Java valodā, Grafiks ir datu struktūra, kas glabā noteiktus datus. Jēdziens par grafikā ir nozagts no matemātikas, kas atbilst datorzinātņu nozares vajadzībām. Tas attēlo tīklu, kas savieno vairākus punktus viens ar otru. Šajā sadaļā mēs detalizēti apgūsim Java Graph datu struktūru. Tāpat mēs apgūsim Grafu veidi , to īstenošana un šķērsošana pa grafiku.

Grafiks

A grafikā ir grafiku terminoloģija

Virsotne: Virsotnes ir punkts, kas savieno malas. Tas atspoguļo datus. To sauc arī par mezglu. Tas ir apzīmēts ar apli, un tam jābūt marķētam. Lai izveidotu grafiku, ir jābūt vismaz mezglam. Piemēram, māja, autobusa pietura utt.

Mala: Mala ir līnija, kas savieno divas virsotnes. Tas atspoguļo attiecību starp virsotnēm. Malas ir apzīmētas ar līniju. Piemēram, ceļš uz autobusu pieturu no jūsu mājas.

Svars: Tas ir marķēts līdz malai. Piemēram, attālums starp divām pilsētām ir 100 km, tad attālumu sauc par svaru malai.

Ceļš: Ceļš ir veids, kā secībā sasniegt galamērķi no sākuma punkta.

Grafu veidi

Svērtais grafiks:Svērtā grafikā katra mala satur dažus datus (svars), piemēram, attālums, svars, augstums utt. Tas apzīmēts kā w(e). To izmanto, lai aprēķinātu izmaksas, kas saistītas ar pārvietošanos no vienas virsotnes uz otru. Nākamajā attēlā ir attēlots svērtais grafiks.
Nesvērts grafiks:Grafu, kurā malas nav saistītas ar nevienu vērtību, sauc par nesvērto grafiku. Nākamajā attēlā ir attēlots nesvērts grafiks.
Režisēts grafiks:Grafu, kurā malas attēlo virzienu, sauc par virzītu grafiku. Virzītā grafikā līniju (malu) vietā izmantojam bultiņas. Virziens apzīmē veidu, kā sasniegt no viena mezgla uz otru mezglu. Ņemiet vērā, ka virzītā grafikā mēs varam pārvietoties vai nu vienā virzienā, vai abos virzienos. Nākamajā attēlā ir attēlots virzīts grafiks.
Nevirzīts grafiks:Grafu, kurā malas ir divvirzienu, sauc par nevirzītu grafiku. Nevirzītā grafikā mēs varam pārvietoties jebkurā virzienā. Ņemiet vērā, ka atgriešanai varam izmantot to pašu ceļu, pa kuru esam šķērsojuši. Atrodoties virzītajā grafikā, mēs nevaram atgriezties no tā paša ceļa.
Savienotais grafiks:Grafu sauc par savienotu, ja starp katru virsotņu pāri ir vismaz viens ceļš. Ņemiet vērā, ka grafs ar tikai virsotni ir savienots grafs.

Ir divu veidu savienotie grafiki.
Iknedēļas savienotais grafiks:Grafiku, kurā mezglus nevar apmeklēt pa vienu ceļu, sauc par nedēļas savienoto grafiku.
Cieši saistīts grafiks:Grafiku, kurā mezglus var apmeklēt pa vienu ceļu, sauc par cieši saistītu grafiku.

Atvienots grafiks:Grafu sauc par atvienotu, ja starp virsotņu pāriem nav ceļa, sauc par atvienotu grafiku. Atvienots grafiks var sastāvēt no diviem vai vairākiem savienotiem grafikiem.
Vairāki grafiki:Grafiks, kuram ir vairākas malas, kas savieno vienu un to pašu mezglu pāri. Nākamajā attēlā ir attēlots daudzgrafiks.
Blīvs grafiks:Grafu, kurā malu skaits ir tuvu maksimālajam malu skaitam, grafu sauc par blīvo grafiku. Nākamajā attēlā ir attēlots blīvs grafiks.
Rets grafiks:Grafu, kurā šķautņu skaits ir tuvu minimālajam malu skaitam, grafu sauc par reto grafiku. Tas var būt atvienots grafiks. Sekojošais attēls attēlo retu grafiku.

