# OOMPA Lecture 17

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OOMPA Lecture 17. Artificial intelligence and game playing Course evaluation &amp; discussion C++ standard template library. Lab4. Design and implement a general game playing framework for deterministic two player zero-sum games Implement Min-Max-search Implement the games TicTacToe
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OOMPA Lecture 17
• Artificial intelligence and game playing
• Course evaluation & discussion
• C++ standard template library
• Lab4
• Design and implement a general game playing framework for deterministic two player zero-sum games
• Implement Min-Max-search
• Implement the games
• TicTacToe
• Connect-Four
• Extra point
• Implement alpha-beta pruning
• Implement checkers
• Games as Search Problems
• The behavior / actions of the opponent are unpredictable, therefore search for a “worst-case”-plan.
• Time limit, therefore complete search is not feasible and an approximation is needed
• Algorithm for perfect play (van Neumann 1944)
• Finite horizon, approximate evaluation (Zuse 1945, Shannon 1950, Samuel 1952)
• Pruning search tree (McCarthy 1956)
• Types of GameMiniMax
• Optimal strategy for deterministic, perfect-information game
• Idea: Choose move that results in position with highest minmax-value = best achievable payoff against best opponents play
• 5Max:A3A1A2Min:352A11A13A21A23A31A33A12A22A323128579427MiniMaxFunction MINIMAX-DECISION(game) returns a move for each move in PossibleMoves[game] do value[move] <- MINIMAX-VALUE(apply(move,state),game) end return the move with the highest value[move]Function MINIMAX-VALUE(state, game) returns a utility value if TERMINAL-TEST[game](state) then return UTILITY[game](state) else if MAX is to move in state return the highest MINIMAX-VALUE of SUCCESSORS(state) else return the lowest MINIMAX-VALUE of SUCCESSORS(state)MiniMax Properties
• Complete: yes, if search tree is finite
• Optimal : yes, if opponent plays optimal
• Time complexity : O(bm)
• Space complexity : O(bm) depth first search
• Chess b~35 possible moves in each state, m~100 moves per game -> exact solution infeasible
• Standard solution
• cutoff test for search (e.g. depth limit)
• Evaluation function : approximates utility of board position
• Evaluation Functions
• For chess for example typically linear weighted sum of features
• Eval(s) = w1 f1(s) + w2 f2(s) + …wn fn(s)
• w1=9 f1(s)= #white queens - #black queens w2=5 f2(s) = #white rooks - #black rooks etc.Cutting of Search
• MINIMAXCUTOFF is identical to MINIMAXVALUE except
• 1. TERMINAL? is replaced by CUTOFF?
• 2. UTILITY is replaced by EVAL
• Ply = one half-move (move by one player)
• Chess:
• 4-ply = novice
• 8-ply = PC, human master
• 12-ply = Deep Blue, Kasparov
• Pruning ExampleMax:3A3A1A2Min:325A11A13A21A23A21A12A22A2231282??572A232Standard Template Library
• The standard template library (STL) contains
• Containers
• Algorithms
• Iterators
• A container is a way that stored data is organized in memory, for example an array of elements.
• Algorithms in the STL are procedures that are applied to containers to process their data, for example search for an element in an array, or sort an array.
• Iterators are a generalization of the concept of pointers, they point to elements in a container, for example you can increment an iterator to point to the next element in an array
• Containers, Iterators, AlgorithmsAlgorithms use iterators to interact with objectsstored in containersContainerContainerIteratorAlgorithmIteratorObjectsAlgorithmIteratorIteratorAlgorithmContainers
• A container is a way to store data, either built-in data
• types like int and float, or class objects
• The STL provides several basic kinds of containers
• <vector> : one-dimensional array
• <list> : double linked list
• <deque> : double-ended queue
• <queue> : queue
• <stack> : stack
• <set> : set
• <map> : associative array
• Sequence Containers
• A sequence container stores a set of elements in
• sequence, in other words each element (except for the first and last one) is preceded by one specific element and followed by another, <vector>, <list> and <deque> are sequential containers
• In an ordinary C++ array the size is fixed and can
• not change during run-time, it is also tedious to insert or delete elements. Advantage: quick random access
• <vector> is an expandable array that can shrink or
• grow in size, but still has the disadvantage that inserting or deleting elements in the middle is costly as it requires to copy chunks of memorySequence Containers
• <list> is a double linked list (each element has
• points to its successor and predecessor), it is quick to insert or delete elements but provides no random access (e.g. return 5th element in list)
• <deque> is a double-ended queue, that means one
• can insert and delete elements from both ends, it is a kind of combination between a stack (last in first out) and a queue (first in first out) and constitutes a compromise between a <vector> and a <list>Associative Containers
• An associative container is non-sequential but uses
• a key to access elements. The keys, typically a number or a string, are used by the container to arrange the stored elements in a specific order, for example in a dictionary the entries are ordered alphabetically.Associative Containers
• A <set> stores a number of items which contain keys
• The keys are the attributes used to order the items, for example a set might store objects of the class Person which are ordered alphabetically using their name
• A <map> stores pairs of objects: a key object and
• an associated value object. A <map> is somehow similar to an array except instead of accessing its elements with index numbers, you access them with indices of an arbitrary type.
