N-Queens Problem Backtracking Demo

A visualization and explanation of how a backtracking algorithm searches for a solution to a problem.

For performance reasons n is bound between 4 and 10.

Note: Requires canvas supported browser. Tested on Chrome, Safari, Edge, Firefox.

N-queens problem

If I have a chessboard of width and length n where n is a number.

How can n queens be placed so that none of the queens are attacking one another?

Try it yourself here with 8 queens.

What would the algorithm do without backtracking?

Without backtracking a program would place all n queens before checking if any queens are attacking. This leads to wasteful solutions such as an entire row of queens.

We don’t need a whole row full of queens before we know that the solution failed. Instead we only need 2 queens to be attacking each other to know that the solution is wrong.

Introducing backtracking

A backtracking algorithm is a way of computing a solution to a problem when constraints are known.

The algorithm places one queen at a time. If the queen placed is attacking another queen, the queen is removed and we try again in the next position. This is the backtracking step.

If you want to see this in action. Run the animation and look for the queens being taken off the board. This is obvious when solving for 10 queens.

For more detail check out the wiki page on backtracking.