Java grafika ieviešana

Grafiku ieviešanai iekšā Java mēs izmantosim Vispārējs klasē. Lai izveidotu Java Generic klases objektu, mēs izmantojam šādu sintaksi:

 BaseType obj = new BaseType (); 

Atcerieties, ka mēs nevaram izmantot primitīvo tipu parametru tipam.

Izveidosim Java programmu, kas ievieš Graph.

GraphImplementation.java

 import java.util.*; class Graph { //creating an object of the Map class that stores the edges of the graph private Map<t, list> map = new HashMap(); //the method adds a new vertex to the graph public void addNewVertex(T s) { map.put(s, new LinkedList()); } //the method adds an edge between source and destination public void addNewEdge(T source, T destination, boolean bidirectional) { // if (!map.containsKey(source)) addNewVertex(source); if (!map.containsKey(destination)) addNewVertex(destination); map.get(source).add(destination); if (bidirectional == true) { map.get(destination).add(source); } } //the method counts the number of vertices public void countVertices() { System.out.println(&apos;Total number of vertices: &apos;+ map.keySet().size()); } //the method counts the number of edges public void countEdges(boolean bidirection) { //variable to store number of edges int count = 0; for (T v : map.keySet()) { count = count + map.get(v).size(); } if (bidirection == true) { count = count / 2; } System.out.println(&apos;Total number of edges: &apos;+ count); } //checks a graph has vertex or not public void containsVertex(T s) { if (map.containsKey(s)) { System.out.println(&apos;The graph contains &apos;+ s + &apos; as a vertex.&apos;); } else { System.out.println(&apos;The graph does not contain &apos;+ s + &apos; as a vertex.&apos;); } } //checks a graph has edge or not //where s and d are the two parameters that represent source(vertex) and destination (vertex) public void containsEdge(T s, T d) { if (map.get(s).contains(d)) { System.out.println(&apos;The graph has an edge between &apos;+ s + &apos; and &apos; + d + &apos;.&apos;); } else { System.out.println(&apos;There is no edge between &apos;+ s + &apos; and &apos; + d + &apos;.&apos;); } } //prints the adjacencyS list of each vertex //here we have overridden the toString() method of the StringBuilder class @Override public String toString() { StringBuilder builder = new StringBuilder(); //foreach loop that iterates over the keys for (T v : map.keySet()) { builder.append(v.toString() + &apos;: &apos;); //foreach loop for getting the vertices for (T w : map.get(v)) { builder.append(w.toString() + &apos; &apos;); } builder.append(&apos;
&apos;); } return (builder.toString()); } } //creating a class in which we have implemented the driver code public class GraphImplementation { public static void main(String args[]) { //creating an object of the Graph class Graph graph=new Graph(); //adding edges to the graph graph.addNewEdge(0, 1, true); graph.addNewEdge(0, 4, true); graph.addNewEdge(1, 2, true); graph.addNewEdge(1, 3, false); graph.addNewEdge(1, 4, true); graph.addNewEdge(2, 3, true); graph.addNewEdge(2, 4, true); graph.addNewEdge(3, 0, true); graph.addNewEdge(2, 0, true); //prints the adjacency matrix that represents the graph System.out.println(&apos;Adjacency List for the graph:
&apos;+ graph.toString()); //counts the number of vertices in the graph graph.countVertices(); //counts the number of edges in the graph graph.countEdges(true); //checks whether an edge is present or not between the two specified vertices graph.containsEdge(3, 4); graph.containsEdge(2, 4); //checks whether vertex is present or not graph.containsVertex(3); graph.containsVertex(5); } } </t,>

