重庆大学数据结构英文课件Graph_02

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数据结构 (2).ppt

INSERT(L,x,i)
DELETE(L,i)
2020/5/10
数据结构
22
顺序表的特点：用物理位置上的邻接关系表示结点间的逻辑关系
顺序表的优点：（1）无须增加额外的存储空间表示结点间的逻辑关系。
（2）可以方便地随机存取表中任一结点。
顺序表的缺点：（1）插入和删除运算不方便，通常须移动大量结点，效率较低。（2）难以进行连续的存储空间的预分配，尤其是当表变化较大时。
数据结构
15
第一章概论
本章要求:
1、掌握数据、数据元素、数据结构等基本概念。 2、掌握数据逻辑结构和物理结构的分类。 3、学会算法分析的基本方法。
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数据结构
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第二章线性表
本章要学习的主要内容 1、线性表的逻辑结构及基本运算 2、线性表的顺序存储结构 3、线性表的链式存储结构：单链表、循环链表、双链表、静态链表 4、顺序表和链表的比较
2.数据元素(Data Element): 数据的基本单位, 即数据集合中的一个个体。也称元素、结点、顶点、记录
数据元素由数据项(data item)组成
数据项:是具有独立含义的最小标识单位关键字（key)：唯一能识别一个数据元素的数据项。
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数据结构
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3、数据类型(Data Type): 是具有相同性质的计算机数据的集合及在这个
顺序表是一种随机存取结构
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数据结构
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4、顺序表的描述：
typedef int datetype; #define maxsize 1024 typedef struct { datatype data[maxsize];

图(Graph)是一种比线性表和树更为复杂的数据结构在图形....ppt

网的邻接矩阵：
A[i][
j]
w i,j
若 vi ,v j 或(vi ,v j ) VR 反之
第七章
25
构造无向网的算法：
Status CreateUDN (MGraph &G){ //采用数组表示法(邻接矩阵) ，构造无向网G。
sacnf(&G,vexnum, &G.arcnum, &IncInfo); //IncInfo为0则各弧不含其它信息
例如:G1 = (V1, {R1})
其中：
A
V1={A, B, C, D, E}
R1={<A,B>, <A,E>,
B
E <B,C>, <C,D>, <D, A>,
<D, B >, <E,C> }
C
D
第七章
9
无向图
若<v, w>VR 必有<w, v>VR, 则称顶点 v 和顶点 w 之间存在一条边(v,w) 。
生成树生成树第七章2072图的存储结构72图的存储结构一数组表示法邻接矩阵二邻接表存储表示三有向图的十字链表存储表示四无向图的邻接多重表存储表示第七章21用两个数组分别存储数据元素顶点的信息和数据元素之间的关系边或弧的信息
第七章图
图(Graph)是一种比线性表和树更为复杂的数据结构。在图形结构中，结点之间的关系可以是任意的，图中任意两个数据元素之间都可能相关。在人工智能、工程、数学、物理、化学、生物和计算机科学等领域中，图结构有着广泛的应用。
//若弧含有相关信息，则输入 iGf .(aIrnccsI[i{nnj]ft[oiL)]=oIGncifapn.otaurtertVic(;(ise=*[xiG0(];M[.ija<]Gr；Gcrs.av[ipe]x[hjn]G.uinm,cfh;oia)+；r+u) )

数据结构样卷2(英文)

