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Data Structure

Learn about data abstraction, pointers, customized data types, and abstract data types. Understand how to model data and use arrays and lists effectively.

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Data Structure

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  1. Data Structure 10/23/2019 Che-Rung Lee CS135601 Introduction to Information Engineering

  2. Data abstraction • Main memory is organized as a sequence of addressable cells, but the data we want to model is usually not. • Use “model” and “simulation” CS135601 Introduction to Information Engineering

  3. Pointers • What is a pointer? • A special data that records memory address • Example in C int a = 3; int*p = NULL; p = &a; *p = 5; 3 5 0 0x03 CS135601 Introduction to Information Engineering

  4. Outline • Customized data type • Array and list • Stack and queue • Trees • Hash table CS135601 Introduction to Information Engineering

  5. Customized Data Type CS135601 Introduction to Information Engineering

  6. How to model a warrior? • Class • Skills • Equipments • Life point • Magic point • Money • … Diablo III But computers only have primitive data types: integer, real, character, and Boolean. CS135601 Introduction to Information Engineering

  7. User-defined data type An instance of type Warrior User-defined data types • Conglomerate of primitive data types collected under a single name • Example in C: struct typedefstruct { char class[10]; // Barbarian, Witch, Wizard or Monk int lifePoint; // min is 0, max is 100 int level; // min is 1, max is 72 … } Warrior; Warrior player1; player1.lifePoint = 100; CS135601 Introduction to Information Engineering

  8. Abstract data type • A full model of abstract data type should include the operations of the model • Like +-*/, input, output for primitive data types • Example in C++: class • This is called an object, which we will talk more in the programming language lesson. class Warrior { char class[10]; // Barbarian, Witch, Wizard or Monk … void fight(….); // function that defines the action “fight” }; CS135601 Introduction to Information Engineering

  9. Heterogeneous array • The storage that contains different types of data is called a heterogeneous array • struct and class are heterogeneous arrays • The items are called components. • The storage that contains the same type of data is called a homogeneous array • Example struct { char Name[25]; int Age; int SkillRating;} Employee; CS135601 Introduction to Information Engineering

  10. pointers Meredith W Linsmeyer 23 6.2 Storage of heterogeneous array • Static method: • components are stored one after the other in a contiguous block • Dynamic method: • components are stored in separate locations identified by pointers CS135601 Introduction to Information Engineering

  11. Array and List CS135601 Introduction to Information Engineering

  12. When to use arrays? • Stock prices, student names, temperature readings • One dimensional array • Matrix, images, the grades of class, train schedule • Two dimensional array • Computed Tomography(斷層掃描) • Three dimensional array CS135601 Introduction to Information Engineering

  13. Relative addresscalled “index” 0 1 In C, the indexstarts from 0 2 3 Storing arrays • Use a variable to denote the address of the first element • Ex: int Readings[24]; CS135601 Introduction to Information Engineering

  14. Two dimensional array • Two dimensional array is stored in a one dimensional memory cells. • Two ways to order the data • What is the memory location of A[2][3] in the row (column) major order? column Row major order row Column major order CS135601 Introduction to Information Engineering

  15. High dimensional array • Consider the dimensional array A[m][n][k] • What is the size of the array? • What is the memory location of A[1][2][3] in the row major order? • The row major order • What is the memory location of A[1][2][3] in the column major order? • The row major order This changes first This changes first CS135601 Introduction to Information Engineering

  16. When to use list? • List is a collection of data which are arranged sequentially. • One dimensional array is a list of elements • Two dimensional array can be viewed as a list of rows/columns • A string is a list of characters • Music is a list of sounds • Stacks and queues can be implemented using lists • We will talk those later CS135601 Introduction to Information Engineering

  17. Contiguous list • List is stored in a contiguous block of memory cells (an array) • Ex: list of names. Each name is occupied 8 bytes. CS135601 Introduction to Information Engineering

  18. Use customized data type to define Linked list • List in which each entries are linked by pointers • Head pointer: Pointer to first entry in list • NIL pointer: A “non-pointer” value used to indicate end of list CS135601 Introduction to Information Engineering

  19. Static v.s. dynamic data structures • Static data structures: • Size and shape does not change • Contiguous list • Easily to locate elements. No need to store address. • Dynamic data structures: • Size and shape can change • Linked list • Easily to delete/insert elements CS135601 Introduction to Information Engineering

  20. Linked list: delete/insert element • Delete • Insert CS135601 Introduction to Information Engineering

  21. Stack and Queue CS135601 Introduction to Information Engineering

  22. top bottom What is a stack? • A list in which entries are removed and inserted only at the head • Top: The head of stack • Bottom or base: The tail of stack • Push: To insert an entry at the top • Pop: To remove the entry at the top • LIFO: Last-in-first-out CS135601 Introduction to Information Engineering

  23. When to use stacks? • When the algorithm needs data LIFO? • EX1: reverse a word, ABCCBA • Push A • Push B • Push C • EX2: check matching parentheses (3*[(1+1)*2] • Push “(“ • Push “[“ • Push “(“ • Pop C • Pop B • Pop A A B C • Find “)”, pop “(“, matched • Find “]”, pop “[“, matched • No more “)”, but still one “(“ in stack, not matched CS135601 Introduction to Information Engineering

  24. Stack implementation • Using a list + a pointer (head) CS135601 Introduction to Information Engineering

  25. Tail Head Queue • A list in which entries are removed at the head and are inserted at the tail. • Enqueue: insert an entry at the tail • Dequeue: remove an entry at the head • FIFO: First-in-first-out CS135601 Introduction to Information Engineering

