数据结构——八皇后问题递归代码实现

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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_Hconst 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 <iostream>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 <iostream>#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;}

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