            cout << 'Q' << " ";
         else
            cout << '_' << " ";
      }

      cout << endl;
   }
}   

int main(int argc, char* argv[])
{
    if (argc < 2)
    {
        cout << "Usage: nqueens [Board Size] [Number of Solutions]" << endl;
    return 1;
    }

    int board_size = atoi(argv[1]);
    //int solution_count = atoi(argv[2]);
    vector<int> state;
    state.resize(board_size);

    Board *my_board = new Board(board_size);
    my_board->backtrack(state, board_size);

    print_solutions(my_board, state, board_size);

    return 0;
}

Answer 1

在这个解决方案中，我保留了大部分原始方法和代码:

#include <cstdlib>
#include <iomanip>
#include <cmath>
#include <vector>
#include <iostream>

using namespace std;

class Board
{
private:
    bool** spaces;
    int size;

public:
    Board(int size)
    {
        this->size = size;
        spaces = new bool*[size];
        for (int i = 0; i < size; ++i)
        {
            spaces[i] = new bool[size];
        }
    }

    bool isSafe(int row, int column, vector<int>& state)
    {
       //check row conflict
       //no need to check for column conflicts
       //because the board is beimg filled column
       //by column
       for(int i = 0; i < column; ++i)
       {
          if(state[i] == row)
             return false;
       }

       //check for diagonal conflicts
       int columnDiff = 0;
       int rowDiff = 0;
       for(int i = 0; i < column; ++i)
       {
          columnDiff = abs(column - i);
          rowDiff = abs(row - state[i]);
          if(columnDiff == rowDiff)
             return false;
       }

       return true;

    }

    int getSize()
    {
        return size;
    }

    bool getSpace(int x, int y)
    {
        return spaces[y][x];
    }

    void setSpace(int x, int y, bool value)
    {
        spaces[y][x] = value;
    }

    Board(Board& other)
    {
        this->size = other.getSize();
        spaces = new bool*[size];
        for (int i = 0; i < size; ++i)
        {
            spaces[i] = new bool[size];
            for (int j = 0; j < size; ++j)
            {
                spaces[i][j] = other.getSpace(j, i);
            }
        }
    }

    bool backtrack(vector<int>& state, int& column, int board_size)
  {
     int row = 0;
     bool backtrack = column == board_size;

     while(column < board_size || backtrack)
     {
        {
           if(backtrack)
           {
              if (column == 0)
                 return false;
              column--;
              row = state[column] + 1;
              if(row == board_size)
              {
                 backtrack = true;
                 continue;
              }

              backtrack = false;
           }

           if(isSafe(row, column, state))
           {
              state[column] = row;
              row = 0;
              column++; //advance
              backtrack = false;
              continue;
           }

           else
           {
              if(row == (board_size - 1))
              {
                 backtrack = true;
              }
              else
              {
                 row++;
              }
           }
        }
     }
     return true;
  }
};

void print_solutions(Board *board, vector<int>& state, int board_size)
{
   for(int i=0; i < board_size; ++i)
   {
      for(int j=0; j < board_size; ++j)
      {
         if(state[i] == j)
            cout << 'Q' << " ";
         else
            cout << '_' << " ";
      }

      cout << endl;
   }
    cout << endl;
}   

int main(int argc, char* argv[])
{
    if (argc < 3)
    {
        cout << "Usage: nqueens [Board Size] [Number of Solutions]" << endl;
    return 1;
    }

    int board_size = atoi(argv[1]);
    int solution_count = atoi(argv[2]);
    vector<int> state;
    state.resize(board_size);

    Board *my_board = new Board(board_size);
    int column = 0;
    while (solution_count-- > 0 && my_board->backtrack(state, column, board_size))
        print_solutions(my_board, state, board_size);

    return 0;
}

• 已修复:编译错误:cout 未知 -> #include iostream
• 添加:print_solutions 中的额外换行符分离多个解决方案
• 修复:print_solutions打印转置表
• 修复:编译错误:print_solutions不返回值 -> void
• 修复:argc检查
• 已添加:solution_count搬家支持column调用网站
• 修复:回溯代码重复(column--，row = 0)
• 修复:不必要的内部循环(row < board_size)
• 未修复:my_board被泄露了
• 不固定:整个Board类及其实例是不必要的