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A* ALGORITHM BASICS FOR PATH FINDING & HEURISTICS METHODS : ARTIFICIAL INTELLIGENCE

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 A* ALGORITHM BASICS FOR PATH FINDING A* , widely used  known form of best-first search & path planning algorithm nowadays in mobile robots,games. this is the function for A*,                                     f(n) = g(n) + h(n) g ( n ) is the cost of the path from the start node to n , and h ( n ) is a heuristic function that estimates the cost of the cheapest path from n to the goal This will find cheapest f(n) value in neighbor nodes to archive goal node. check below image  A to B path finding with g(n),h(n),f(n) value In the final level check below image Now we will check the Algorithm // A* Search Algorithm 1. Initialize the open list 2. Initialize the closed list put the starting node on the open list (you can leave its f at zero) 3. while the open list is not empty a) find the node with the least f on the open list, call it "q" b) pop q off the open list c) generate q's 8 successors
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BACKTRACKING ALGORITHM FOR THE N QUEENS PROBLEM & PYTHON IMPLEMENTATION: ARTIFICIAL INTELLIGENCE

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 ALGORITHM

The problem is to place n queens on an n * n chessboard, so that no two queens are attacking each other.this means that no two queens are in the same row, the same column, or the same diagonal.


This is the algorithm for n queens backtracking :

PLACEQUEENS(Q[1..N],r):
       if r=n+1
            print Q[1...n]
       else
            for j <-- 1 to n
                 legal <--- TRUE
                 for i <-- 1 to r-1
                      if (Q[i]=j) or (Q[i]=j+r-i) or (Q[i] =j-r+i)  :
                                 legal <-- FALSE
                 
                 if legal
                         Q[r] <-- j
                         PLACEQUEENS(Q[1..N],r+1)   //recursion

Here represent the positions of the queens using an array Q[1 .. n], where Q[i] indicates which square in row i contains a queen. When backtrack is called, the input parameter r is the index of the first empty row, and the prefix Q[1 .. r 1] contains the positions of the first r-1 queens. In particular, to compute all n-queens solutions with no restrictions, we would call backtrack (Q[1 .. n], 1). The outer for-loop considers all possible placements of a queen on row r; the inner for-loop checks whether a candidate placement of row r is consistent with the queens that are already on the first r 1 rows

PYTHON IMPLEMENTATION
  
Just  download python script through below github link & run it
BACKTRACKING-ALGORITHM-PYTHON

 check below Demo

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