数据结构——八皇后问题递归代码实现

Reference Book: 《Data Structures and Program Design in C++》

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1. Queens类

1.（1）Queens.h

#ifndef QUEENS_H
#define QUEENS_H

const int max_board = 30;

class Queens
{
    public:
        Queens(int size);

        bool unguarded(int col)const;
        void insert(int col);
        void remove(int col);
        bool is_solved()const;
        void print()const;
        int board_size;

    protected:

    private:
        int count;
        bool col_free[max_board];   // 存储列是否被占据
        bool upward_free[2*max_board-1];    // 存储自左下到右上的对角线是否被占据
        bool downward_free[2*max_board-1];  // 存储自右下到左上的对角线是否被占据
        int queen_in_row[max_board];   // 存储每一行queen的列号
        static int success;
};

#endif // QUEENS_H

1（2）Queens.cpp

#include "Queens.h"
#include 

using namespace std;

int Queens::success = 1;

Queens::Queens(int size)
/*Post: 初始化一个Queens类的对象.
*/
{
    board_size = size;
    count = 0;
    int i;
    for(i = 0; i < board_size; i++)col_free[i] = true;
    for(i = 0; i < (board_size*2-1); i++)upward_free[i] = true;
    for(i = 0; i < (board_size*2-1); i++)downward_free[i] = true;
    for(i = 0; i < board_size; i++)queen_in_row[i] = -1;
}

bool Queens::unguarded(int col)const
/*Post: 检查第一个空行(count)的col列是否未被皇后守卫, 若是返回true否则返回false
*/
{
    return col_free[col] && upward_free[count+col]
           && downward_free[count-col+board_size-1];
}

void Queens::insert(int col)
/*Post: 向第一个空行的col列添加皇后, 并设置列及对角线被守卫.
*/
{
    queen_in_row[count] = col;  // 第一个空行的索引为count
    col_free[col] = false;
    upward_free[count+col] = false;
    downward_free[count-col+board_size-1] = false;
    count++;
}

void Queens::remove(int col)
/*Post: 移除最后一个非空行col列的皇后, 并重新设置列及对角线未被守卫.
*/
{
    count--;
    queen_in_row[count] = -1;
    col_free[col] = true;
    upward_free[count+col] = true;
    downward_free[count-col+board_size-1] = true;
}

bool Queens::is_solved()const
/*Post: 若填入的皇后数等于棋盘大小返回true, 否则返回false.
*/
{
    return count==board_size;
}

void Queens::print()const
/*Post: 打印出皇后在棋盘上的分布图.
*/
{
    cout << "case #" << success++ << ":" << endl;
    for(int row = 0; row < board_size; row++)
    {
        for(int col = 0; col < board_size; col++)
        {
            if(queen_in_row[row]==col)
                cout << "*";
            else
                cout << "-";
        }
        cout << endl;
    }
    cout << endl;
}

2. main.cpp

#include 
#include "Queens.h"

using namespace std;

void solve_from(Queens &configuration)
/*Post: 对于大小为board_size的棋盘, 通过插入和移除回溯的方法寻找可行的棋盘配置并打印.
  Uses: Queens类和回溯的方法.
*/
{
    if(configuration.is_solved())configuration.print();
    else
        for(int col = 0; col < configuration.board_size; col++)
            if(configuration.unguarded(col))
            {
                configuration.insert(col);
                solve_from(configuration);
                configuration.remove(col);
            }
}

int main()
{
    int board_size;
    cin >> board_size;
    if(board_size<0 || board_size>max_board)
        cout << "The number is out of range!" << endl;
    else
    {
        Queens configuration(board_size);
        solve_from(configuration);
    }

    return 0;
}