Genetic algorithm vs. Backtracking: N-Queen Problem – Towards Data Science

One of the most famous problems solved by genetic algorithms is the n-queen problem. I implemented my genetic solver, plus the famous old backtracking.

N Queen Problem | Backtracking-3 – GeeksforGeeks

The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. … The expected output is a binary matrix which has 1s for the blocks where queens are placed. For example, following is the output matrix for above 4 queen solution.

```
/* C/C++ program to solve N Queen Problem using
backtracking */
#define N 4
#include
```
#include
/* 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("\n");
}
}
/* 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 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))
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 cannot 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.*/
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;
}

## One comment on “N queen problems”

## russell harun

December 24, 2019 at 10:57 pmNice