CS 463 Search

Consider a state space where the start state is the number 1 and each state 𝑘 has two successors: the numbers 2𝑘 and 2𝑘 + 1. (The space is a binary tree.) Draw the portion of the state space for states 1 to 15.

(1) (2) (3) (4) (5) (6). (7) (8) (9) (10) (11) (12) (13). (14). (15)

Suppose the goal state is 11. List the order in which nodes will be visited for breadth-first search.

BFS: 1 2 3 4 5 6 7 8 9 10 11

How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search?

Bidirectional search is very useful, because the branching factor when moving down the tree is 2, but the branching factor when moving up the tree is only 1 (and thus will converge on the answer faster).

Suppose the goal state is 11. List the order in which nodes will be visited for depth-limited search with a limit of 3

DLS with limit 3: 1 2 4 8 9 5 10 11

rook on a chessboard can move any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces. Manhattan distance is an admissible heuristic for the problem of moving the rook from square A to square B in the smallest number of moves.

False. A rook can travel multiple squares in a single move. Imagine an empty board with a rook on file A who needs to go to file H. The Manhattan distance between files A and H is 7, but the rook can go there in only 1 move.

Depth-first search always expands at least as many nodes as A* search with an admissible heuristic.

False. While A* usually performs better, it is always possible to construct a graph in which DFS gets lucky and expands fewer nodes.

Suppose the goal state is 11. List the order in which nodes will be visited for iterative deepening search.

ID DFS: 1; 1 2 3; 1 2 4 5 3 6 7; 1 2 4 8 9 5 10 11

Does the answer to (e) above suggest a reformulation of the problem that would allow you to solve the problem of getting from state 1 to a given goal state with almost no search? (1 point)

Rather than starting at initial state and moving down the tree, simply start at the goal and move up the tree. Since each node has only 1 parent, no search is needed

Breadth-first search is complete even if zero step costs are allowed

True. Breadth first search does not take cost into account, so it is still complete even with steps of cost 0.

h(𝑛) = 0 is an admissible heuristic for the 8-puzzle

True. While ℎ(𝑛)=0 is not a very good heuristic, it will never overestimate and is thus admissible.

A* is of no use in robotics because percepts, states, and actions are continuous

x False. A* is frequently used in robotics. Continuous spaces can be discretized (broken up into discrete units), and A* can be applied to them. Also, as the book describes toward the end of Chapter 3, A* can be adapted to work with continuous values.