8 Queens Problem - Artificial Intelligence-Unit-1-Problem Solving-4 Queens Problem

Unit – 1 – Problem Solving
Problem Formulation - 4 and 8 Queens Problem

4 Queens Problem
In chess, a queen can move as far as she pleases, horizontally, vertically, or diagonally.
A chess board has 4 rows and 4 columns.
The standard 4 by 4 Queen’s problem asks how to place 4 queens on an ordinary chess board so that none of them can hit any other in one move.

8 - Queens Problem
In chess, a queen can move as far as she pleases, horizontally, vertically, or diagonally.
A chess board has 8 rows and 8 columns.
The standard 8 by 8 Queen’s problem asks how to place 8 queens on an ordinary chess board so that none of them can hit any other in one move

The problem Components for Incremental Formulation
States : any arrangement of 0 to 8 Queens on the board.
Initial State : Empty board
Successor function : Add a Queen to an empty space
Goal Test : 8 queens are on the board but none of them should attack each other.
Path cost : for each action cost will be 1. so default is 8 (but the cost will be varied based on number of iterations to takes to complete the problem)

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