INTRODUCTION TO COMPUTER SCIENCE HANDOUT #4. THE LIST DATA MODEL K5 & K6, Computer Science Department, Vaên Lang University Second semester Feb, 2002 Instructor: Traàn Ñöùc Quang Major themes: 1. Basic Concepts 2. Stacks 3. Queues Reading: Sections 6.2, 6.6, and 6.8. 4.1 BASIC CONCEPTS Computer programs usually operate on tables of information. In most cases these tables are not simply amorphous masses of numerical values; they involve important structural relationships between the data elements. In its simplest form, a table might be a linear list of elements, when its relevant structural properties might include the answers to such questions as: Which element is first in the list? Which is last? Which elements precede and follow a given one? How many elements are in the list? In this handout, we only consider linear lists. Conceptually, a linear list (or simply list) is a finite sequence of zero or more ele- ments. We generally expect the elements of a list to be of some one type. For example, if the elements of a list are all of integers, we may call it a list of integers. Character strings are special lists. In C, a string is stored in an array ending with a null marker ’\0’. All the library functions have a test for this marker. Linked Lists A list may be implemented as a linked list of elements, each is allocated a cell or node consisting of an area for data and a pointer to the next element in the list, as shown in the following figure. See more in Section 6.4 (textbook) and Handout #1. Element 1 Element 2 Element 3 Element 4 Info1 Info2 Info3 Info4 • 24 INTRODUCTION TO COMPUTER SCIENCE: HANDOUT #4. THE LIST DATA MODEL 4.2 STACKS A stack is a special kind of lists in which all operations are performed at one end of the list, which is called the top of the list. The term "LIFO (for last-in first-out) list" is a synonym for stack. Because of this restriction, stacks have two specialized operations: push and pop where push(x) puts the element x on the top of the stack and pop removes the topmost element from the stack. The figure illustrates how to use a stack with push and pop operations to compute the value of the postfix expression 3 4 + 2 ×. The details can be explained in class. Stacks can be implemented by an array or linked list. We only discuss an array- based implementation with elements to be of type int. SYMBOL PROCESSED STACK ACTIONS Initial 3 4 + 2 × ε 3 3, 4 ε 7 7, 2 ε 14 push 3 push 4 pop 4; pop 3 compute 7 = 3 + 4 push 7 push 2 pop 2; pop 7 compute 14 = 7× 2 push 14 a 0 a 1 a n−1 . . . . . . 0 1 n − 1 MAX − 1 4.2 STACKS 25 A smart way to implement a stack by an array is to create a structure consisting of: 1. An array to hold the elements, and 2. A variable top to keep track of the top of stack. In the listing, we represent the declaration for an array-based stack of integers and its operations. You should read the listing carefully. typedef struct { int A[MAX]; int top; } STACK; BOOLEAN isEmpty(STACK *pS) { return (pS->top < 0); } BOOLEAN isFull(STACK *pS) { return (pS->top >= MAX−−1); } BOOLEAN pop(STACK *pS, int *px) { if (isEmpty(pS)) return FALSE; else { (*px) = pS->A[(pS->top)−−−−]; return TRUE; } } BOOLEAN push(int x, STACK *pS) { if (isFull(pS)) return FALSE; else { pS->A[++(pS->top)] = x; return TRUE; } } A very important application of stacks is to implement function calls. I recommend you to read this in Section 6.7 (textbook). 26 INTRODUCTION TO COMPUTER SCIENCE: HANDOUT #4. THE LIST DATA MODEL 4.3 QUEUES A queue is a restricted form of list in which elements are inserted at one end, the rear, and removed from the other end, the front. The term "FIFO (first-in first-out) list" is a synonym for queue. The intuitive idea behind a queue is a line at a cashier’s window. People enter the line at the rear and receive service once they reach the front. Unlike a stack, there is fairness to a queue; people are served in the order in which they enter the line. Thus the person who has waited the longest is the one who is served next. Like a stack, there is two specialized operations on queues: enqueue and dequeue; enqueue(x) adds x to the rear of a queue, dequeue removes the element from the front of the queue. As with stacks, an array or linked list can be used to implement queues. For our purpose, we describe a linked list implementation with the following structure for cells. As usual, elements are of type int. typedef struct CELL *LIST; struct CELL { int element; LIST next; }; A queue itself is a structure with two pointers  one to the front cell and another to the rear cell. typedef struct { LIST front, rear; } QUEUE; We also present the listing of operations of queues below. You should read it carefully to capture why those operations can work properly. BOOLEAN isEmpty(QUEUE *pQ) { return (pQ->front == NULL); } BOOLEAN isFull(QUEUE *pQ) { return FALSE; } 4.4 GLOSSARY 27 BOOLEAN dequeue(QUEUE *pQ, int *px) { if (isEmpty(pQ)) return FALSE; else { (*px) = pQ->front->element; pQ->front = pQ->front->next; return TRUE; } } BOOLEAN enqueue(int x, QUEUE *pQ) { if (isEmpty(pQ)) { pQ->front = (LIST) malloc(sizeof(struct CELL)); pQ->rear = pQ->front; } else { pQ->rear->next = (LIST) malloc(sizeof(struct CELL)); pQ->rear = pQ->rear->next; } pQ->rear->element = x; pQ->rear->next = NULL; return TRUE; } 4.4 GLOSSARY List: Danh sách. See the text. Linear list: Danh sách tuyến tính. Linked List: Danh sách liên kết. A physical data structure used to implement high- level data structures such as lists, trees, graphs, etc. The counterpart of linked lists is arrays. Relationship: Mối liên hệ, quan hệ. In computer terminology, relationship informally stands for relation with a little difference. Character string, string: Chuỗi ký tự, xâu ký tự. See the text. Stack: Chồng xếp, ngăn xếp. top: Đỉnh (chồng xếp). 28 INTRODUCTION TO COMPUTER SCIENCE: HANDOUT #4. THE LIST DATA MODEL push: Đẩy (vào chồng xếp). pop: Nhặt, lấy (ra khỏi chồng xếp). Postfix expression: Biểu thức hậu vò. An expression in which operators are between their operands. Declaration: Khai báo. A statement introducing a name or identifier into a program. In C, every identifier must be declared before use. Call: Lời gọi. A statement with the name of a function, and perhaps a list of actual parameters to tranfer control to that function. Also function call or procedure call. Queue: Hàng đợi. See the text. front: đầu hàng. rear: cuối hàng. enqueue: vào hàng. dequeue: rời hàng. . pQ->front; } else { pQ->rear->next = (LIST) malloc(sizeof(struct CELL)); pQ->rear = pQ->rear->next; } pQ->rear->element = x; pQ->rear->next = NULL; return TRUE; } 4. 4 GLOSSARY List:. INTRODUCTION TO COMPUTER SCIENCE HANDOUT #4. THE LIST DATA MODEL K5 & K6, Computer Science Department, Vaên Lang University Second semester Feb, 2002 Instructor: Traàn Ñöùc. application of stacks is to implement function calls. I recommend you to read this in Section 6.7 (textbook). 26 INTRODUCTION TO COMPUTER SCIENCE: HANDOUT #4. THE LIST DATA MODEL 4. 3 QUEUES A queue