Backtracking | Set 3 (N Queen Problem) | 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.
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The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other.
1) Start in the leftmost column
2) If all queens are placed
return true
3) Try all rows in the current column. Do following for every tried row.
a) If the queen can be placed safely in this row then mark this [row,
column] as part of the solution and recursively check if placing
queen here leads to a solution.
b) If placing queen in [row, column] leads to a solution then return
true.
c) If placing queen doesn't lead to a solution then umark this [row,
column] (Backtrack) and go to step (a) to try other rows.
3) If all rows have been tried and nothing worked, return false to trigger
backtracking.
/* 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 */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) == 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;}