Lecture 2. Binary Trees & Implementations. Yusuf Pisan

Transcription

1 CSS 343 Data Structures, Algorithms, and Discrete Math II Lecture 2 Binary Trees & Implementations Yusuf Pisan

2 Overview 1. Huffman Coding and Arithmetic Expressions Topics a. Pointers & References b. Templates c. Algorithm Complexity (later) d. Recursion (later) 3. Ass-1 a. Dynamically allocating arrays b. Overloaded operator signatures c. Efficiency 4. Trees - Implementation 2

3 Huffman Coding Exercise Top letters by frequency in English: d:4, r:6, s:6, h:6, i:7, n:7, a:8, t:9, o:8, e:13, ddddrrrrrrsssssshhhhhhiiiiiiiaaaaaaaatttttttttooooooooeeeeeeeeeeeee Create the Huffman encoding Encode `stained` How many bits is it?

4 Call by Value, Reference, const Reference struct Rectangle { int length; int width; }; // int Area(Rectangle rect) - value rect is copied // int Area(Rectangle &rect) - reference, we can change the value // int Area(const Rectangle &rect) - const reference, cannot change it { int temp; temp = rect. length; rect.length = 35; return (temp * rect. width); } void TestRectangle() { int result; Rectangle r = {3, 3}; result = Area(r); std::cout << "length = " << r.length << std::endl; std::cout << "width = " << r.width << std::endl; std::cout << "Area = " << result << std::endl; }

5 // by value void swap(std::string a, std::string b) { std::string tmp = a; a = b; b = tmp; } // by reference void swap(std::string& a, std::string& b) { std::string tmp = a; a = b; b = tmp; } // by const reference void swap(const std::string& a, const std::string& b) { std::string tmp = a; a = b; b = tmp; }

6 findmax - which version is appropriate int findmax(vector< int> a) int findmax(vector< int> &a) int findmax(const vector<int> &a) { } int max = a[0]; int i; for (i = 1; i < a.size(); i++) if (a[i] > max) max = a[i]; return max;

7 Templates void displayit(int i) { cout << "[" << i << "]" << endl; } void displayit(string str) { cout << "[" << str << "]" << endl; } void displayit(rectangle rect) { cout << "[" << rect << "]" << endl; } template<typename T> void displayit(t i) { } cout << "[" << i << "]" << endl; // also template<class ItemType>

8 Templates - class template<class ItemType> class Box { public: Box(const ItemType& theitem); private: ItemType item; }; // in cpp template<class ItemType> Box<ItemType>::Box(const ItemType& theitem) : item{theitem} { }... Box<string> bs("hello"); // on stack Box<string> *bs = new Box<string>("hello"); // on heap

9 Templates Compiler uses the templates to generate the necessary classes or functions Normally,.cpp files are compiled to get object files, which are later linked to get an executable BUT, a template file for a cpp is not fully defined, so cannot be compiled to an object file Solutions: 1. Put definition and implementation in.h file 2. Get.h file to include.cpp file AND tell IDE not to compile the.cpp file (using #include at the end of.h file)

10 Pointers void testpointer() { int i = 10; // iptr is a integer pointer, // iptr has the memory address for i int *iptr = &i; // defining jptr as a integer pointer int *jptr; // assigning jptr to address of i jptr = &i; int *kptr; // kptr and jptr are both integer pointers kptr = jptr; assert(*iptr == i && *kptr == i); assert(iptr == jptr); *iptr = 20; assert(*iptr == i && iptr == jptr && *jptr == i); } 10

11 Pointers void testpointer2() { // i is a Square object on the Stack Square i; // iptr is a pointer to a Square on the Heap Square *iptr = new Square(); // defining jptr as a pointer Square *jptr; // assigning jptr to address of i jptr = &i; Square *kptr; kptr = iptr; } delete iptr; 11

12 Pointers // a box object on the heap Box<string> *bs = new Box<string>("hello"); delete bs; // an integer array to hold 200 integers int *ax = new int[200]; delete[] ax; // only if Box allows empty constructor Box<int> *arrayofboxes = new Box<int>[10]; arrayofboxes[0].item = 25; delete[] arrayofboxes; 12

13 Pointers Box<int> **arrayofboxpointers = new Box<int> *[10]; // not valid, array is full of pointers not objects // arrayofboxpointers[0]->item = 25; arrayofboxpointers[0] = new Box<int>(45); delete arrayofboxpointers[0]; delete[] arrayofboxpointers; int q = 25; changeme(&q); Box<int> *b = new Box<int>(25); changebox(b); cout << "box is" << b->item << endl; cout << "box is" << (*b).item << endl; void changeme(int *p) { *p = 100;} void changebox(box<int> *p) { p->item = 100; } 13

