## Graphs
Graph is a useful data structure for representing most of the real-world problems involving a set of users/candidates/nodes and their relations. A graph consists of two parameters:
```
V = a set of vertices
E = a set of edges
```
Each edge in `E` connects any two vertices from `V`. Based on the type of edge, graphs can be of two types:
1. **Directed**: The edges are directed in nature, which means that when there is an edge from node `A` to `B`, it does not imply that there is an edge from `B` to `A`. An example of a directed edge graph is the **follow** feature of social media. If you follow a celebrity, it doesn't imply that they follow you.
2. **Undirected**: The edges don't have any direction. So if `A` and `B` are connected, we can assume that there is an edge from both `A` to `B` and `B` to `A`. For example, in a social media graph, if two persons are friends, it implies that both are friends with each other.
### Components of a Graph
**Vertices:** Vertices are the fundamental units of the graph. Sometimes, vertices are also known as vertex or nodes. Every node/vertex can be labeled or unlabelled.
**Edges:** Edges are used to connect two nodes of the graph. They can be an ordered pair of nodes in a directed graph. Edges can connect any two nodes in any possible way. There are no rules. Sometimes, edges are also known as arcs. Every edge can be labeled/unlabeled.
Graphs are used to solve many real-life problems. Graphs are used to represent networks. The networks may include paths in a city, telephone network, or circuit network. Graphs are also used in social networks like LinkedIn, Facebook. For example, on Facebook, each person is represented with a vertex (or node). Each node is a structure and contains information like person id, name, gender, locale, etc.
### Graph Representation
Graph can be represented in the following ways:
**Set Representation:** Set representation of a graph involves two sets: Set of vertices V = {V1, V2, V3, V4} and set of edges E = {{V1, V2}, {V2, V3}, {V3, V4}, {V4, V1}}. This representation is efficient for memory but does not allow parallel edges.
**Sequential Representation:** This representation of a graph can be represented by means of matrices: Adjacency Matrix, Incidence matrix, and Path matrix.
**Adjacency Matrix:** This matrix includes information about the adjacent nodes. Here, aij = 1 if there is an edge from Vi to Vj; otherwise, it's 0. It is a matrix of order V×V.
**Incidence Matrix:** This matrix includes information about the incidence of edges on the nodes. Here, aij = 1 if the jth edge Ej is incident on the ith vertex Vi; otherwise, it's 0. It is a matrix of order V×E.
**Path Matrix:** This matrix includes information about the simple path between two vertices. Here, Pij = 1 if there is a path from Vi to Vj; otherwise, it's 0. It is also called the reachability matrix of graph G.
**Linked Representation:** This representation gives information about the nodes to which a specific node is connected, i.e., adjacency lists. This representation gives the adjacency lists of the vertices with the help of arrays and linked lists. In the adjacency lists, the vertices connected to the specific vertex are arranged in the form of lists that are connected to that vertex.
### Real-Time Applications of Graph
Graphs are used to represent the flow of control in computers.
Graphs are used in social networking sites where users act as nodes, and connections between them act as edges.
In an operating system, graphs are used as resource allocation graphs.
Graphs are used in Google Maps to find the shortest route.
Graphs are also used in the airline system for effective route optimization.
In state transition diagrams, the graph is used to represent states and their transitions.
In transportation, graphs are used to find the shortest path.
In circuits, graphs can be used to represent circuit points as nodes and wires as edges.
Graphs are used in solving puzzles with only one solution, such as mazes.
Graphs are used in computer networks for Peer to Peer (P2P) applications.
Graphs, basically in the form of DAG (Directed Acyclic Graph), are used as an alternative to blockchain for cryptocurrency. For example, cryptocurrencies like IOTA and Nano are mainly based on DAG.
### Advantages of Graph
Using graphs, we can easily find the shortest path, neighbors of the nodes, and many more.
Graphs are used to implement algorithms like DFS and BFS.
They are used to find minimum spanning trees, which have many practical applications.
Graphs help in organizing data.
Because of their non-linear structure, graphs help in understanding complex problems and their visualization.
### Disadvantages of Graph
Graphs use lots of pointers, which can be complex to handle.
They can have large memory complexity.
If the graph is represented with an adjacency matrix, then it does not allow parallel edges, and multiplication of the graph is also difficult.
### Representation
1. **Adjacency Lists**: Each node is represented as an entry, and all the edges are represented as a list emerging from the corresponding node. So, if vertex 1 has edges to 2, 3, and 6, the list corresponding to 1 will have 2, 3, and 6 as entries. Consider the following graph:
```
0: 1-->2-->3
1: 0-->2
2: 0-->1
3: 0-->4
4: 3
```
It means there are edges from 0 to 1, 2, and 3; from 1 to 0 and 2, and so on.