• <set> and <map> only allow one key of each value,
• whereas <multiset> and <multimap> allow multiple identical key valuesVector Containerint array = {12, 7, 9, 21, 13 };vector<int> v(array,array+5);12792113v.push_back(15);v.pop_back();13…127921127921150 1 2 3 412792115v.begin();vVector Container#include <vector>#include <iostream>vector<int> v(3); // create a vector of ints of size 3v=23;v=12;v=9; // vector full v.push_back(17); // put a new value at the end of arrayfor (int i=0; i<v.size(); i++) // member function size() of vector cout << v[i] << ” ”; // random access to i-th elementcout << endl;Constructors for Vector
• A vector can be initialized by specifying its size and
• a prototype element or by another vectorvector<Date> x(1000); // creates vector of size 1000, // requires default constructor for Datevector<Date> dates(10,Date(17,12,1999)); // initializes // all elements with 17.12.1999vector<Date> y(x); // initializes vector y with vector xIterators
• Iterators are pointer-like entities that are used to
• access individual elements in a container.
• Often they are used to move sequentially from element to element, a process called iterating through a container.
• vector<int>array_17vector<int>::iterator423The iterator corresponding tothe class vector<int> is ofthe type vector<int>::iterator 12size_4Iterators
• The container member functions begin() and end() return an iterator to the first and past the last element of a container
• vector<int> vv.begin()array_17423v.end()12size_4Iterators
• One can have multiple iterators pointing to different or identical elements in the container
• vector<int> vi1array_174i22312i3size_4Iterators#include <vector>#include <iostream>vector<int> v; // initialize empty vector v.push_back(13);v.push_back(9);v.push_back(8);vector<int>::iterator iter=v.begin(); // iterator for class vector// define iterator for vector and point it to first element of vcout << ”first element of v=” << *iter; // de-reference iteriter++; // move iterator to next elementiter=v.end()-1; // move iterator to last element Iteratorsint max(vector<int>::iterator start, vector<int>::iterator end){ int tmpmax=*start; while(start != stop) { if (*start > tmpmax) tmpmax=*start; ++start; } return tmpmax;}cout << ”max of v = ” << max(v.begin(),v.end());Iterator Categories
• Not every iterator can be used with every container for example the list class provides no random access iterator
• Every algorithm requires an iterator with a certain level of capability for example to use the [] operator you need a random access iterator
• Iterators are divided into five categories in which a higher (more specific) category always subsumes a lower (more general) category, e.g. An algorithm that
• accepts a forward iterator will also work with a bidirectional iterator and a random access iterator inputforwardbidirectionalrandomaccessoutputFor_Each() Algorithm#include <vector>#include <algorithm>#include <iostream>void show(int n) { cout << n << ” ”; } int arr[] = { 12, 3, 17, 8 }; // standard C arrayvector<int> v(arr, arr+4); // initialize vector with C array for_each (v.begin(), v.end(), show); // apply function show // to each element of vector vFind() Algorithm#include <vector>#include <algorithm>#include <iostream>int key;int arr[] = { 12, 3, 17, 8, 34, 56, 9 }; // standard C arrayvector<int> v(arr, arr+7); // initialize vector with C array vector<int>::iterator iter;cout << ”enter value :”;cin >> key;iter=find(v.begin(),v.end(),key); // finds integer key in vif (iter != v.end()) // found the element cout << ”Element ” << key << ” found” << endl;else cout << ”Element ” << key << ” not in vector v” << endl;Find_If() Algorithm#include <vector>#include <algorithm>#include <iostream>Bool mytest(int n) { return (n>21) && (n <36); };int arr[] = { 12, 3, 17, 8, 34, 56, 9 }; // standard C arrayvector<int> v(arr, arr+7); // initialize vector with C array vector<int>::iterator iter;iter=find_if(v.begin(),v.end(),mytest); // finds element in v for which mytest is true if (iter != v.end()) // found the element cout << ”found ” << *iter << endl;else cout << ”not found” << endl;Count_If() Algorithm#include <vector>#include <algorithm>#include <iostream>Bool mytest(int n) { return (n>14) && (n <36); };int arr[] = { 12, 3, 17, 8, 34, 56, 9 }; // standard C arrayvector<int> v(arr, arr+7); // initialize vector with C array int n=count_if(v.begin(),v.end(),mytest); // counts element in v for which mytest is true cout << ”found ” << n << ” elements” << endl;Linked List
• A linked list is composed of a chain of elements (links). Each element contains some data and a pointer to the next element in the list.
