8 Queen Problem and 4 Queen problem in Artificial Intelligence

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. Let us consider, N = 8. Then 8-Queens Problem is to place eight queens on an 8 x 8 chessboard so that o to attak, that is, o to of the ae o the sae o, olu, o diagoal.All solutions to the 8-queens problem can be represented as 8-tuples (x1... x8), where xi is the column of the ith row where the ith queen is placed. The promising function must check whether two queens are in the same column or diagonal: Suppose two queens are placed at positions (i, j) and (k, l) Then: • Column Conflicts: Two queens conflict if their xi values are identical. • Diagonal conflict: Two queens i and j are on the same diagonal if: i - j = k - I.This implies, j - 1 = i - k Algorithm 1) Start in the leftmost 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. #nqueensproblem #nqueenproblem #nqueen #nqueenproblemusingbacktracking #algorithm #ada #gatesmashers #daa #8 queen problem in artificial intelligence #8 queen problem in ai #8 queen problem backtracking #8 queen problem state space tree