2. **Adjacency Matrix**: The graph is represented as a matrix of size |V| x |V|, and an entry 1 in cell (i, j) implies that there is an edge from i to j. 0 represents no edge. The matrix for the above graph:
```
0 1 2 3 4
0 0 1 1 1 0
1 1 0 1 0 0
2 1 1 0 0 0
3 1 0 0 0 1
4 0 0 0 1 0
```
没有合适的资源?快使用搜索试试~ 我知道了~
java实现所有算法大全
共863个文件
java:827个
md:13个
yml:11个
需积分: 0 2 下载量 170 浏览量
2024-05-14
14:56:44
上传
评论
收藏 816KB ZIP 举报
温馨提示
这个资源是一个完整的 Java 实现算法的集合,旨在帮助开发人员轻松地访问和使用各种常见算法。无论是在学术研究、编程竞赛还是实际项目开发中,这个资源都将成为你的得力助手。 **内容概述:** 1. **用户认证算法**:提供了用于验证用户身份的认证算法,包括基于用户名密码的验证逻辑。 2. **课程管理算法**:包括课程查找、添加、删除等功能的算法实现,用于管理高校课程信息。 3. **选课管理算法**:实现了选课系统的核心功能,包括选课冲突检测、选课记录管理等。 4. **成绩管理算法**:提供了成绩计算、成绩分布统计等算法,帮助教师和管理员有效管理学生成绩。 5. **推荐算法**:基于学生兴趣和历史选课记录,实现了课程推荐功能,帮助学生更好地选择适合自己的课程。 6. **通知与提醒算法**:提供了向用户发送通知和提醒的算法,包括选课截止日期提醒、课程变动通知等功能。 7. **报表与统计算法**:实现了各种报表和统计数据的生成算法,帮助管理员了解课程选课情况、学生成绩分布等信息。 **资源特点:** - **全
资源推荐
资源详情
资源评论
收起资源包目录
java实现所有算法大全 (863个子文件)
.clang-format 4KB
CODEOWNERS 40B
Dockerfile 1KB
.gitpod.dockerfile 554B
.gitignore 708B
AES.java 47KB
Blowfish.java 30KB
SinglyLinkedList.java 13KB
KDTree.java 13KB
FibonacciHeap.java 12KB
ClosestPair.java 12KB
MemoryManagementAlgorithms.java 12KB
DoublyLinkedList.java 12KB
DES.java 11KB
AhoCorasick.java 11KB
MatrixGraphs.java 11KB
SquareFreeIntegerTest.java 10KB
SkipList.java 10KB
LinkListSort.java 10KB
BinaryTree.java 9KB
BSTRecursiveGeneric.java 9KB
RedBlackBST.java 9KB
ConwayTest.java 9KB
KochSnowflake.java 9KB
FFT.java 8KB
QuickSelectTest.java 8KB
SinglyLinkedListTest.java 8KB
HashMapCuckooHashing.java 8KB
Mandelbrot.java 8KB
BoruvkaAlgorithmTest.java 7KB
Dijkstra.java 7KB
ColumnarTranspositionCipher.java 7KB
RgbHsvConversion.java 7KB
HorspoolSearch.java 7KB
A_Star.java 7KB
Deques.java 7KB
BoruvkaAlgorithm.java 7KB
BankersAlgorithm.java 6KB
QuickSortLinkedList.java 6KB
MatrixRank.java 6KB
MazeRecursion.java 6KB
MatrixUtil.java 6KB
CheckIfBinaryTreeBalanced.java 6KB
GenericTree.java 6KB
CRCAlgorithm.java 6KB
Luhn.java 6KB
BSTIterative.java 6KB
RegexMatching.java 6KB
HillCipher.java 6KB
MonteCarloTreeSearch.java 6KB
SkylineAlgorithm.java 6KB
MedianOfRunningArrayTest.java 6KB
BellmanFord.java 6KB
Anagrams.java 6KB
Area.java 6KB
AVLTree.java 6KB
Verhoeff.java 6KB
PerlinNoise.java 6KB
DynamicArray.java 6KB
AnyBaseToAnyBase.java 6KB
ORSet.java 6KB
GrahamScan.java 5KB
SortingAlgorithmTest.java 5KB
PriorityQueues.java 5KB
BinarySearch2dArrayTest.java 5KB
CursorLinkedList.java 5KB
BufferedReader.java 5KB
MaxHeap.java 5KB
LazySegmentTree.java 5KB
MinHeap.java 5KB
AhoCorasickTest.java 5KB
QueueUsingTwoStacks.java 5KB
Implementing_auto_completing_features_using_trie.java 5KB
WelshPowellTest.java 5KB
OptimalJobScheduling.java 5KB
FFTTest.java 5KB
CircularBufferTest.java 5KB
WordBoggle.java 5KB
NQueens.java 5KB
EulerMethod.java 4KB
BSTRecursive.java 4KB
Kosaraju.java 4KB
ColorContrastRatio.java 4KB
LinearDiophantineEquationsSolver.java 4KB
StrassenMatrixMultiplication.java 4KB
LRUCache.java 4KB
AESEncryption.java 4KB
LWWElementSet.java 4KB
TarjansAlgorithm.java 4KB
LinkedQueue.java 4KB
MRUCache.java 4KB
PlayfairCipher.java 4KB
StackArray.java 4KB
QuickSelect.java 4KB
TrieImp.java 4KB
EditDistance.java 4KB
Kruskal.java 4KB
Graphs.java 4KB
Queues.java 4KB
MiniMaxAlgorithm.java 4KB
共 863 条
- 1
- 2
- 3
- 4
- 5
- 6
- 9
资源评论
编程资源宝库
- 粉丝: 2826
- 资源: 141
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
最新资源
- 基于Java的本科探索学习项目设计源码 - 本科探索
- 基于Javascript和Python的微商城项目设计源码 - MicroMall
- 基于Java的网上订餐系统设计源码 - online ordering system
- 基于Javascript的超级美眉网络资源管理应用模块设计源码
- 基于Typescript和PHP的编程知识储备库设计源码 - study-php
- Screenshot_2024-05-28-11-40-58-177_com.tencent.mm.jpg
- 基于Dart的Flutter小提琴调音器APP设计源码 - violinhelper
- 基于JavaScript和CSS的随寻订购网页设计源码 - web-order
- 基于MATLAB的声纹识别系统设计源码 - VoiceprintRecognition
- 基于Java的微服务插件集合设计源码 - wsy-plugins
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功