n-queens.cs

using System;
using System.Collections.Generic;
using System.Linq;

namespace n_queen
{
    
    class Program
    {
        static int gridSize = 4;
        static int[] queens = Enumerable.Repeat(-1, gridSize).ToArray();

        static bool validPosition(int row, int col) {
        // We do not have to check Horizontal because
        // we are only placing one queen per row

            // Check Vertical
            foreach(var each in queens)
            {
                if (each == col)
                {
                    return false;
                }
            }
            // Check Diagonal
            var upRight     = foundQueenOnPath(row , col, -1,  1);
            var upLeft      = foundQueenOnPath(row , col, -1, -1);
            var downRight   = foundQueenOnPath(row , col,  1,  1);
            var downLeft    = foundQueenOnPath(row , col,  1, -1);

            var foundQueen = upRight || upLeft || downRight || downLeft;
            return !foundQueen;

        }

        static bool foundQueenOnPath(int row, int col, int rowIncrement, int colIncrement)
        {
            if (col < 0 || col >= gridSize)
            {
                return false;
            }

            if (row < 0 || row >= gridSize)
            {
                return false;
            }

            var value = queens[row];

            if(value == col) 
            {
                return true;
            }

            row += rowIncrement;
            col += colIncrement;

            return foundQueenOnPath(row, col, rowIncrement, colIncrement);
        }

        static void Main(string[] args)
        {

            var row = 0;
            var col = 0;
            for (; row < gridSize; row += 1)
            {
                for (; col < gridSize; col += 1)
                {
                    Console.WriteLine(string.Join(", ", queens));

                    if (validPosition(row, col))
                    {
                        queens[row] = col;
                        col = 0;
                        break;

                    }

                    // reached the end without placing a queen.
                    if (col == gridSize - 1)
                    {
                        queens[row] = -1;

                        row += -1;
                        if(row < 0)
                        {
                            return;
                        }

                        col = queens[row] - 1;
                        }

                }
                Console.WriteLine(string.Join(", ", queens));

            }

        }
    }
}