Today we take a break to look at No queens problem. This problem talks about placing N queens in a NxN board so that no queen can attack each other. Before we look at the solution, let's first see that when N = 2 and when N = 3 there are no solutions. And now let us take a NxN chessboard here we find there us a solution possible. So how do we arrive at that solution ? Let's say we placed one queen in one row. That queen can attack any other horizontally, vertically and diagonally. So one queen can occupy one row and there are N positions to choose from so we have nxn choose N positions that is quite large for large N. We could improve that by putting one queen on one row only and then we have N power N way to choose from. This is much smaller than the previous way
Next we look at a recursive  method where we place a queen on the board and eliminate the cells where other queen can  be placed Then we use this to place the other queens in a depth first manner . This strategy is called branch and bound. We set up a while loop where we eliminate the previous cells and place the next queen. In each recursion if we could pick the sub problem that is most promising and also eliminate the sub problem that doesn't have a solution, we will have a faster path to the solution.