Izvade:

xd xd nozīme

Directed Graph ieviešana

DirectedGraph.java

 import java.util.*; //Creating a class named Edge that stores the edges of the graph class Edge { //the variable source and destination represent the vertices int s, d; //creating a constructor of the class Edge Edge(int s, int d) { this.s = s; this.d = d; } } //a class to represent a graph object class Graph { //note that we have created an adjacency list (i.e. List of List) List<list> adjlist = new ArrayList(); //creating a constructor of the class Graph that construct a graph public Graph(List edges) { int n = 0; //foreach loop that iterates over the edge for (Edge e: edges) { //determines the maximum numbered vertex n = Integer.max(n, Integer.max(e.s, e.d)); } //reserve the space for the adjacency list for (int i = 0; i <= 1 n; i++) { adjlist.add(i, new arraylist()); } adds the edges to undirected graph for (edge current: edges) allocate node in adjacency list from source destination adjlist.get(current.s).add(current.d); function print representation of a public static void showgraph(graph graph) int s="0;" determines size n="graph.adjlist.size();" while (s ' + d ')	'); system.out.println(); increments by s++; implementing driver code class directedgraph main (string args[]) creating edge(0, 1), edge(1, 2), edge(2, 4), edge(4, 1),new edge(3, 5), edge(5, 1)); construct given graph(edges); prints that represents graph.showgraph(graph); < pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/19/java-graph-13.webp" alt="Java Graph"> <h2>Implementation of Weighted Graph</h2> <p> <strong>WeightedGraph.java</strong> </p> <pre> import java.util.*; //the class stores the edges of the graph class Edge { int s, d, w; //creating a constructor of the class Edge Edge(int src, int dest, int weight) { this.s = src; this.d = dest; this.w = weight; } } //a class to store adjacency list nodes class Node { int value, weight; //creating a constructor of the class Vertex Node(int value, int weight) { this.value = value; this.weight = weight; } //overrides the toString() method @Override public String toString() { return this.value + &apos; (&apos; + this.weight + &apos;)&apos;; } } //a class to represent a graph object class Graph { //note that we have created an adjacency list (i.e. List of List) List<list> adjlist = new ArrayList(); //creating a constructor of the class Graph that creates graph public Graph(List edges) { //find the maximum numbered vertex int n = 0; //iterates over the edges of the graph for (Edge e: edges) { //determines the maximum numbered vertex n = Integer.max(n, Integer.max(e.s, e.d)); } //reserve the space for the adjacency list for (int i = 0; i <= 1 n; i++) { adjlist.add(i, new arraylist()); } adds the edges to undirected graph for (edge e: edges) creating a node (from source destination) in adjacency list adjlist.get(e.s).add(new node(e.d, e.w)); uncomment following statement adj.get(e.dest).add(new node(e.src, e.weight)); method that prints of public static void printgraph(graph graph) int src="0;" n="graph.adjlist.size();" system.out.printf('adjacency is: '); while (src %s	', src, edge); system.out.println(); increments by src++; implementing driver code class weightedgraph main (string args[]) with their associated weight edge(1, 4, 3), edge(4, 2, 5), edge(2, 5, 10), edge(5, 1, 6), edge(3, 9), 1), 2)); creates declared above graph(edges); corresponding graph.printgraph(graph); < pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/19/java-graph-14.webp" alt="Java Graph"> <h2>Graph Traversal</h2> <p>Traversal over the graph means visit each and every vertex and edge at least once. To traverse over the graph, Graph data structure provides two algorithms:</p> <ul> <li>Depth-First Search (DFS)</li> <li>Breadth-First Search (DFS)</li> </ul> <h3>Depth-First Search (DFS)</h3> <p> <a href="/dfs-algorithm">DFS algorithm</a> is a recursive algorithm that is based on the backtracking concept. The algorithm starts from the initial node and searches in depth until it finds the goal node (a node that has no child). Backtracking allows us to move in the backward direction on the same path from which we have traversed in the forward direction.