前言 

回溯法（探索与回溯法）是一种选优搜索法，又称为试探法，按选优条件向前搜索，以达到目标。但当探索到某一步时，发现原先选择并不优或达不到目标，就退回一步重新选择，这种走不通就退回再走的技术为回溯法，而满足回溯条件的某个状态的点称为“回溯点”。

代码（C#）

public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            int n = 6;
            N_Queen(n);
        }

        public Boolean Place(int[] Column, int index)
        {
            int i;
            for (i = 1; i < index; i++)
            {
                int Colunm_differ = System.Math.Abs(Column[index] - Column[i]);
                int Row_differ = System.Math.Abs(index - i);
                if (Column[i] == Column[index] || Colunm_differ == Row_differ)
                {
                    return false;
                }
            }
            return true;
        }

        public void N_Queen(int n)
        {
            int[] Column_Num = new int[n + 1];
            int index = 1;
            int i;
            int answer_num = 0;
            for (i = 1; i <= n; i++)
            {
                Column_Num[i] = 0;
                while (index > 0)
                {
                    Column_Num[index]++;
                    while (Column_Num[index] <= n && !Place(Column_Num, index))
                    {
                        Column_Num[index]++;
                    }
                    if (Column_Num[index] <= n)
                    {
                        if (index == n)
                        {
                            answer_num++;
                            txt1.Text = txt1.Text + "\r\n" + "方案" + answer_num;
                            for (i = 1; i <= n; i++)
                            {
                                txt1.Text = txt1.Text + "(" + i + "," + Column_Num[i] + ")";
                            }

                            for (i = 1; i <= n; i++)
                            {
                                Column_Num[index]++;
                            }
                        }
                        else
                        {
                            index++;
                            Column_Num[index] = 0;
                        }
                    }
                    else
                    {
                        index--;
                    }
                }
            }
        }