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6:28 < + 50 VIE 81% children be visited in any particular order, we will visit the children of a node from left to right in the applications in this chapter. Figure 5.1 shows a depth-first search of a tree performed in this manner. The nodes are numbered in the order in which they are visited. Notice that in a depth- first search, a path is followed as deeply as possible until a dead end is reached. At a dead end we back up until we reach a node with an unvisited child, and then we again proceed to go as deep as possible. Figure 5.1 A tree with nodes numbered according to a depth-first search. 8 11 7 9 10 12 13 16 14 15 There is a simple recursive algorithm for doing a depth-first search. Because we are presently interested only in preorder traversals of trees, we give a version that specifically accomplishes this. The procedure is called by passing the root at the top level. void depth_first_tree_search (node v) { } node u; visit v; for (each child u of v) depth_first_tree_search(u); This general-purpose algorithm does not state that the children must be visited in any particular order. However, as mentioned previously, we visit them from left to right. Now let's illustrate the backtracking technique with the instance of the n- Queens problem when n = 4. Our task is to position four queens on a 4×4 chessboard so that no two queens threaten each other. We can immediately simplify matters by realizing that no two queens can be in the same row. The instance can then be solved by assigning each queen a different row and checking which column combinations yield solutions. Because each queen can be placed in one of four columns there are 4 x 4 x 4 x 4 = 256 candidate Authorize the system to edit this file. A 4 Authorize + Edit Annotate Fill & Sign Convert All

6:28 < + 50 VIE 81% children be visited in any particular order, we will visit the children of a node from left to right in the applications in this chapter. Figure 5.1 shows a depth-first search of a tree performed in this manner. The nodes are numbered in the order in which they are visited. Notice that in a depth- first search, a path is followed as deeply as possible until a dead end is reached. At a dead end we back up until we reach a node with an unvisited child, and then we again proceed to go as deep as possible. Figure 5.1 A tree with nodes numbered according to a depth-first search. 8 11 7 9 10 12 13 16 14 15 There is a simple recursive algorithm for doing a depth-first search. Because we are presently interested only in preorder traversals of trees, we give a version that specifically accomplishes this. The procedure is called by passing the root at the top level. void depth_first_tree_search (node v) { } node u; visit v; for (each child u of v) depth_first_tree_search(u); This general-purpose algorithm does not state that the children must be visited in any particular order. However, as mentioned previously, we visit them from left to right. Now let's illustrate the backtracking technique with the instance of the n- Queens problem when n = 4. Our task is to position four queens on a 4×4 chessboard so that no two queens threaten each other. We can immediately simplify matters by realizing that no two queens can be in the same row. The instance can then be solved by assigning each queen a different row and checking which column combinations yield solutions. Because each queen can be placed in one of four columns there are 4 x 4 x 4 x 4 = 256 candidate Authorize the system to edit this file. A 4 Authorize + Edit Annotate Fill & Sign Convert All

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter17: Linked Lists
Section: Chapter Questions
Problem 9PE
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Question

Trace a State Space Tree introduced in the Chapter 5.1 using algorithms depth_first_search (page 205), checknode (page 207), and expand (page 210).

 

 

 

Assume that State Space Tree is a two-level full binary tree (root is level 0). Node #2 (according to notation used in the Figure 5.1, page 204) is non-promising.

 

Count the number of steps performed by each of those three algorithms. Consider execution of instructions like "visit node" or execution of "promising function" as one step, "write a solution" as an exit call.    

 

Note: no need to print or a draw a whole tree. Just provide three numbers as an answer

6:28 < + 50 VIE 81% children be visited in any particular order, we will visit the children of a node from left to right in the applications in this chapter. Figure 5.1 shows a depth-first search of a tree performed in this manner. The nodes are numbered in the order in which they are visited. Notice that in a depth- first search, a path is followed as deeply as possible until a dead end is reached. At a dead end we back up until we reach a node with an unvisited child, and then we again proceed to go as deep as possible. Figure 5.1 A tree with nodes numbered according to a depth-first search. 8 11 7 9 10 12 13 16 14 15 There is a simple recursive algorithm for doing a depth-first search. Because we are presently interested only in preorder traversals of trees, we give a version that specifically accomplishes this. The procedure is called by passing the root at the top level. void depth_first_tree_search (node v) { } node u; visit v; for (each child u of v) depth_first_tree_search(u); This general-purpose algorithm does not state that the children must be visited in any particular order. However, as mentioned previously, we visit them from left to right. Now let's illustrate the backtracking technique with the instance of the n- Queens problem when n = 4. Our task is to position four queens on a 4×4 chessboard so that no two queens threaten each other. We can immediately simplify matters by realizing that no two queens can be in the same row. The instance can then be solved by assigning each queen a different row and checking which column combinations yield solutions. Because each queen can be placed in one of four columns there are 4 x 4 x 4 x 4 = 256 candidate Authorize the system to edit this file. A 4 Authorize + Edit Annotate Fill & Sign Convert All
Transcribed Image Text:6:28 < + 50 VIE 81% children be visited in any particular order, we will visit the children of a node from left to right in the applications in this chapter. Figure 5.1 shows a depth-first search of a tree performed in this manner. The nodes are numbered in the order in which they are visited. Notice that in a depth- first search, a path is followed as deeply as possible until a dead end is reached. At a dead end we back up until we reach a node with an unvisited child, and then we again proceed to go as deep as possible. Figure 5.1 A tree with nodes numbered according to a depth-first search. 8 11 7 9 10 12 13 16 14 15 There is a simple recursive algorithm for doing a depth-first search. Because we are presently interested only in preorder traversals of trees, we give a version that specifically accomplishes this. The procedure is called by passing the root at the top level. void depth_first_tree_search (node v) { } node u; visit v; for (each child u of v) depth_first_tree_search(u); This general-purpose algorithm does not state that the children must be visited in any particular order. However, as mentioned previously, we visit them from left to right. Now let's illustrate the backtracking technique with the instance of the n- Queens problem when n = 4. Our task is to position four queens on a 4×4 chessboard so that no two queens threaten each other. We can immediately simplify matters by realizing that no two queens can be in the same row. The instance can then be solved by assigning each queen a different row and checking which column combinations yield solutions. Because each queen can be placed in one of four columns there are 4 x 4 x 4 x 4 = 256 candidate Authorize the system to edit this file. A 4 Authorize + Edit Annotate Fill & Sign Convert All
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