重庆大学数据结构课程样卷2开课学院：计算机学院课程号： 18001035 考试日期：考试方式：考试时间： 120 分钟一． Single choice1． The linear list (a1, a2, ... an), which is in Sequential Storage , whenwe delete any node, the average number of moving nodes ( ). A. n B. n/2 C. (n-1)/2 D. (n+1)/2 2． Which is wrong among the following statements ( ).A. Data element is the basic unit of the dataB. Data element is the smallest unit of the dataC. Data can be composed of a number of data elementsD. Data items can be composed of a number of data elements3． To insert a data element in a linear structure data conveniently, thebest data structure is ( ).A. Sequential storageB. Linked storageC.Index storageD. Hash storage4． If insert a new node into the doubly linked list which the number ofnodes is n, the measurement level of time complexity is ( ).A.O(1)B. O(n)C. O(nlog 2n)D. O(n 2)5． In virtue of a child’s Brother linked lists as a tree, if we want tofind the fifth child of the node x, as long as finding the first child of x, and then ( ).A. pointer scans 5 nodes continuously from the child domainB. pointer scans 4 nodes continously from the child domainC. pointer scans 5 nodes continously from the brother domainD. pointer scans 4 nodes continously from the brother domain 6． The character of Tree structure is: a node can have( )A. More than one direct pre-trendB. More than one direct successorsC. More than one pre-trendD. A successor7． Assume that there are 13 numbers, they form a Huffman tree, calculatethe number of nodes on this Huffman tree ( ). A. 13 B. 12 C. 26 D. 258． A spanning tree of the undirected connected graph is a ( ) whichcontains the whole vertices of this connected graph.A. Minimal connected subgraphB. Minimal subgraphC. Significantly connected sub-graphD. Significantly sub-graph 9． Which is wrong in the following statements ( ).A. Each vertex is only visited once during the graph traversal.B. There are two methods, Depth-First Search and Breadth-First Search,to traverse a graph.C. Depth-First Search of a graph isn ’t fit to a directed graphD. Depth-first search of a graph is a recursive process10． In sequential search algorithm of static table, if we set up a sentryat the head of a list, the right way to find the element is ( ) A. Looking for the data element from the first element to the back B. Looking for the data element from the second element to the back C. Looking for the data element from the (n+1)th element to the front D. I t is nothing to do with the search for order11． In order to find the number 85 in an ordered list(18,20,25,34,48,62,74,85), how many times do we need to compare( ) A.Once B. Twice C. 3 times D. 4 times12． Assume that the length of Hash table is m=14, Hash function H(key) =key % 11. There have been 4 nodes in the table, and their addresses are: 4,5,6,7. Other addresses are NULL. In virtue of quadratic probing re-hash to deal with conflict, calculate the address of node whose keyword is 9 ( ).A. 8B. 3C. 5D. 913． Using Quicksort to sort the following four sequences, and choose the命题人：组题人：审题人：命题时间：教务处制学院专业、班年级学号姓名公平竞争、诚实守信、严肃考纪、拒绝作弊封线密first element as the benchmark to divide. During the first division,in the following sequences which need to move the most times ( )A.70,75,82,90,23,16,10,68B.70,75,68,23,10,16,90,82C.82,75,70,16,10,90,68,23D.23,10,16,70,82,75,68,9014．There are 10000 elements in a sequence, the best way to get the very smallest 10 elements in the sequence is ( ).A. QuicksortB. HeapsortC. Insertion sortD. Merge sort15．If the sequence is almost in order, take compare times of key code and move times of key code into account, the best way to sort is( )A. Merge sortB. Insertion sortC. Straight selection sortD.Quicksort二．Fill the blanks1．In order to insert a new node s after the node which pointer q points to in a circular doubly linked list, we need to execute the followingstatements:s->prior=q; s->next=q->next; _____________________;q->next=s;2．In the doubly linked list, if d is a pointer points to a node in the list, then:d->next->__________=d->prior->__________=__________;3．Stack can be considered as an operation restricted linked list ,one end that can insert and remove is called _____________。

数据结构课件第2章

SqStack S; ElemType e;
InitStack_Sq(S, 10, 5); // 栈S的初始容量为10
while(N!=0) {
Push_Sq(S, N%8); // 将N除以8的余数入栈
N /= 8;
// N取值为其除以8的商
}
while(FALSE==StackEmpty_Sq(S)) {
括号匹配
int i = 0; ElemType e; SqStack S; InitStack_Sq(S, n, 5);
Status Matching(char *exp, int n)
while(i<n) { switch(exp[i]) {
当读入完所有括号时，检查栈：
case '(': case '[': Push_Sq(S, exp[i]); i++;
本章主要内容
2.1 典型线性数据结构 2.2 顺序栈 2.3 循环队列 2.4 顺序表 2.5 链栈与链队列 2.6 线性表的链式表示与实现 2.7 线性表两种存储结构的比较
2.1典型的线性结构
栈(stack)：只允许在序列末端进行操作的线性结构；
队列(queue)：只允许在序列两端进行操作的线性结构；
样式：数据指针
或指针数据指针
数据域：存储元素数值数据
指针域：存储直接后继或者直接前驱的存储位置
1.7.3节的链表存储结构
链式存储
线性结构的链式存储表示
a1
a2
…
an ∧
栈、队列和线性表的链式存储表示
链栈链队列单链表、双向链表、循环链表、双向循环链表
2.2 栈的顺序表示和实现

数据结构英文教程

数据结构英文教程Data structures are an essential concept in computer science. 数据结构在计算机科学中是一个基本概念。

They are used to organize, store, and manipulate data efficiently. 它们用于高效地组织、存储和操作数据。

By understanding different data structures, programmers can optimize their algorithms and improve the performance of their applications. 通过了解不同的数据结构，程序员可以优化他们的算法，并提高他们应用程序的性能。

There are various types of data structures, such as arrays, linked lists, stacks, queues, trees, and graphs. 有各种各样的数据结构，比如数组、链表、栈、队列、树和图。