</p> <p>Let&apos;s implement the DFS algorithm in a Java program.</p> <p> <strong>DepthFirstSearch.java</strong> </p> <pre> import java.io.*; import java.util.*; //creates an undirected graph class Graph { //stores the number of vertices private int Vertices; //creates a linked list for the adjacency list of the graph private LinkedList adjlist[]; //creating a constructor of the Graph class Graph(int count_v) { //assigning the number of vertices to the passed parameter Vertices = count_v; adjlist = new LinkedList[count_v]; //loop for creating the adjacency lists for (int i=0; i<count_v; 3 10 ++i) adjlist[i]="new" linkedlist(); } method that adds a new edge to the graph void addnewedge(int v, int w) { adjlist[v].add(w); add w v's list. logic of dfs traversal starts from root node traversaldfs(int boolean vnodelist[]) if current (root node) is visited, it vnodelist vnodelist[v]="true;" system.out.print(v+' '); detrmines negihboring nodes iterates over list iterator i="adjlist[v].listIterator();" while (i.hasnext()) returns next element in iteration and store variable n (!vnodelist[n]) calling function performs depth first traversaldfs(n, vnodelist); dfs(int v) creates an array type for visited initially all are unvisited visited[]="new" boolean[vertices]; call recursive traversaldfs() traversaldfs(v, visited); implementing driver code public class depthfirstsearch static main(string args[]) having vertices g="new" graph(10); edges g.addnewedge(1, 2); g.addnewedge(2, 3); g.addnewedge(3, 4); g.addnewedge(4, 5); g.addnewedge(5, 7); 6); print sequencnce which bfs done system.out.println('depth-first is: (as g.dfs(1); < pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/19/java-graph-15.webp" alt="Java Graph"> <h3>Breadth First Search (BFS)</h3> <p> <a href="/bfs-algorithm">BFS algorithm</a> is the most common approach to traverse over the graph. The traversal starts from the source node and scans its neighboring nodes (child of the current node). In short, traverse horizontally and visit all the nodes of the current layer. After that, move to the next layer and perform the same.</p> <p>Let&apos;s implement the BFS algorithm in a Java program.</p> <p> <strong>BreadthFirstSearch.java</strong> </p> <pre> import java.io.*; import java.util.*; //creates an undirected graph class Graph { //stores the number of vertices private int vertices; //creates a linked list for the adjacency list of the graph private LinkedList adjlist[]; //creating a constructor of the Graph class Graph(int count_v) { //assigning the number of vertices to the passed parameter vertices = count_v; adjlist = new LinkedList[count_v]; //loop for creating the adjacency lists for (int i=0; i<count_v; 10 ++i) adjlist[i]="new" linkedlist(); } method that adds a new edge to the graph void addnewedge(int v, int w) { adjlist[v].add(w); traversal starts from root node traversalbfs(int rnode) creates an array of boolean type for visited initially all nodes are unvisited visitednode[]="new" boolean[vertices]; creating another list storing linkedlist vnodelist="new" if current (root node) is visited, add it visitednode[rnode]="true;" inserts into vnodelist.add(rnode); while loop executes until we have (vnodelist.size() !="0)" deque entry queue and process poll() retrieves removes head (first element) this rnode="vnodelist.poll();" system.out.print(rnode+' '); detrmines negihboring iterates over iterator i="adjlist[rnode].listIterator();" (i.hasnext()) returns next element in iteration store variable n checks or not (!visitednode[n]) above if-statement true, visits visitednode[n]="true;" vnodelist.add(n); implementing driver code public class breadthfirstsearch static main(string args[]) having vertices graph(10); edges graph.addnewedge(2, 5); graph.addnewedge(3, graph.addnewedge(1, 2); 4); graph.addnewedge(4, 1); graph.addnewedge(6, graph.addnewedge(5, 6); 3); graph.addnewedge(7, 7); print sequence which bfs execute system.out.println('breadth-first is: graph.traversalbfs(2); < pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/19/java-graph-16.webp" alt="Java Graph"> <hr></count_v;></pre></count_v;></pre></=></list></pre></=></list>