L19JDM1short - Lecture Outline Issues: (a) Representing...

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1 Lecture Outline Lecture Outline Issues: (a) Representing problems (c) Expertise 1. Problems and problem representation Well-structured vs. ill-structured problems Stages in problem solving The importance of problem representation 2. Common flaws in problem solving Analogies Hindrances to forming appropriate representations 3. Problem solving methods Algorithms and heuristics Heuristics: Hill climbing, means-ends analysis, working backward 4. Expertise Very domain specific (chess study) Power law of practice Characteristics of expertise
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2 Basic logic of Means-end analysis Match current state to goal state to find the most important difference Subgoal: Eliminate the difference Difference detected SUCCESS SUCCESS No Differences FAIL FAIL Search for operator relevant to reducing the difference Match condition of operator to current state to find most important difference Subgoal: Eliminate the difference SUCCESS No Differences FAIL None found Apply Operator Difference detected Flowchart 1: Transform current state into goal state Flowchart 2: Eliminate a difference
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3 IF the peg 3 is clear and the largest disk is free THEN move the largest disk to peg 3. IF the largest disk is not free, THEN set a subgoal to free it. IF a subgoal is to free the largest disk and a smaller disk is on it, THEN move the smaller disk off. Productions for Tower of Hanoi
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4 Problem-solving: Problem-solving: Working backward Working backward Transform goal state so it is more similar to the initial state. Useful if too many paths leading from initial state. Initial State Goal State
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5 Working Working backward backward useful for mazes:
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6 A B C D A geometry problem: Given that ABDC is a rectangle, prove that AD and CB are congruent. Working backward: Working backward: Start at end: what would make AD and CB are congruent?
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8 1 1 31 1073741824 61 1152921504606850000 2 2 32 2147483648 62 2305843009213690000 3 4 33 4294967296 63 4611686018427390000 4 8 34 8589934592 64 9223372036854780000 5 16 35 17179869184 65 18446744073709600000 6 32 36 34359738368 66 36893488147419100000 7 64 37 68719476736 67 73786976294838200000 8 128 38 137438953472 68 147573952589676000000 9 256 39 274877906944 69 295147905179353000000 10 512 40 549755813888 70 590295810358706000000 11 1024 41 1099511627776 71 1180591620717410000000 12 2048 42 2199023255552 72 2361183241434820000000 13 4096 43 4398046511104 73 4722366482869650000000 14 8192 44 8796093022208 74 9444732965739290000000 15 16384 45 17592186044416 75 18889465931478600000000 16 32768 46 35184372088832 76 37778931862957200000000 17 65536 47 70368744177664 77 75557863725914300000000 18 131072 48 140737488355328 78 151115727451829000000000 19 262144 49 281474976710656 79 302231454903657000000000 20 524288 50 562949953421312 80 604462909807315000000000 21 1048576 51 1125899906842620 81 1208925819614630000000000 22 2097152 52 2251799813685250 82 2417851639229260000000000
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L19JDM1short - Lecture Outline Issues: (a) Representing...

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