Question

Write a JAVA program for the following scenario. Given an n × n × n cube containing n3 cells. PLEASE NOTE THAT THIS BOARD HAS 3 DIMENSIONS. We are to place n queens in the cube so that no two queens challenge each other (so that no two queens are in the same row, column, or diagonal). In JAVA, implement it on your system to solve problem instances in which n = 4 and n = 8.

Answer 1

/* Java program to solve N Queen Problem using
backtracking */
public class NQueenProblem {
   final int N = 4;

   /* A utility function to print solution */
   void printSolution(int board[][])
   {
       for (int i = 0; i < N; i++) {
           for (int j = 0; j < N; j++)
               System.out.print(" " + board[i][j]
                               + " ");
           System.out.println();
       }
   }

   /* A utility function to check if a queen can
   be placed on board[row][col]. Note that this
   function is called when "col" queens are already
   placeed in columns from 0 to col -1. So we need
   to check only left side for attacking queens */
   boolean isSafe(int board[][], int row, int col)
   {
       int i, j;

       /* Check this row on left side */
       for (i = 0; i < col; i++)
           if (board[row][i] == 1)
               return false;

       /* Check upper diagonal on left side */
       for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
           if (board[i][j] == 1)
               return false;

       /* Check lower diagonal on left side */
       for (i = row, j = col; j >= 0 && i < N; i++, j--)
           if (board[i][j] == 1)
               return false;

       return true;
   }

   /* A recursive utility function to solve N
   Queen problem */
   boolean solveNQUtil(int board[][], int col)
   {
       /* base case: If all queens are placed
       then return true */
       if (col >= N)
           return true;

       /* Consider this column and try placing
       this queen in all rows one by one */
       for (int i = 0; i < N; i++) {
           /* Check if the queen can be placed on
           board[i][col] */
           if (isSafe(board, i, col)) {
               /* Place this queen in board[i][col] */
               board[i][col] = 1;

               /* recur to place rest of the queens */
               if (solveNQUtil(board, col + 1) == true)
                   return true;

               /* If placing queen in board[i][col]
               doesn't lead to a solution then
               remove queen from board[i][col] */
               board[i][col] = 0; // BACKTRACK
           }
       }

       /* If the queen can not be placed in any row in
       this colum col, then return false */
       return false;
   }

   /* This function solves the N Queen problem using
   Backtracking. It mainly uses solveNQUtil () to
   solve the problem. It returns false if queens
   cannot be placed, otherwise, return true and
   prints placement of queens in the form of 1s.
   Please note that there may be more than one
   solutions, this function prints one of the
   feasible solutions.*/
   boolean solveNQ()
   {
       int board[][] = { { 0, 0, 0, 0 },
                       { 0, 0, 0, 0 },
                       { 0, 0, 0, 0 },
                       { 0, 0, 0, 0 } };

       if (solveNQUtil(board, 0) == false) {
           System.out.print("Solution does not exist");
           return false;
       }

       printSolution(board);
       return true;
   }

   // driver program to test above function
   public static void main(String args[])
   {
       NQueenProblem Queen = new NQueenProblem();
       Queen.solveNQ();
   }
}