N Queen Problem

The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. For example, following is a solution for 4 Queen problem.

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.

              { 0,  1,  0,  0}
              { 0,  0,  0,  1}
              { 1,  0,  0,  0}
              { 0,  0,  1,  0}

Naive Algorithm Generate all possible configurations of queens on board and print a configuration that satisfies the given constraints.

while there are untried configurations
{
   generate the next configuration
   if queens don't attack in this configuration then
   {
      print this configuration;
   }
}

Backtracking Algorithm The goal is to position queens in different columns one by one, starting with the leftmost column. We check for conflicts with already placed queens when placing a queen in a column. If we locate a row in the current column with no collision, we mark that row and column as part of the solution. We backtrack and return false if we can't discover such a row owing to conflicts.

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 the queen in [row, column] leads to
       a solution then return true.
    c) If placing queen doesn't lead to a solution then
       unmark this [row, column] (Backtrack) and go to 
       step (a) to try other rows.

4) If all rows have been tried and nothing worked,
   return false to trigger backtracking.