14 1. const int MAX = 100; const MAX is a constant. You cannot change it. 2. Account::displayBalance(const Account &acc) acc is passed as a constant reference, so no copy is created displaybalance can access acc, but not modify it 3. int Account::getBalance() const getbalance is not allowed to make any changes to the object (cannot modify this or any member variables) 4. const string& getnamebyreference(); Rare - returning a string by reference so it is not copied, but make sure the caller cannot change it

15 Overloading * member function class Rational { public: // Op Overloads?1 operator*(?2)?3;

16 Overloading +,-,*,/ as member functions class Rational { public: // Op Overloads Rational operator*(const Rational &rat) const; Rational operator/(const Rational &rat) const; Rational operator-(const Rational &rat) const; Rational operator+(const Rational &rat) const; operator* and others create a new object that is returned by value

17 Overloading *= member function class Rational { public: // Op Overloads?1 operator*=(?2)?3;

18 Overloading +=,-=,*=,/= as member functions Rational& operator*=(const Rational &rat); Rational& operator/=(const Rational &rat); Rational& operator-=(const Rational &rat); Rational& operator+=(const Rational &rat); operator*= and others modify the existing object and return a reference to that object Valid Statement: r4 = r1 + (r1 += r2);

19 Overloading +=,-=,*=,/= as non-member functions friend Rational operator+(const Rational &rat1, const Rational &rat2);

20 Overloading == and!= bool operator==(const Rational &rat) const; bool operator!=(const Rational &rat) const; Same approach for >, <, >=, and others

21 Overloading input/output <<, >> class Rational { public: friend ostream& operator<<(ostream &outstream, const Rational &rat); friend istream& operator>>(istream &instream, Rational &rat); Rational class and other sample code at

22 Constructors / Destructors class Rational { public: // 0 param constructor?1 Rational(); // 2 param constructor?2 Rational(int, int); // 1 param constructor?3 Rational(int numerator); // 2 optional params constructor?4 Rational(int numerator = 0, int denominator = 1); // copy constructor?5 Rational(?6); // destructor?7 ~Rational(?8);

23 class Rational { public:?1 operator=(?2)?3; Assignment operator= Must check for self assignment We do not cover move operator or increment/decrement operator

24 class Rational { public:?1 getnumerator(?2)?3;?4 setnumerator(?5)?6; accessor functions

25 TurtleProgram Remember to use compiler flags -Wall -Wextra -Wpedantic -Weffc++ and even -Werror Remember to dynamically allocate the array to be just the right size (not string[100])

26 Binary Search Tree - Definition Search Left child value less than parent Right child value greater than parent Assume no duplicates Inserting items from a sorted list? search(bst, target) if (BST is empy) item not found else if target == data in BST item found else if target < data search(left subtree, target) else search(right subtree, target)

27 Linked Nodes vs Array New node goes to the free index All free indexes connected by rightchild

28 Class Exercise 1. Create a balanced BST using A, B, C, D, E, F, G, H, I Is it a complete? Is it full? What is the order of insertions? 2. How would you make an exact copy of a tree? Write out the pseudocode 3. How do you add a new element to a tree, so the tree remains balanced (not a BST, nodes can go anywhere)?

29 Copy Constructor

30 void printit(string s) { cout << "[" << s << "]"; } Functions as Parameters void searchfunction(void visitor(string str), const vector<string>& vs) { for (int i = 0; i < vs.size(); ++i) { visitor(vs[i]); } } void testfunctionasparameter() { vector<string> v{"3", "5", "7"}; searchfunction(printit, v); }

31 inorder Traversal Can we have visit(treeptr->getitem)?

32 Remove an Item from BST 1. N is a leaf - easy, set parent to nullptr 2. N has one child - ok, promote child to N s position 3. N has two children - difficult For Case 3, we need a different strategy. Pick another node M to remove. Copy the item in M to N s location, therefore deleting the item at N. Remove the node M How can we choose M so we preserve the BST properties?

33 Remove an Item from BST (2) Move the inorder successor of n node with the smallest value that has a value larger than n

34 Removing Nodes Start with original tree for each exercise 1. Remove 50, Remove Remove Remove 60

35 BST to an Array Save the BST using inorder traversal, we get a sorted list of items, smallest to largest. Reading it back, we want the middle item to be the root, so If n is odd, read n/2 items as left subtree, read root, read n/2 items as right subtree. If n is even, one subtree needs to have one extra element.

36 Tree Sort Put all elements from an array into a tree and then do inorder traversal to get all items in order. What is the complexity for average and worst cases?

37 Before Next Class Keep working on Ass-1 Test using valgrind, cpplint and cppcheck in CSS Linux Labs Test using given file AND your own test file Carrano 16 Tree Implementation Quiz - Monday, Oct 8 Carrano 17 Heaps Quiz - Monday, Oct 15