我的 N 皇后问题一直有效，直到 n = 5，我不知道为什么 C++答案

【问题标题】：My N Queen Problem works up until n = 5 and I don't know why C++我的 N 皇后问题一直有效，直到 n = 5，我不知道为什么 C++
【发布时间】：2021-06-02 15:43:47
【问题描述】：

我对编码还很陌生，所以放轻松，但我正在研究 N Queen 问题，该问题需要为 n 大小的板提供大量解决方案，您可以在每行放置一个皇后。我的代码工作到 n=4，然后 n=5 输出 11 和输出 0 之后的所有 n。-1s 出现在位置 [] 中直到 n=5，然后它们不会输入到数组中。我现在很无能为力，因此不胜感激。

#include <iostream>
using namespace std;

//MAXROWS is same as MAXCOLUMNS or BOARDSIZE
const int MAXROWS = 20;

//queens' placements in each row
int placements[MAXROWS];
int n = 0;
int solutionsCount = 0;

bool canPlaceQueen(int row, int column)
{
    for(int j = 0; j < row; j++)
        if((placements[j] == column) // is there a queen in same column?
            || (abs(placements[j] - column) == abs(j-row))) // checks diagonals
            return false;           // column difference is same as row difference?

    return true;
}

bool correctSolution()
{
   
   for (int i = 0; i < n; i++)
   {
    for (int j = i + 1; j < n; j++)
        if (placements[i] == placements[j])
        {
            return false;
        }
   }
   
   for (int k = 0; k < n; k++)
   {
      if (placements[k] == -1)
      {
         return false;
      }
   }
   
   return true;
}

void placeQueens(int row) {
    //try to place queen in each column in current row
    //then continue to explore: placeQueens(row+1)
    //for each successful queen placement in final row, increment solutionsCount!
    
   for (int i = 0; i < n; i++)
   {
      if (canPlaceQueen(row, i))
      {
         placements[row] = i;
         if (row < n-1)
         {
            placeQueens(row+1);
         }
      }
      else
      {
         placements[row] = -1;
      }
      
      if (correctSolution())
      {
         solutionsCount++;
         cout << "add" << placements[0] << placements [1] << placements[2] << placements[3] << endl;
      }
         
   } 
   
   cout << "new" << placements[0] << placements [1] << placements[2] << placements[3] << endl;
    
    
   for (int j = 0; j < n; j++)
   {
      placements[j] = 0;
   }
}

int main() {
    cout << "Enter the board size: ";
    cin >> n;

    placeQueens(0);
    cout << "Number of solutions: " << solutionsCount << endl;
}

【问题讨论】：

我认为 correctSolution() 不起作用。放置数组告诉你皇后在哪一列上一行。想象一下n = 8。如果您在 (0,0) 上有一个皇后，即 Placements[0] = 0，而在 (7,7) 上有一个皇后，即 Placements[7] = 7，那么 Placements[0] 是 != 对 Placements[7]，但这是一个无效的解决方案（同一对角线上的两个皇后）。您的检查仅检查两个皇后是否在同一列。实际上我认为你可以让整个对角线都充满皇后，它仍然可以通过检查。
几周前我在方案中做了这个问题。我的递归策略是从第 n 列开始，找到 n-1 列的解决方案列表（递归步骤）。然后我采用这些解决方案中的每一个并生成一个新的潜在解决方案，方法是在第 n 列的第 0 行放置一个女王并检查它，将女王更改为第 1 行并再次检查它等等。只保留那些有效的解决方案。假设网格是 8x8，所以函数从第 7 列开始，所以它只需要 6 列的解决方案（但仍然是 7 行！），这反过来又需要 5 列的解决方案等，向下和向后递归。

标签： c++ n-queens

【解决方案1】：

希望这对您和您的努力有所帮助，运动！

#include <iostream>
using namespace std;

//MAXROWS is same as MAXCOLUMNS or BOARDSIZE
const int MAXROWS = 20;

//queens' placements in each row
int placements[MAXROWS];
int n = 0;
int solutionsCount = 0;

bool canPlaceQueen(int row, int column)
{
    for (int j = 0; j < row; j++)
        if ((placements[j] == column)                         // is there a queen in same column?
            || (abs(placements[j] - column) == abs(j - row))) // checks diagonals
            return false;                                     // column difference is same as row difference?

    return true;
}

void placeQueens(int row)
{
    //try to place queen in each column in current row
    //then continue to explore: placeQueens(row+1)
    //for each successful queen placement in final row, increment solutionsCount!

    if (row == n) //If the last row has been reached then there is a solution
    {
        solutionsCount++; //incrementing the solution count
        return;           //returning back
    }

    for (int column = 1; column <= n; column++) // To check all the columns from 1 to n
    {
        if (canPlaceQueen(row, column) == true)
        {
            placements[row] = column; //placing the queen in Row row on Column column

            placeQueens(row + 1); //calling the next row

            placements[row] = 0; //removing the queen from this column
        }
    }
}

int main()
{
    cout << "Enter the board size: ";
    cin >> n;

    placeQueens(0);

    cout << "Number of solutions: " << solutionsCount << endl;
}

此致，

迈克

【讨论】：