Each type has its own strengths and weaknesses, making them suitable for different tasks. 每种类型都有其优点和缺点，使它们适用于不同的任务。

One of the most basic data structures is an array. Arrays are used to store a collection of elements of the same data type in contiguous memory locations. 一个最基本的数据结构是数组。

数组用于在连续内存位置中存储相同数据类型的元素的集合。

They provide fast access to elements based on their index and are suitable for tasks that require random access to elements. 它们根据索引快速访问元素，适用于需要对元素进行随机访问的任务。

【重庆大学本科四门专业课PPT】组成原理3.Arithmetic+for+Computers

sign extend – addi, addiu, slti, sltiu zero extend – andi, ori, xori overflow detection – add, addi, sub
3.1 Introduction
Computer words are composed of bits; thus words can be represented as binary numbers.
Binary, Decimal, and Hexadecimal Equivalents
Converting Binary to Hexadecimal
❖ Each hexadecimal digit corresponds to 4 binary bits ❖ Example:
Convert the 32-bit binary number to hexadecimal 1110 1011 0001 0110 1010 0111 1001 0100 ❖ Solution:
Unsigned and signed integersMost
Characters
Significant Bit
Least Significant Bit
Floating-point numbers Images, sound, etc.
76 543 210 10011101
27 26 25 24 23 22 21 20
Each bit represents a power of 2 Every binary number is a sum of powers of 2 Decimal Value = (dn-1 2n-1) + ... + (d1 21) + (d0 20) Binary (10011101)2 = 27 + 24 + 23 + 22 + 1 = 157

20_Graph_03

Example
Data Structure
Graph_03
All-Pairs Shortest Paths

The problem of finding the shortest distance between all pairs of vertices in the graph called all-pairs shortest paths. Using the above shortest path algorithm, we can find the shortest path between all pairs of vertices, vi and vj, i≠j.

In applications, the weight may be a measure of the length of a route, the capacity of a line, the energy required to move between locations along a route, etc.
0 1 2 3
6 8 5 4 1 9
3
0 1 11 0 D(3) 3 4 9 10
Data Structure
9 3 8 2 0 6 6 0
3
0 1 2 3 0
2
1
Graph_03
Floyd’s Algorithm

Define a two-dimension array path[][] to record all shortest paths. If path[i][j]=k, the shortest path from vertex i to vertex j go through vertex k. that is, the shortest path from vertex i to vertex j is (i,..,k,..j). It is evident that (i,…,k) and (k,…,j) are the shortest path from i to k and k to j. We can output all shortest paths using path[][]

数据结构课件CHAPTER2

a1
a2
a3
a4
a5
a6
直接前驱和直接后继描述了结点之间的逻辑关系（即邻接关系）
Department of Computer Science & Technology, Nanjing university fall
线性表的抽象基类 template <class T, class E> class LinearList { public: LinearList(); //构造函数 //析构函数〜～LinearList(); virtual int Size() const = 0; //求表最大大体积 virtual int Length() const = 0; //求表⻓长度 virtual int Search(T x) const = 0; //搜索 virtual int Locate(int i) const = 0; //定位 virtual E* getData(int i) const = 0; //取值 virtual void setData(int i, E x) = 0; //赋值
Nanjing university
fall
删除的主要思想： (1) 在顺序表中查找x,如果x在表中不存在，则不能删除；
Data Structures
(2)如果x在表中存在，设x在顺序表中的位置为i; (3) 将顺序表的最后位置减1； (4)把顺序表中原来第i+1至第n-1个表项依次向前移动一个表项位置
Department of Computer Science & Technology, Nanjing university fall
Data Structures

数据结构Chap8 graph

need two vertices.
To identify a arc
need both source and destination vertices.
Find Vertex
Retrieve vertex traverses a graph looking for a specified vertex.
8-4-1 Adjacency Matrix 8-4-2 Adjacency List
8-5 graph algorithms 8-6 Graph ADT 8-7 networks
8-7-1 minimum spanning tree 8-7-2 shortest path algorithm
8-1 terminology
If the vertex is found, its data are returned. If it is not found, an error is indicated.
Data Structures and Algorithms
Chapter 8: Graphs
College of Electronic and Information Engineering Chongqing University of Science and Technology
Instructor: Xiong Qian
More Graph Concepts
Two vertices are adjacent if an edge directly connects them
A path is a sequence of adjacent vertices A cycle is a path that starts and ends with