• In a double linked list, each element also contains a pointer to its predecessor.
• ElementElementElementnextdatanextdatanextdataElementElementElementnextprevdatanextprevdatanextprevdataList Container
• A list container is a double linked list, in which
• each element contains a pointer to its successor and predecessor.
• It is possible to insert and remove elements at arbitrary location in the list, without having to copy large chunks of memory as with vectors
• Lists do not allow random access but are efficient to
• insert new elements and to sort and merge listsList Containerint array = {12, 7, 9, 21, 13 };list<int> li(array,array+5);12792113li.push_back(15);li.pop_back();13…12792112792115li.pop_front();li.push_front(8);12…8127921157921li.insert()19712172123Sort & Merge
• Sort and merge allow you to sort and merge elements in a container
• #include <list> int arr1[]= { 6, 4, 9, 1, 7 };int arr2[]= { 4, 2, 1, 3, 8 };list<int> l1(arr1, arr1+5); // initialize l1 with arr1list<int> l2(arr2, arr2+5); // initialize l2 with arr2l1.sort(); // l1 = {1, 4, 6, 7, 9}l2.sort(); // l2= {1, 2, 3, 4, 8 }l1.merge(l2); // merges l2 into l1 // l1 = { 1, 1, 2, 3, 4, 4, 6, 7, 8, 9}, l2= {}Functions Objects
• Some algorithms like sort, merge, accumulate can take a function object as argument.
• A function object is an object of a template class that has a single member function : the overloaded operator ()
• It is also possible to use user-defined functions instead of pre-defined function objects
• #include <list>#include <functional> int arr1[]= { 6, 4, 9, 1, 7 };list<int> l1(arr1, arr1+5); // initialize l1 with arr1l1.sort(greater<int>()); // uses function object greater<int>// for sorting in reverse order l1 = { 9, 7, 6, 4, 1 }Function Objects
• The accumulate algorithm accumulates data over the elements of the containing, for example computing the sum of elements
• #include <list>#include <functional> #include <numeric>int arr1[]= { 6, 4, 9, 1, 7 };list<int> l1(arr1, arr1+5); // initialize l1 with arr1int sum = accumulate(l1.begin(), l1.end() , 0, plus<int>());int sum = accumulate(l1.begin(), l1.end(),0); // equivalentint fac = accumulate(l1.begin(), l1.end() , 0, times<int>());User Defined Function Objectsclass squared _sum // user-defined function object{ public: int operator()(int n1, int n2) { return n1+n2*n2; } }; int sq = accumulate(l1.begin(), l1.end() , 0, squared_sum() );// computes the sum of squaresUser Defined Function Objectstemplate <class T>class squared _sum // user-defined function object{ public: T operator()(T n1, T n2) { return n1+n2*n2; } }; vector<complex> vc;complex sum_vc;vc.push_back(complex(2,3));vc.push_back(complex(1,5));vc.push_back(complex(-2,4));sum_vc = accumulate(vc.begin(), vc.end() , complex(0,0) , squared_sum<complex>() );// computes the sum of squares of a vector of complex numbersAssociative Containers
• In an associative container the items are not arranged in sequence, but usually as a tree structure or a hash table.
