八皇后问题-回溯法

1.利用二维数组保存棋盘上的状态

#include<cstdio>

int arry[8][8] = { 0 };//棋盘，放皇后
int result = 0;//存放结果数量

bool check(int row, int col);
void print();

void FindQueen(int row)
{
    if (row > 7)
    {
        //有解
        result++;
        print();
        return;
    }

    for (int col = 0; col < 8; col++)
    {
        //回溯递归
        if (check(row, col))
        {
            arry[row][col] = 1;
            FindQueen(row + 1);
            arry[row][col] = 0;//清零，以免回溯的时候出现脏数据
        }
    }
}

bool check(int row, int col)
{
    //检查列冲突
    for (int i = 0; i < 8; i++)
        if (arry[i][col] == 1)
            return false;

    //检查左对角线
    for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--)
        if (arry[i][j] == 1)
            return false;
    for (int i = row + 1, j = col + 1; i < 8 && j < 8; i++, j++)
        if (arry[i][j] == 1)
            return false;

    //检查右对角线
    for (int i = row + 1, j = col - 1; i < 8 && j >= 0; i++, j--)
        if (arry[i][j] == 1)
            return false;
    for (int i = row - 1, j = col + 1; i >= 0 && j < 8; i--, j++)
        if (arry[i][j] == 1)
            return false;

    return true;
}

void print()
{
    printf("方案%d:\n", result);
    for (int i = 0; i < 8; i++)
    {
        for (int j = 0; j < 8; j++)
            if (arry[i][j] == 1)
                printf("O ");
            else
                printf("+ ");
        printf("\n");
    }    
}

int main()
{
    FindQueen(0);
    return 0;
}

 

2.使用一维数组存放皇后的位置，下标表示行，值表示列

#include<iostream>
using namespace std;

static int chessboardQueen[8] = { 0 };//存储每行皇后的位置
static int nCount = 0;//存储方法数

void print()
{
    cout << "方案" << nCount << ":" << endl;
    for (int i = 0; i < 8; i++)
    {
        int inner;
        for (inner = 0; inner < chessboardQueen[i]; inner++)
            cout << "o";
        cout << "*";
        for (inner = chessboardQueen[i] + 1; inner < 8; inner++)
            cout << "o";
        cout << endl;
    }
    cout << "================================" << endl;
}

int isSafePosition(int loop, int value)
{
    int index;
    int data;
    for (index = 0; index < loop; ++index)
    {
        data = chessboardQueen[index];
        //同一列有两个皇后
        if (value == data)
            return 0;
        //主对角线有两个皇后
        if ((index + data) == (loop + value))
            return 0;
        //副对角线有两个皇后
        if ((index - data) == (loop - value))
            return 0;
    }
    return 1;
}

void eightQueen(int index)
{
    int loop;
    for (loop = 0; loop < 8; ++loop)
    {
        if (isSafePosition(index, loop))
        {
            chessboardQueen[index] = loop;
            if (7 == index)//如果index等于7则说明已经成功从第一行遍历到第八行了
            {
                nCount++;
                print();
                chessboardQueen[index] = 0;
                return;
            }
            eightQueen(index + 1);//递归调用
            chessboardQueen[index] = 0;//当不再递归时，说明index+1位置不满足条件
        }
    }
}

int main()
{
    eightQueen(0);
    cout << "total=" << nCount << endl;
    return 0;
}