N Queen Algorithm
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The document discusses the N-Queens problem, which involves placing N queens on an N×N chessboard such that no two queens can attack each other. It outlines various approaches to solving the problem, including brute force, backtracking, and mathematical methods. A detailed explanation of the backtracking algorithm for finding solutions is also provided.
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![Backtracking Algorithm :
1) Start from the left most column.
2) If all Queens are placed
return true.
3) Try all rows in the current column. Do following for every tried row.
a) If the queen can be placed safely in this row then mark this [row,
column] as part of the solution and recursively check if placing
queen here leads to a solution.
b) If placing queen in [row, column] leads to a solution then return
true.
c) If placing queen doesn't lead to a solution then unmark this [row,
column] (Backtrack) and go to step (a) to try other rows.
4) If all rows have been tried and nothing worked, return false to trigger
backtracking.](https://image.slidesharecdn.com/nqueenalgorithm-170411204309/85/N-Queen-Algorithm-11-320.jpg)
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Genetic Algorithm Artificial IntelligenceLamisaNoor The document discusses the 4-queen and 8-queen problems, initially presenting a narrative about a king who seeks help in placing queens so they do not see each other. It explores solutions through backtracking methods and introduces genetic algorithms as a more efficient approach for larger problems, detailing the principles and procedures of genetic algorithms. The document concludes with a comparison of backtracking and genetic algorithm approaches in solving the n-queen problem.
data structures- back tracking
data structures- back trackingAbinaya B The document describes the backtracking algorithm and its application to solve the 8 queens problem. It provides an overview of backtracking as a general method for problems that search for solutions or require an optimal solution. It then gives a maze pathfinding problem as an example of a backtracking algorithm. The document outlines the recursive pseudo code for backtracking and applies it to the 8 queens problem, describing the problem and providing an algorithm to find all solutions by placing queens on an 8x8 chessboard without any attacking each other. It provides two examples of solutions to the 8 queens problem.
Lecture2b algorithm
Lecture2b algorithmmbadhi barnabas This document discusses various algorithms and problems including:
1) The Towers of Hanoi puzzle and its solution requiring 2n-1 moves for n disks.
2) Permutations and two methods for generating all possible permutations.
3) The n-queens problem of placing n queens on an n×n chessboard without any queens threatening each other, solved using backtracking.
4) Backtracking as a general method for constraint satisfaction problems.
Solving N-queen Problem Using Genetic Algorithm by Advance Mutation Operator
Solving N-queen Problem Using Genetic Algorithm by Advance Mutation Operator IJECEIAES The document presents a new genetic algorithm with an advanced mutation operator to solve the n-queen problem, which is a well-known NP-hard constraint satisfaction problem. The proposed algorithm demonstrated superior performance by significantly reducing execution time compared to existing methods for different instances of the n-queen problem, including cases with up to 50 queens. The authors conclude that this algorithm could be further optimized for larger instances in future work.
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N Queen Algorithm
- 1. 1
- 2. W E L C O M E ! Thank you for coming today! 2
- 4. INTRODUCTION
- 5. 5 N Q u e e n P r o b l e m The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. For example, following is a solution for 4 Queen problem.
- 6. Solutions
- 7. V a r i o u s a p p r o a c h e s : 7 Brute force Backtracking Permutation generation Graph theory concepts Divide and conquer approach Mathematical solutions
- 8. Backtracking Solution : 0 1 2 3 0 1 2 3 0 1 2 3 Positions:
- 9. 9 F i n a l S o l u t i o n Q Q Q Q
- 10. Bac k trac k ing Algorithm
- 11. Backtracking Algorithm : 1) Start from the left most column. 2) If all Queens are placed return true. 3) Try all rows in the current column. Do following for every tried row. a) If the queen can be placed safely in this row then mark this [row, column] as part of the solution and recursively check if placing queen here leads to a solution. b) If placing queen in [row, column] leads to a solution then return true. c) If placing queen doesn't lead to a solution then unmark this [row, column] (Backtrack) and go to step (a) to try other rows. 4) If all rows have been tried and nothing worked, return false to trigger backtracking.
- 12. T H A N K Y O U ! A N Y Q U E S T I O N S ?
Editor's Notes
- #4: No slide master