Consider a tree with 22 nodes numbered 1-22. I need to be able to explain how us

Question

Consider a tree with 22 nodes numbered 1-22. I need to be able to explain how using a heuristic function alters the search pattern if the goal is at node 20. The actual heuristic used is not so important. Level 0 consists of node 1, level two consists of nodes 2,3,4, level 3 consists of nodes 5,6,7,8,9,10 and so forth. Typically with depth-first I would just drop down the left side. Adding the heuristic into this search, and computing h values for each node, how and when are the h values used to help determine the best path? Some detail please

Explanation / Answer

heuristic is a function, h(n) defined on the nodes of a search tree, which serves as an estimate of the cost of the cheapest path from that node to the goal node.

In any searching problem where there are b choices at each node and a depth of d at the goal node, a naive searching algorithm would have to potentially search around bd nodes before finding a solution. Heuristics improve the efficiency of search algorithms by reducing the branching factor from b to a lower constant b', using a cutoff mechanism. The branching factor can be used for defining a partial order on the heuristics, such that h1(n) < h2(n) if h1(n) has a lower branch factor than h2(n) for a given node n of the search tree.

                                  so in this case i think there  are 4 level require to arrange the all 22 nodes of a tree.

so we need to remove the left  child of the tree  and in DFS  so firstly went to node 12 using DFS and find out there value of d=4(depth from the root) ,and b=12(left most node on which heuristic will apply firstly).

                                     So h(12)=124 mod 10.

                                  similarly we follow  the same procedure to find out the h(n) ,heuristic function for all nodes of tree.

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