Abstract In this lab you will implement recursive solutions to classic CS ques-
ID: 3730166 • Letter: A
Question
Abstract In this lab you will implement recursive solutions to classic CS ques- tions. One will be a chess problem, and the other is Towers of Hanoi. 1 Backtracking with Recursion - Featuring Chess Choose and complete one of the two following chess problems. These problems can be solved using the backtracking algorithm shown below. boolean solve(board, pos) if( pos is such that there is nothing left to solve) ( return true; for each possible choice t if(valid (choice)) mark board at pos with choice; if(solve(board, pos + 1) == true){ return true; clear any choices entered at pos on board; return false; // backtrackExplanation / Answer
Please find below the code for the above problem. I have used N=8 (Number of Queens) in the solution. You can change N and solve the problem for any number of Queens. Thus the solution has the class name of NQueenProblem, and can be used for any general case by changing N and the chess board initialization.
import java.util.*;
import java.lang.*;
import java.io.*;
class NQueenProblem
{
final int N = 8;
/* 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 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 queen can not be place 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.
*/
boolean solveNQ()
{
int board[][] = {{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{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();
}
}