Data Structure数据结构 课件 第一章

1.4.1.1 Definition Algorithm is a set of finite rules which defined a sequence of operations to solve a given problem. 1.4.1.2 Characteristic Finiteness Doubtlessness Feasibility Input Output
1.3.2 Operations in Data Structure
• Insertion
• Deletion • Update/Modification • Retrieving/Search • Sorting
1.4 Algorithm and Efficiency 1.4.1 Algorithm
1.4.3 Measurement of Algorithm Analysis
1.4.3.1 Method Estimate in advance Test after the events 1.4.3.2 Guide Line Time Complexity Space Complexity 1.4.3.3 O(f(n)) if exist constant c, when n > n0, f(n) ≤ cg(n) Then T(n)= O(f(n))= O(g(n))
1.4.1.3 Description Natural Language Formalized Language Program Flow Chart
1.4.2 Algorithm Analysis

Correctness Readability Robustness Time and Space Efficiency
Data Structure
Zhuang Lei ielzhuang@
Chapter 1 Introduction
1.1 History of Data Structure 1.2 Contents of Data Structure 1.3 Basic Term and Operation
1.4 Algorithm and Efficiency
1.1 History of Data Structure
1.2 Applications of Data Structure
Examples:
Ex1: Scientific Calculation——Finite Element Method
∵Kij is a positive definite symmetric matrix ∴kij = kji then
k11 k 21 ... k n1 k12 k 22 ... kn 2 ... ... ... ... k1n k11 k2n k 21 ... ... k nn k n1 0 k 22 ... kn 2 ... ... ... ...
' 0 k11 0 0 ... ... k nn 0
0 k 22 ... 0
'
... ... ... ...
0 0 ... ' k nn
∴ only the elements on the diagonal need to store
We can model this problem with a mathematical structure known as a Graph.
Conclusion
Data Structure is a subject of studying the computer operational objects and their relationships in the non-numeric calculative program design.
} resultname ADT of process: description
Example: ADT Triplet { Data Objects: D={ e1, e2, e3 | e1, e2, e3 ∈ ElemSet } Data Relationships: R1= { < e1, e2 >, < e2, e3 > } Elementary Processes: InitTriplet ( &T, v1, v2, v3 ) result: Triplet T which elements e1, e2 and e3 assigned value v1, v2 and v3 constructed. DestroyTriplet ( &T ) condition: Triplet T exists. result: Triplet T destroyed. Get ( T, i, &e ) condition: Triplet T exists, 1 ≤ i ≤ 3.
Ex: f(n)=n2+4n+1
Then
f(n)=n2(1+4/n+1/n2)
(when n=4) =n2(1+4/4+1/42) < n2(1+1+1)
Therefore, when n > 4, f(n) < 3n2
so c=3, g(n)=n2, then O(f(n))=O(n2)
In General, O(f(n)) can be classified as 7 types
1.3 Basic Term and Operation 1.3.1 Basic conception
Data Type——all the data categories that each variable Data——the set of numbers, characters, which possessed defined in one program design language. describe the external objects, and all information which can be input into of data elements with some Data Structure——the set the computer and processed by computer programs. special relationships. Data Element——the basic unit of data; also called node, acme or record. Each data element can be consist of several Data Items (the minimal unit of Data). Data Object——the set of data elements with same attribute. It is the subset of Data and can be either finite or infie 1) Set 2) Linear list 3) Trees 4) Graphs Storage Structure 1) Sequential Storage 2) Linked Storage 3) Indexed Storage 4) Hashing Storage
P is processes in D
Definition:
ADT name {
Data objects: < definition > Data relationships: < definition > Elementary operation name ( parameter list ) Elementary operations: < definition > initial condition: description
To transform a quadratic functional equation to a group of linear equations with a positive definite symmetric coefficient matrix.
K
j 1
n
ij
X
j
i P 1, 2, ..., n i
Abstract Data Type (ADT)——a mathematic model and the set of all operations defined on it. ADT can be presented by a triplet ( D, S, P ), while
D is data objects S is set of relationship on D
1. Sorting by names with ascending/descending order. 2. Sorting by numbers with ascending/descending order.
3. Sorting by input order.
Ex3: Creating A Human Resource Document
Management School Business Administration Economy Accounting MIS Teachers 2001 2002 Technical Finance Students 2003 2004
Ex4: Traffic Light Problems on Multi-path Intersection A intersection are one way, the Roads C and Eoccurs by a watering D E hole called JoJo’s near Princeton others two way. There are 13 turns one C University, at this intersection. Some might make and it has been known to A cause some navigational difficulty, pairs of turns, like AB and EC can be B especially simultaneously, while carried outon the return trip. others, like AD and EB, cause lines of traffic to cross and therefore cannot be carried out simultaneously. The light at the intersection must permit turns in such an order that AD and EB are never permitted at the same time, while the light might permit AB and EC to be made simultaneously.