Next time, Adversarial Search Search to Solve Word Ladders Be as long as e we consider He

Next time, Adversarial Search Search to Solve Word Ladders Be as long as e we consider He www.phwiki.com

Next time, Adversarial Search Search to Solve Word Ladders Be as long as e we consider He

McMahon, Pat, Host has reference to this Academic Journal, PHwiki organized this Journal Next time, Adversarial Search Search to Solve Word Ladders Be as long as e we consider Heuristic Search, let us review a little first We will begin by considering a new problem space, as long as Word Ladders . Example of a word ladder Change DOG to CAT. Change ONLY one letter at a time in addition to as long as m a new legal word at each step.

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What is the depth of the solution Since all three letters are different in the two words, in addition to we have to change only one letter at a time, it is clear that we have to take at least three steps. As it happens, there is a solution at depth three What is the diameter of the Word Ladder problem in general In other words, what two English words could you give me, that would require the deepest tree The two words are “charge” in addition to “comedo”, in addition to the tree is of depth 49. (Note: this is using a st in addition to ard English dictionary, no plurals or verb conjugations) {“charge”, “change”, “chance”, “chancy”, “chanty”, “shanty”, “shanny”, “shinny”, “whinny”, “whiney”, “whiner”, “shiner”, “shiver”, “shaver”, “sharer”, “scarer”, “scaler”, “sealer”, “healer”, “header”, “reader”, “render”, “renter”, “ranter”, “ranker”, “hanker”, “hacker”, “hackee”, “hackle”, “heckle”, “deckle”, “decile”, “defile”, “define”, “refine”, “repine”, “rapine”, “ravine”, “raving”, “roving”, “roping”, “coping”, “coming”, “homing”, “hominy”, “homily”, “homely”, “comely”, “comedy”, “comedo”}

Invented by Lewis Carroll He suggested: APE ARE ERE ERR EAR MAR MAN But we can do: APE APT OPT OAT MAT MAN which takes one less move 1832 –1898 Review point: A problem may have multiple solutions. Different solutions may have different costs. We generally want the cheapest solution, the optimal solution. Some problems may have no solutions This problem has no solution Can you change FROG to TOAD

This time we are given the tree depth, here it is six. The branching factor is the number of letters in the word (4), times 25. 100 is a huge branching factor, but the fairly limited tree depth means it might be tenable. We can use depth-limited search, L = 6 But how do we know the legal paths In other words, how do we know what are legal words It would be best if we had a dictionary of legal words, but if needed :::: AROG has 1,060,00 hits FROM has 25,270,000,000 hits Actually 25,270,000,000 is the max Google allows

Number of Google Hits The “Google hits” strategy suggests a way to do greedy search, or hill-climbing search. We can exp in addition to the nodes with the highest count first That way we are very unlikely to waste time exploring the: FROG CROG subtree etc

G J Assume we have this tree. We have two goal states (highlighted). To underst in addition to all our algorithms, we can ask: “in what order do the nodes get REMOVE-FRONT (dequeued) as long as a given algorithm. G J I am going to do Depth First Search (Enqueue nodes in LIFO (last-in, first-out) order) You should do all algorithms (except perhaps bi-directional search) in addition to make up new trees etc. G J Depth First Search A Nodes Be as long as e entering the loop, the initial state A is enqueued We now enter the loop as long as the first time (next slide), in addition to do a test as long as an empty nodes data structure

Depth First Search Nodes The front of Nodes is dequeued, it was A We ask A, are you the goal Since the answer is no, we exp in addition to all A’s children (do every operator) in addition to enqueue them in Nodes. C B Nodes We now jump back to the top of the loop G J Depth First Search C Nodes The front of Nodes is dequeued, it was B We ask B, are you the goal Since the answer is no, we exp in addition to all B’s children (do every operator) in addition to enqueue them in Nodes. C E D Nodes We now jump back to the top of the loop G J Depth First Search C E Nodes The front of Nodes is dequeued, it was D We ask D, are you the goal Since the answer is no, we exp in addition to all D’s children (do every operator) in addition to enqueue them in Nodes. C E I H Nodes We now jump back to the top of the loop G J

Depth First Search C E I Nodes The front of Nodes is dequeued, it was H We ask H, are you the goal Since the answer is no, we exp in addition to all H’s children. As it happens, there are none C E I Nodes We now jump back to the top of the loop G J Depth First Search C E Nodes The front of Nodes is dequeued, it was I We ask I, are you the goal Since the answer is no, we exp in addition to all I’s children. As it happens, there are none C E Nodes We now jump back to the top of the loop G J Depth First Search C Nodes The front of Nodes is dequeued, it was E We ask E, are you the goal Since the answer is no, we exp in addition to all E’s children (do every operator) in addition to enqueue them in Nodes. C J Nodes We now jump back to the top of the loop G J

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Depth First Search C Nodes The front of Nodes is dequeued, it was J We ask J, are you the goal Since the answer is yes, we report success! G J Heuristic Search The search techniques we have seen so far Breadth first search Uni as long as m cost search Depth first search Depth limited search Iterative Deepening Bi-directional Search are all too slow as long as most real world problems unin as long as med search blind search

Sometimes we can tell that some states appear better that others we can use this knowledge of the relative merit of states to guide search Heuristic Search (in as long as med search) A Heuristic is a function that, when applied to a state, returns a number that is an estimate of the merit of the state, with respect to the goal. In other words, the heuristic tells us approximately how far the state is from the goal state. Note we said “approximately”. Heuristics might underestimate or overestimate the merit of a state. But as long as reasons which we will see, heuristics that only underestimate are very desirable, in addition to are called admissible. I.e Smaller numbers are better Heuristics as long as 8-puzzle I The number of misplaced tiles (not including the blank) In this case, only “8” is misplaced, so the heuristic function evaluates to 1. In other words, the heuristic is telling us, that it thinks a solution might be available in just 1 more move. Goal State Current State Notation: h(n) h(current state) = 1

Success! Please watch the video A Pathfinding Algorithm Visualization https://www.youtube.com/watchv=19h1g22hby8

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