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N-Queens!

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A python script that allows you to have all formations of n-queens puzzle!

Brief Summary

Logo! The n-queens puzzle is the problem of placing n chess queens on an n×n chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. Solutions exist for all natural numbers n with the exception of n=2 and n=3.


fig.1: A sample iterations for finding a correct formation of 8 queens.

Counting Solutions

The following tables give the number of solutions for placing n queens on an n × n board, both fundamental (sequence A002562 in the OEIS) and all (sequence A000170 in the OEIS).

n fundamental all
1 1 1
2 0 0
3 0 0
4 1 2
5 2 10
6 1 4
7 6 40
8 12 92
9 46 352
10 92 724
11 341 2,680
12 1,787 14,200
13 9,233 73,712
14 45,752 365,596
15 285,053 2,279,184
16 1,846,955 14,772,512
17 11,977,939 95,815,104
18 83,263,591 666,090,624
19 621,012,754 4,968,057,848
20 4,878,666,808 39,029,188,884
21 39,333,324,973 314,666,222,712
22 336,376,244,042 2,691,008,701,644
23 3,029,242,658,210 24,233,937,684,440
24 28,439,272,956,934 227,514,171,973,736
25 275,986,683,743,434 2,207,893,435,808,352
26 2,789,712,466,510,289 22,317,699,616,364,044
27 29,363,495,934,315,694 234,907,967,154,122,528

The six queens puzzle has fewer solutions than the five queens puzzle. There is no known formula for the exact number of solutions, or even for its asymptotic behaviour. The 27×27 board is the highest-order board that has been completely enumerated.

Installation Steps

  1. Clone 'n-queens' from git:
    git clone https://github.com/black-fractal/n-queens.git

  2. Change the directory:
    cd n-queens-main

  3. Install the requirements:
    pip3 install -r requirements.txt

  4. Enjoy the program:+1:

Update to latest version:

Use following command to update to latest version:
git pull

Usage

  • To run with the ASCII visualizer:
    cd src
    python3 n-queens.py
    output-of-n-queens
    Sample output

License

This tools is licensed under the GPL-3.0 License. take a look at the LICENSE for information about it.

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