Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Python Programming

Source: Beazley,David;Jones,BrianK.(2013). PythonCookbook (3rded.).

Breadth-FirstSearch

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Search

Tiers

Strategy:expandashallowestnodefirst

Implementation:FringeisaFIFOqueue

Depth-FirstSearch

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Strategy:expandadeepestnodefirst

Implementation:FringeisaLIFOstack

DFSvsBFS

IterativeDeepening

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• Idea:getDFS’sspaceadvantagewithBFS’stime/shallow-solutionadvantages• RunaDFSwithdepthlimit1.Ifnosolution…• RunaDFSwithdepthlimit2.Ifnosolution…• RunaDFSwithdepthlimit3.…..

• Isn’tthatwastefullyredundant?• Generallymostworkhappensinthelowestlevelsearched,sonotsobad!

Python Code for IterativeDeepening

Cost-SensitiveSearch

BFSfindstheshortestpathintermsofnumberofactions.Itdoesnotfindtheleast-costpath.Wewillnowcoverasimilaralgorithmwhichdoesfindtheleast-costpath.

START

GOAL

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UniformCostSearch

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Strategy:expandacheapestnodefirst:

Fringeisapriorityqueue(priority:cumulativecost) S

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Costcontours

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UniformCostSearch(UCS)Properties

• WhatnodesdoesUCSexpand?• Processesallnodeswithcostlessthancheapestsolution!• IfthatsolutioncostsC* andarcscostatleaste , thenthe“effectivedepth”isroughlyC*/e

• TakestimeO(bC*/e)(exponentialineffectivedepth)

• Howmuchspacedoesthefringetake?• Hasroughlythelasttier,soO(bC*/e)

• Isitcomplete?• Assumingbestsolutionhasafinitecostandminimumarccostispositive,yes!

• Isitoptimal?• Yes!(skippingtheprooffornow)

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C*/e “tiers”c£ 3

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UniformCostIssues

• Remember:UCSexploresincreasingcostcontours

• Thegood:UCSiscompleteandoptimal!

• Thebad:• Exploresoptionsinevery“direction”• Noinformationaboutgoallocation

• We’llfixthatsoon!Start Goal

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BFS/DFS/UCS

• Breadth-firstsearch• Good:optimal,workswellwhenmanyoptions,butnotmanyactionsrequired• Bad:assumesallactionshaveequalcost

• Depth-firstsearch• Good:memory-efficient,workswellwhenfewoptions,butlotsofactionsrequired• Bad:notoptimal,canruninfinitely,assumesallactionshaveequalcost

• Uniform-costsearch• Good:optimal,handlesvariable-costactions• Bad:exploresalloptions,noinformationaboutgoallocation BasicallyDijkstra’s

Algorithm!

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Strategy:expandacheapestnodefirst:

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Costcontours

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Dijkstra‘salgorithm (Uniform-cost search)

Searchexample:PancakeProblem

Rule: a spatula canbeinsertedatanyinterval andflipallpancakesaboveit.Cost:Numberofpancakes flipped.

PancakeBFS

Draw it by yourself!

PancakeUCS

Draw it by yourself!

PancakeDFS

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Statespacegraphwithcostsasweights

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Goal

3Cost:16#Steps:6

PancakeOptimal

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Statespacegraphwithcostsasweights

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Goal

3Cost:7#Steps:2

Project 1: Search (due 09/13)

Incorporatinggoalinformation

Howtoefficiently solvesearchproblemswithvariable-costactions,usinginformation

aboutthegoalstate?

Ø HeuristicsØ GreedyapproachØ A*search

SearchHeuristics

§ Aheuristicis:§ Afunctionthatestimates howcloseastateistoagoal§ Designedforaparticularsearchproblem§ Examples:Manhattandistance,Euclideandistancefor

pathing

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Note thattheheuristicisapropertyofthestate,nottheactiontakentogettothestate!

PancakeHeuristics

Heuristic1:thenumberofpancakes thatare outofplace

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PancakeHeuristics

Heuristic2:howmanypancakesareontopofasmallerpancake?

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PancakeHeuristics

Heuristic3:Allzeros(akanullheuristic,or”Ilikewafflesbetteranyway”)

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Straight-lineHeuristicinRomania

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GreedySearch

GreedyStraight-LineSearchinRomania

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Greedyo Cost:450

Optimalo Cost:418

• Expandthenodethatseemsclosest…

GreedySearch

• Strategy:expandanodethatyouthinkisclosesttoagoalstate• Heuristic:estimateofdistancetonearestgoalforeachstate

• Acommoncase:• Best-firsttakesyoustraighttothe(non-optimal)goal

• Worst-case:likeabadly-guidedDFS

• Whatgoeswrong?• Doesn’ttakereal pathcostintoaccount

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Next class

A*search