# N queens problem

The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. … The expected output is a binary matrix which has 1s for the blocks where queens are placed. For example, following is the output matrix for above 4 queen solution.

It has long been known that there are 92 solutions to the problem. Of these 92, there are 12 distinct patterns. All of the 92 solutions can be transformed into one of these 12 unique patterns using rotations and reflections.

**A quantum-inspired differential evolution algorithm for solving the N – queens problem **

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In this paper, a quantum-inspired differential evolution algorithm for solving the N – queens problem is presented. The N – queens problem aims at placing N queens on an NxN chessboard, in such a way that no queen could capture any of the others. The proposed

**Solving the n – queens problem with a binary Hopfield-type network. Synchronous and asynchronous model**

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The application of a discrete Hopfield-type neural network to solving the NP-Hard optimization problem -the N – Queens Problem (NQP) is presented. The applied network is binary, and at every moment each neuron potential is equal to either 0 or 1. The network can

**Solving the n – queens problem using a tuned hybrid imperialist competitive algorithm.**

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The n – queens problem is a classical combinatorial optimization problem which has been proved to be NP-hard. The goal is to place n non-attacking queens on an n n chessboard. In this paper, the Imperialist Competitive Algorithm (ICA), which is a recent evolutionary

**Comparative Study of Different Algorithms To Solve N – Queens Problem **

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This Paper provides a brief description of the Genetic Algorithm (GA), the Simulated Annealing (SA) Algorithm, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm and attempts to explain the way as how the Proposed Genetic Algorithm (GA), the This paper presents a multivalued Hopfield-type neural network as a method for solving combinatorial optimization problems with a formulation free of fine-tuning parameters. As benchmark of the performance of the network we have used N -Queen problems. Computer

**New Mathematical Models of N – Queens Problem and its Solution by a Derivative-Free Method of Optimization**

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Most of the optimization methods do not inherit convergence proofs. One of the measures to rank them is their potential to solve challenging problems specially formulated for this purpose. In this paper the problem involves two main issues. Firstly we present new

**Efficiency of parallel genetic algorithm for solving N – queens problem on multicomputer platform**

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The paper investigates the efficiency of parallel genetic algorithm for solving N – queens problem on a multicomputer platform. The proposed parallel computational model of the genetic algorithm is based on a parallel algorithmic paradigm of synchronous iterations

**A new approach to solve n – queens problem based on series**

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The N – queens problem is a popular classic puzzle where numbers of queen were to be placed on an nxn matrix such that no queen can attack any other queen. The Branching Factor grows in a roughly linear way, which is an important consideration for the

**Particle swarm optimization for N – queens problem **

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The N -Queen is one of the prominent toy problems for performance assessment in the domain of Computational Intelligence. The problem greatly helps to examine the diverse aspects of solving techniques, counting the potential of obtaining feasible solution and

**An Algebraic Method for the N – Queens Problem Based on Permutation Operation Group**

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to analyze N – Queens problem in permutation space, this paper defines isomorphic operations of permutation to dihedral group D4. With these operations to find elements within an orbit, two operations on orbits are also defined to generate new orbit from existing

**A Solution to the N – Queens Problem Using Biogeography-Based Optimization.**

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Biogeography-based Optimization (BBO) is a global optimization algorithm based on population, governed by mathematics of biogeography, and dealing with geographical distribution of biological organisms. The BBO algorithm was used in the present study to

**Basic and Hybrid Imperialist Competitive Algorithms for Solving the n – Queens Problem .**

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The n – queens problem is a classical combinatorial optimization problem which has been proved to be NP-hard. The goal is to place n non-attacking queens on an n n chessboard. In this paper, the Imperialist Competitive Algorithm (ICA), which is a recent evolutionary

**Results for the n – queens problem on the M bius board.**

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In this paper we consider the extension of the n – queens problem to the M bius strip; that is, the problem of placing a maximum number of nonattacking queens on the mn chessboard for which the left and right edges are twisted connected. We prove the existence of solutions

**Quantum algorithm for n – queens problem **

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In the game of chess the queen piece can move in any direction (horizontal, vertical and di- agonal) and jump over any number of spaces. The n – queens problem is a classical combi- natorial problem related with the distribu- tion of n number of queens on an nxn chess board. The queens

**A Novel Approach to Solving N – Queens Problem **

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Placing n mutually non-attacking queens on an n by n chessboard is a classical problem in the artificial intelligence (AI) area. Over the past few decades, this problem has become important to computer scientists for providing solutions to many useful and practical

**Common Search Strategies and Heuristics With Respect to the N – Queens Problem **

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Page 1. Common Search Strategies and Heuristics With Respect to the N – Queens Problem by Sheldon Dealy Page 2. Topics Problem History of N – Queens Searches Used Heuristics Implementation Methods Results Discussion Page 3. Problem Given an NxN chess

**An Approach to N – Queens Problem Using Chaos Neural Network-Challenge to Finding All Solutions of N – Queens Problem **

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In this study, we investigate three different update methods of the chaos neural network in order to approach to finding all solutions of the N – Queens problem . By computer simulations for various sizes of the N – Queens problem , we confirm that the method to change the

**Load Balancing using N – Queens Problem **

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A distributed system can be viewed as a collection of computing and communication resources shared by active users. These resources are distributed and possibly owned by different agents or organization. When the demand for computing power increases the load

**Investigation of the Regularities in the Formation of Solutions n – Queens Problem **

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The n – Queens problem is considered. A description of the regularities in a sequential list of all solutions, both complete and short, is given. Determined that: 1. The fraction of total solutions in the general list of all solutions decreases, with increasing value of n . 2

**A Hybrid Approach Using Particle Swarm Optimization and Parallel Simulated Annealing: A Case Study of n – Queens Problem **

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This paper presents a hybrid approach by a combination of particle swarm optimization (PSO) and parallel simulated annealing (PSA) algorithms. PSO is a population based heuristic method that sometimes traps in local maximum. To cope with this problem , we

The worst case “brute force” solution for the N-queens puzzle has an O(n^n) time complexity. This means it will look through every position on an NxN board, N times, for N queens. It is by far the slowest and most impractical method.

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