Development of Algorithms for Ranking and Un-ranking Function of N-Queens Problem
DOI:
https://doi.org/10.64882/ijrt.v14.iS1.1071Keywords:
N-queens Problem, Ranking Function-ranking Function, Constraint Satisfaction Problem, Euler Project 24Abstract
The n-queens Problem, introduced in 1850 by Carl Gauss, the problem requires us to find the placement of N queens on an NXN chessboard such that no queen is attacking the other. This paper mainly composed of following problems: 1. To evaluate all the solutions for given number of queens. 2. Ranking Function: For given solution, to find rank or index of that solution in set of solution space. 3. Un-ranking Function: For given index find that solution in set of solutions.
We have covered these problems in this, we have conducted an extensive study on these problems and realised that no simple formula is there to solve these problems. There are many algorithms to generate all the solutions of n-queens problem, but in this paper we have considered backtracking. Ranking function: Ranking function states that to find index of solution in set of all solution. Un-ranking function: un-ranking function states that to find particular solution for particular index. I will discuss definition of n-queens problem, its relationship with CSP and history, various method of solving n-queens problem, normal method to find ranking and un-ranking function, at last we will discuss new concept of ranking and un-ranking function respectively.
References
3rd N QUEENS ETSI PlugtestsTM CONTEST Counting the number of solutions Single and Distributed Program.
http://nguyendangbinh.org/Proceedings/IPCV08/Papers/GEM4444.pdf
Hynek, J. Genetic Algorithms for the N-Queens Problem. Available at:
International Journal of Advanced Research in Computer Science and Software Engineering- A Novel Method for Solving N-Queens Problem by Avani Gupta , S.Ravi Rohith and Satya Pramodh Mazumdar SCSE, VIT University, India.
International Journal of Advanced Research in Computer Science and Software Engineering Solving N Queen Problem Using Various Algorithms – A Survey S. Pothumani Department of CSE, Bharath University,
International Journal of Computer Applications (0975 – 8887) Volume 43– No.12, an Unique Solution for N queen Problem April 2012
Lexicographic generation of ordered tree by S. ZAKS , Department of Computer Science University of Illinois Urbana IL 61801 U.S.A.
Modified Genetic Algorithm for Solving n-Queens Problem -Jalaleddin Aghazadeh heris Faculty of Mathematics and Computer Science Allameh Tabataba University Tehran, Iran j.aghazadeh@st.atu.ac.ir Mohammadreza Asgari Oskoei Faculty of Mathematics and Computer Science Allameh Tabataba University Tehran, Iran oskoei@atu.ac.ir.
Solution of n-Queen Problem Using ACO-Salabat Khan, Mohsin Bilal, M. Sharif, Malik Sajid, Rauf BaigNational University Of Computer and Emerging Science Islamabad, Pakistan Email: salabat.khan@nu.edu.pk Telephone: (+92)51-4532308
Vishal Kesri, Prasant Ku. Pattnaik School of Computer Engineering KIIT University, India Vaibhav Kesri Department of Electrical Engineering NIT Kurukshetra, India.
Downloads
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
