• Place N queens on said N×N chessboard so that no two queens threaten each other.
  • The Queen can move in it’s line or row, or diagonally, any number of squares

N-Queens Solution ExampleQueen Movement


This is my solution for this problem/puzzle.

This algorithm shows only one solution by time runned.

  • Made using Javascript.

Solution Explanation

For this solution we found very important the use of HashSet objets to reduce the complexity and simplify the validation of rows and diagonals.

This is posible due to the HashSet.has() method which it’s complexity is O(1).

Variable Name Description Type Size Visual Explanation
n Input Number Integer
Disp Numbers of the rows available Array n
q Stores the row of each queen HashSet n q
Dpos Stores the number of Positive Diagonal which is no more longer available HashSet (n*2)-1 Dpos
Dneg Stores the number of Negative Diagonal which is no more longer available HashSet (n*2)-1 Dneg


To install this repository correctly follow the next steps.

  1. First of all, in the terminal put the next code to clone this repository:

    git clone https://github.com/Rafael-Anguiano/N-Queens.git
    cd N-Queens/
  1. The next step is to make sure you have a way to run this code, in this situation we will use Node.js, if you don’t have it installed, we recommend you to download it.

  2. Once you have installed a runner, you are ready to start simulating and editing some code. To run this app use the next command in the terminal (Be sure you are in the correct directory).

    node N-Queens.js


  • There are many different ways to solve this puzzle with the same input.
  • The algorithm have a random percentage, this means you could receive a different solution each time.
  • The Queen can move in its line or row, or diagonally, any number of squares.

ScreenShots of the Results

Case FailedCase 1 Case 4Case 8 Case 10Case 26 Case 45

Developed By:

Rafael de Jesús Anguiano Suárez del Real (April 2022)


View Github