  26. Examples of using queues • Ex1: the job queues in operating system • Ex2: simulation of the Josephus problem • Dequeue 1 • Enqueue 1 • Dequeue 2 • Dequeue 3 • Enqueue 3 6 5 4 3 2 1 Operation counts  2n CS135601 Introduction to Information Engineering

  27. Head pointer Queue implementation • A list + 2 pointers (head+tail) • Enqueue A, B, C • Dequeue A, enqueue D • Dequeue B, enqueue E • If using a static list, the queue crawls throughmemory as entities are inserted and removed. A Tail pointer B C D E CS135601 Introduction to Information Engineering

  28. Circular queue • A technique that uses a fixed region of memory space to implement queue. A head E tail B C D • Enqueue A, B, C • Dequeue A, Enqueue D • Dequeue B, Enqueue E CS135601 Introduction to Information Engineering

  29. Trees CS135601 Introduction to Information Engineering

  30. What is a tree? • A collection of nodes that are linked in a hierarchical structure, in which every node is linked by one parent, except the root. • Node: An entry in a tree • Parent: The node immediately above a specified node • Root: The node at the top • Terminal or leafnode:A node at the bottom CS135601 Introduction to Information Engineering

  31. Hierarchical relations • Parent: The node immediately above a node • The parent of F is B • Child: A node immediately below a node • The children of C are G and H. • Ancestor: Parent, parent of parent, etc. • The ancestor of K are F, B, and A. • Descendent: Child, child of child, etc. • The descendent of B are E, F, K, and L. • Siblings: Nodes sharing a common parent • The siblings of C are B and D. A B C D E F G H I J K L CS135601 Introduction to Information Engineering

  32. Depth and height • Textbook’s definition • The depth of a tree is the longest path from the root to a leaf node • The length of a path is the number of nodes on the path • Ex: the depth of the tree is 4 • Conventional definition • Use the word “height” instead of depth • The length of a path is the number of links on the path • Ex: The height of the tree is 3 (= 4 – 1) A B C D E F G H I J K L CS135601 Introduction to Information Engineering

  33. What are trees used for? • Representing hierarchical data • Organization chart • Searching data • Game tree CS135601 Introduction to Information Engineering

  34. Binary tree • A tree in which each parent has at most two children Left subtree Right subtree Left child Right child CS135601 Introduction to Information Engineering

  35. Storing a binary tree in a list • This is called a heap in some applications. CS135601 Introduction to Information Engineering

  36. Advantages of using heap • Easily to find the index of parent & children • Parent(B) = [index of B] / 2 = 1 • LeftChild(B) = [index of B]*2 = 4 • RightChild(B) = [index of B]*2 + 1= 5 CS135601 Introduction to Information Engineering

  37. Problems for heap • Heap is inefficient for storing the binary tree that is sparse and unbalanced • Sparse: most node has one or zero child • Unbalanced: the right subtree is much larger than the left subtree, or vice versa CS135601 Introduction to Information Engineering

  38. Storing a binary tree using pointers • Each node Use customized data type to define CS135601 Introduction to Information Engineering

  39. Recursive structure • Tree is a recursive structure • The subtrees of a tree are trees • The recursive algorithms for a binary tree may look like this • It is a depth first, in order algorithm for tree procedure some_operation (root)if (root is not NULL) then ( call some_operation(root.left_child) do some operations on root call some_operation(root.right_child)) CS135601 Introduction to Information Engineering

  40. Hash Table CS135601 Introduction to Information Engineering

  41. Search • Search is a common task in daily life • Phone book: given a name, fine the phone number • Dictionary: given a word, find it’s definition • Map: given an address, find the location or route • DNS: given an URL, find it’s IP address • Tree can be used to speedup searches. • How? And what is the operation count? CS135601 Introduction to Information Engineering

  42. Constant time search • Something can be found in constant time • EX: What is fifth element of the array A? A[4] • An array is like a lookup table. One can use the index to query and get the value • Can we use this idea to organize data so that searches can be done in the constant time? • Hash table (or hash map) CS135601 Introduction to Information Engineering

  43. Hash table • Each record of data has a key field • Key is like the index of an array. • An unique identification of the data (ideally) • The storage space is divided into buckets • Each bucket is like an array cell. • Each record is stored in the bucket corresponding to its key, so it can be retrieved in constant time CS135601 Introduction to Information Engineering

  44. We do not want to create such a large array!! How to define the mapping? • Unique identification of a record is usually too large to be the index for storage • For example, the ASCII code for a string CS135601 Introduction to Information Engineering

  45. Hash function • A hash function computes a bucket number for each key value • EX: suppose there are only 41 buckets. CS135601 Introduction to Information Engineering

  46. Problem • Collision: The case of two or more keys hashing to the same bucket • Major problem when table is over 75% full CS135601 Introduction to Information Engineering

  47. Solutions • Use linked lists to store collided data • The search time becomes linear to the number of collided data • Increase the number of buckets and rehash all data • Time/space tradeoff • Design a better hash function/algorithm • It’s a research problem CS135601 Introduction to Information Engineering

  48. References • Textbook 8.1, 8.2, 8.3, 8.5, 9.5 • Wikipedia • Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, “Introduction to Algorithms” • 資料結構，演算法，程式語言 Related courses CS135601 Introduction to Information Engineering

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