• The main advantage of associative containers is the speed of searching (binary search like in a dictionary)
• Searching is done using a key which is usually a single value like a number or string
• The value is an attribute of the objects in the container
• The STL contains two basic associative containers
• sets and multisets
• maps and multimaps
• Sets and Multisets#include <set>string names[] = {”Ole”, ”Hedvig”, ”Juan”, ”Lars”, ”Guido”}; set<string, less<string> > nameSet(names,names+5);// create a set of names in which elements are alphabetically// ordered string is the key and the object itselfnameSet.insert(”Patric”); // inserts more namesnameSet.insert(”Maria”);nameSet.erase(”Juan”); // removes an elementset<string, less<string> >::iterator iter; // set iteratorstring searchname; cin >> searchname;iter=nameSet.find(searchname); // find matching name in setif (iter == nameSet.end()) // check if iterator points to end of set cout << searchname << ” not in set!” <<endl;else cout << searchname << ” is in set!” <<endl;Set and Multisetsstring names[] = {”Ole”, ”Hedvig”, ”Juan”, ”Lars”, ”Guido”, ”Patric”, ”Maria”, ”Ann”}; set<string, less<string> > nameSet(names,names+7);set<string, less<string> >::iterator iter; // set iteratoriter=nameSet.lower_bound(”K”); // set iterator to lower start value ”K”while (iter != nameSet.upper_bound(”Q”)) cout << *iter++ << endl;// displays Lars, Maria, Ole, PatricMaps and Multimaps
• A map stores pairs <key, value> of a key object and associated value object.
• The key object contains a key that will be searched for and the value object contains additional data
• The key could be a string, for example the name of a person and the value could be a number, for example the telephone number of a person
• Maps and Multimaps#include <map>string names[]= {”Ole”, ”Hedvig”, ”Juan”, ”Lars”, ”Guido”, ”Patric”, ”Maria”, ”Ann”};int numbers[]= {75643, 83268, 97353, 87353, 19988, 76455, 77443,12221};map<string, int, less<string> > phonebook;map<string, int, less<string> >::iterator iter;for (int j=0; j<8; j++) phonebook[names[j]]=numbers[j]; // initialize map phonebookfor (iter = phonebook.begin(); iter !=phonebook.end(); iter++) cout << (*iter).first << ” : ” << (*iter).second << endl;cout << ”Lars phone number is ” << phonebook[”Lars”] << endl;Course Analysis
• Fill out the questionaire on the course webpage
• Use the comment boxes for suggestions, complaints, negative and positive aspects of the course.
• Course Analysis
• Do you think the course in general was
• Easy
• Medium
• Difficult
• What was most/least difficult
• Exam
• Seminars
• Labs
• Lectures
• Course Analysis
• Do you think the course was interesting and useful for you?
• Yes
• Partially useful
• No
• Do you think your previous knowledge (e.g. programming experience in JAVA) was sufficient for this course?
• Yes
• Somewhat
• No
• Course Analysis
• What do you think about the course literature Larman book?
• Would you recommend the book to someone else?
• Course Analysis
• What do you think about the lectures?
• Pedagogics
• Presentation
• Lecture notes, references
• Which topics did you find most/least interesting
• OO analysis and design
• Object oriented programming
• Extreme programming
• Design patterns
• UML
• C++
• Smalltalk
• Course Analysis
• What do you think of the seminars?
• Useful
• Partially useful
• Not useful at all
• Assistents
• Competent
• Partially Competent
• Incompetent
• Course Analysis
• What do you think about the style of seminars?
• Presentation by students or rather assistant
• More or fewer discussions
• More or fewer practical exercises
• Did you learn most on OOA/D by
• Attending the lectures
• Attending the seminars
• Reading the book
• Doing the labs
• Course Analysis
• What do you think about the lab hours
• Help by assistents
• Good
• Acceptable
• Unacceptable
• Availability, number of hours, waiting time
• Good
• Acceptable
• Unacceptable
• Course Analysis
• Did you feel that you got enough and competent help in general, help beside the labs, pointers to reading, hints, tips
• Good
• Acceptable
• Unacceptable
• Course Analysis
• What do you think about the lab assignments
• Difficulty
• Easy
• Suitable
• Difficult
• Interesting
• Partially interesting
• Uninteresting
• Course Analysis
• Which lab assignment did you like best/least ?
• Lab 1 class hierarchy (graphics)
• Lab 2 design patterns
• Lab 3 bank (CORBA)
• Lab 4 game playing C++
• Lab 5 Smalltalk
• Course Analysis
• How much time did you spend on the labs in total?
• Less than 60 hours
• 60-120 hours
• More than 120 hours
• What do you think about the lab redovisning?
• Fair
• Mostly fair
• Unfair
• Course Analysis
• What do you think about the exam?
• Difficulty
• Comprehensibility
• Prior information about the exam (test exam)
• Would you like to see more/less
• Practical assignments (drawing UML diagrams)
• Multiple choice questions
• Verbal questions
• Course Analysis
• What is the percentage of your study time this semester that you spend on this course?
• Less t
• Related Search
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