N queen using c++ and backtracking using a dynamic 2D array

Question

I've been trying to solve the N queen problem using backtracking. Most of the approaches that I found online, involved vectors, making it difficult for me to visualize the solutions as some applets on the Internet do.

The solution I came up with, is giving me many problems(which i have a feeling are related to indexing of the dynamic 2D array used) and I'm not able to figure it out using Dev-C++ debugger.Any help and/or constructive criticism is highly appreciated. Many thanks in advance.

Here is the solution that i came up with:

#include<iostream>
#include<string.h>
#include<conio.h>

using namespace std;

void display(char** b, int len);
void initialize(char** &b, int k);
void consider1strow(char ** b, int len);
void markunsafe(char** board, int rowno, int colno);
void marksafe(char** board, int rowno, int colno);
void considerrow(char** board, int rowno);
void backtrack(char** board, int rowno);
bool checksafety(char** board, int rowno, int colno);
void place(char** board, int rowno, int colno);
void solve(char** board, int len);


int state[20] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 };
int len;

void display(char** board, int len)
{
    int i, j;
    cout << endl << "The current state of the board:" << endl;
    for (i = 0; i < len; i++)
    {
        for (j = 0; j < len; j++)
        {
            cout << board[i][j];
        }
        cout << endl;
    }
}

void initialize(char** &b, int k)
{

    int i, j;

    //create dynamic board
    b = new char*[k];
    for (i = 0; i < k; i++)
    {
        b[i] = new char[k];
    }

    //initialize array
    for (i = 0; i < k; i++)
    {
        for (j = 0; j < k; j++)
        {
            b[i][j] = '-';
        }
    }

}

void consider1strow(char ** board, int len)
{
    int col;
    cout << "Enter the column to try for the first row!";
    cin >> col;
    board[0][col - 1] = 'Q';
    state[0] = col - 1;
    markunsafe(board, 0, col - 1);
    display(board, len);
}

void markunsafe(char** board, int rowno, int colno)
{
    int i, j;

    //mark row as unsafe
    for (i = 0; i < len; i++)
    {
        board[rowno][i] = 'x';
    }

    //mark column as unsafe
    for (i = 0; i < len; i++)
    {
        board[i][colno] = 'x';
    }

    //mark unsafe diagonals
    for (i = 0; i < len; i++)
    {
        for (j = 0; j < len; j++)
        {
            if ((rowno + colno) == (i + j))
            {
                board[i][j] = 'x'; //check if index gives a problem of +/- 1 
            }
            if ((rowno - colno) == (i - j))
            {
                board[i][j] = 'x';  //check if index gives a problem of +/- 1
            }
        }
    }
    board[rowno][colno] = 'Q';

}

void marksafe(char** board, int rowno, int colno)
{
    int i, j;

    //mark row as safe
    for (i = 0; i < len; i++)
    {
        board[rowno][i] = '-';
    }

    //mark column as unsafe
    for (i = 0; i < len; i++)
    {
        board[i][colno] = '-';
    }

    //mark unsafe diagonals
    for (i = 0; i < len; i++)
    {
        for (j = 0; j < len; j++)
        {
            if ((rowno + colno) == (i + j))
            {
                board[i][j] = '-'; //check if index gives a problem of +/- 1 
            }
            if ((rowno - colno) == (i - j))
            {
                board[i][j] = '-';  //check if index gives a problem of +/- 1
            }
        }
    }
}


void considerrow(char** board, int rowno)
{
    bool safe = 0;
    int i;

    for (i = 0; i < len; i++)
    {
        safe = checksafety(board, rowno, i);
        if (safe && (i >= state[rowno]))
        {
            break;
        }
    }
    if (safe && (i >= state[rowno]))
    {
        place(board, rowno, i);
    }
    else if (!safe)
    {
        backtrack(board, rowno);
    }
}

void backtrack(char** board, int rowno)
{
    marksafe(board, rowno - 2, state[rowno - 2]);
    considerrow(board, rowno);
}

bool checksafety(char** board, int rowno, int colno)
{
    if (rowno == 0)
    {
        return 1;
    }
    else if (board[rowno][colno] == 'x')
    {
        return 0;
    }
    else if (board[rowno][colno] == '-')
    {
        return 1;
    }
}


void place(char** board, int rowno, int colno)
{
    board[rowno][colno] = 'Q';
    state[rowno] = colno;
    markunsafe(board, rowno, colno);
}

void solve(char** board, int len)
{
    int i = 0;
    if (i == len)
    {
        display(board, len);
    }
    else
    {
        consider1strow(board, len);
        for (i = 1; i < len; i++)
        {
            considerrow(board, i);
        }
    }
}

int main()
{
    char** board;
    cout << "Enter the size of the board!";
    cin >> len;
    initialize(board, len);
    solve(board, len);
    getch();
}

Answer 1

It is running after the initial configuration, but you're not printing it. Change this (inside solve):

for(i=1;i<len;i++)
{considerrow(board,i);}

for this:

for(i=1; i<len; i++) {
      considerrow(board,i);
      display(board,len);
 }

Besides that, there is a problem with the way you are doing backtracking. If no options are available, you are removing the queen from the previous row (that's ok) and then you are marking every cell it was attacking as safe (not ok). The problem is that some of these cells may be under attack by a different queen, so you cannot mark them as safe. Furthermore, you do not place a different queen on that row. I propose some solutions:

First, make it recursive: considerrow would call itself with the following row, and return true (1) if it succeeds or false (0) if it fails. If it fails with the next row, you can use the next queen in the current row and call considerrow again, until you succeed or run out of columns, in which case you return false.

To consider a different queen on a certain row, you can do two things: create a copy of the board which you would pass to considerrow for the next row (and thus keeping a 'before' copy to try a different queen), or mark every cell as safe, and then check all the existing queens to mark cells unsafe.

Edit:

To make it recursive, we are going to make considerrow call itself with the next value.

bool considerrow(char** board,int rowno) {
    //Print the board
    display(board,len);
    bool safe=0;
    int i;

    for(i=0; i<len; i++) {
        safe=checksafety(board,rowno,i);
        if(safe) {
            place(board,rowno,i);
            //Is this the last row? If so, we suceeded
            if (rowno==len-1) return 1;
            //Call itself with next row, check if suceeded
            if (considerrow(board,rowno+1))
                return 1;
            else //Failed, try a different row
                backtrack(board,rowno);
        }
    }
    return 0; //If we got here, then we ran out of colums. Return failure
}

The backtrack function can be modified to revert the current row like this:

void backtrack(char** board, int rowno) {
    //Clear the current row
    marksafe(board,rowno,state[rowno]);
    //Check that every cell attacked by another queen is marked unsafe
    for(int i=0; i<rowno; i++) markunsafe(board,i,state[i]);
}

Doing that, solve will only need to call the first row:

void solve(char** board,int len) {
    considerrow(board,0);
    display(board,len);
}