【重庆大学本科四门专业课PPT】数据结构linear list_02

next->element; // Remember value
Link<E>* ltemp = curr->next; // Remember link node
if (tail == curr->next) tail = curr; // Reset tail
curr->next = curr->next->next; // Remove from list
template <typename E> class LList: public List<E> {
private:
Link<E>* head; // Pointer to list header
Link<E>* tail; // Pointer to last element
Link<E>* curr; // Access to current element
Link(const E& elemval, Link* nextval =NULL)
{ element = elemval; next = nextval; }
Link(Link* nextval =NULL) { next = nextval; }
};
node
Element next
Data Structure
Insertion
Inserting a new element is a three-step process: First, the new list node is created and the new
element is stored into it. Second, the next ﬁeld of the new list node is

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1
Weighted Graphs
In a weighted graph, each edge has an associated weight or cost. 20 Clinton Kingston Bainbridge
60 30 35
Mukilteo
Edmonds Seattle
Bremerton
Strongly connected(directed graph)--- if, for every pair of
Data Structure
05 Graph
Connectivity

the undirected graph obtained by suppressing the directions on the edges of G is connected.
05 Graph
Data Structure
Data Structure
05 Graph
Connectivity

Acycle –a graph without cycles. directed acycle graph(DAG)--a directed graph without cycles. free tree—a connected, undirected graph with cycles. spanning tree—a subgraph of undirected graph G, which is
Data Structure
05 Graph (2)
College of Computer Science, CQU
Outline

Simple Path Connectivity Graph Traversals Topological Sorting
Data Structure
05 Graph
Data Structure
05 Graph
Depth-First Search (DFS)
Assume a particular node has been designated as the starting point. Let A be the last node visited and suppose A has neighbors N1,N2,…,Nk.
2 2 2
2.5
Salt Lake City
2.5
2.5
length(p) = 5 cost(p) = 11.5
San Francisco
Data Structure
3
Dallas
p = {SEA, SLC, CHI, DAL, SFO, SEA}
05 Graph
Simple Paths and Cycles
A C E G I J
05 Graph
D
F H
Data Structure
Directed Acyclic Graphs (DAGs)

DAGs are directed graphs with no cycles Trees DAGs Graphs main()

mult() add()

Graph traversals begin with start vertex, and attempt to visit remaining vertices. There are two problems: If the graph is not connected, it may not be possible to reach all vertices. The graph may contains cycles, and a vertex may be reached more than one times.

A cycle is a path that starts and ends at the same node:

p = {Seattle, Salt Lake City, Dallas, San Francisco, Seattle}
A simple cycle is a cycle that repeats no vertices except that the first vertex is also the last (in undirected graphs, no edge can be repeated)

A depth-first search will: visit N1,then Proceed to traverse all the unvisited neighbors of N1 , then proceed to traverse the remaining neighbors of A in similar fashion
Data Structure 05 Graph
Paths
v2, …, vn} such that (vi, vi+1) E for all 0 i < n.

A path is a list of vertices {v1,
Seattle Salt Lake City San Francisco
A
Data Structure
05 Graph
Graph Density
A
sparse graph has O(|V|) edges
A
dense graph has (|V|2) edges
in between is either sparsish or densy depending on the context.
Directed
Data Structure
05 Graph
Connectivity
are weakly connected if there is a path between any two vertices, ignoring direction
Di-graphs
complete graph has an edge between every pair of vertices
connected and without cycles.
Data Structure
05 Graph
ቤተ መጻሕፍቲ ባይዱ
Connectivity
graphs are connected if there is a path between any two vertices
Undirected
graphs are strongly connected if there is a path from any one vertex to any other
Data Structure 05 Graph
Connectivity
If there is a path from vertex vi to vj, vi and vj are connected.

An undirected graph are connected-----if, for every pair of distinct vertices vi , vj, there is a path from vi i to vj in G.
A simple path repeats no vertices (except that the first can be the last):

p = {Seattle, Salt Lake City, San Francisco, Dallas} p = {Seattle, Salt Lake City, Dallas, San Francisco, Seattle}
Data Structure
05 Graph
Depth-First Search (DFS)
Data Structure
05 Graph
Depth-First Search (DFS)
Assume the node labeled a has been designated as the starting point, a depth-first traversal would visit the graph nodes in the order:

Data Structure
05 Graph
Implementing a DFS
Data Structure

Data Structure
05 Graph
Graph Traversals
The
order in which the vertices are visited is important. There are two common traversals: Depth-first Breadth-first

abecdfghi Note that if the edges taken during the depth-first traversal are marked, they define a tree (not necessarily binary) which includes all the nodes of the graph. Such a tree is a spanning tree for the graph. We call the tree DFS tree.

Connected component(undirected graph)----a maximal connected subgrap.( a tree is graph that is connected and acycle(无环))