CS 2123 Data Structures Recitation 2 Due Friday February 12 Difficulty (out of 5
ID: 3666685 • Letter: C
Question
CS 2123 Data Structures Recitation 2 Due Friday February 12 Difficulty (out of 5) 1. (100 pts) Write a program to solve the NQueens problem reeursively. NQwens problesm investigates whether it is possible to place N queens on an NaN chessboard so that none of them can move to a square occupied by any of the otbers in a single turn. Your program should either display a solution it it finds one ot report that no solution exists. A single queen and squares that can be ocupied in a single turn are shown below Figure 1: Single Queen A sample solution to the S-queens problem is given below Figure 2: Solution for & queens problem Below are some hints to work on the problem to store the pcsitions of queens on the e Use a dynamically allocated 2D array to store the positions of queens on the board. . Number the rows and columns from zero Note that only one Queen can occupy each column . Each column must have a Queen Move across the grid, colun by column. Place a queen in each coln Start with column 0 and move towards column N-1Explanation / Answer
/* C program to solve N Queen Problem using
backtracking */
#define N 4
#include<stdio.h>
/* A utility function to print solution */
void printSolution(int board[N][N])
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
printf(" %d ", board[i][j]);
printf(" ");
}
}
/* 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 placed in columns from 0 to col -1.
So we need to check only left side for
attacking queens */
bool isSafe(int board[N][N], int row, int col)
{
int i, j;
/* Check this row on left side */
for (i = 0; i < col; i++)
if (board[row][i])
return false;
/* Check upper diagonal on left side */
for (i=row, j=col; i>=0 && j>=0; i--, j--)
if (board[i][j])
return false;
/* Check lower diagonal on left side */
for (i=row, j=col; j>=0 && i<N; i++, j--)
if (board[i][j])
return false;
return true;
}
/* A recursive utility function to solve N
Queen problem */
bool solveNQUtil(int board[N][N], 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) )
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.
Please note that there may be more than one
solutions, this function prints one of the
feasible solutions.*/
bool solveNQ()
{
int board[N][N] = { {0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0}
};
if ( solveNQUtil(board, 0) == false )
{
printf("Solution does not exist");
return false;
}
printSolution(board);
return true;
}
// driver program to test above function
int main()
{
solveNQ();
return 0;
}
/*
Output: The 1 values indicate placements of queens
*/