Dsa Using Java 简明教程

DSA using Java - Graph

Overview

图形是一种用于对数学图形进行建模的数据结构。它包含一组连接的成对内容，称为顶点的边。我们可以使用顶点数组和边进行的二维数组来表示图形。

Graph is a datastructure to model the mathematical graphs. It consists of a set of connected pairs called edges of vertices. We can represent a graph using an array of vertices and a two dimentional array of edges.

重要术语

Important terms

Vertex − Each node of the graph is represented as a vertex. In example given below, labeled circle represents vertices. So A to G are vertices. We can represent them using an array as shown in image below. Here A can be identified by index 0. B can be identified using index 1 and so on.
Edge − Edge represents a path between two vertices or a line between two vertices. In example given below, lines from A to B, B to C and so on represents edges. We can use a two dimentional array to represent array as shown in image below. Here AB can be represented as 1 at row 0, column 1, BC as 1 at row 1, column 2 and so on, keeping other combinations as 0.
Adjacency − Two node or vertices are adjacent if they are connected to each other through an edge. In example given below, B is adjacent to A, C is adjacent to B and so on.
Path − Path represents a sequence of edges betweeen two vertices. In example given below, ABCD represents a path from A to D.

Basic Operations

以下是图形的基本主操作。

Following are basic primary operations of a Graph which are following.

Add Vertex − add a vertex to a graph.
Add Edge − add an edge between two vertices of a graph.
Display Vertex − display a vertex of a graph.

Add Vertex Operation

//add vertex to the array of vertex
public void addVertex(char label){
   lstVertices[vertexCount++] = new Vertex(label);
}

Add Edge Operation

//add edge to edge array
public void addEdge(int start,int end){
   adjMatrix[start][end] = 1;
   adjMatrix[end][start] = 1;
}

Display Edge Operation

//display the vertex
public void displayVertex(int vertexIndex){
   System.out.print(lstVertices[vertexIndex].label+" ");
}

Traversal Algorithms

以下是图上的重要遍历算法。

Following are important traversal algorithms on a Graph.

Depth First Search − traverses a graph in depthwards motion.
Breadth First Search − traverses a graph in breadthwards motion.

Depth First Search Algorithm

深度优先搜索算法 (DFS) 以深度方向遍历图并使用一个堆栈记住在任何迭代中发生死锁时获取下一个顶点以开始搜索。

Depth First Search algorithm(DFS) traverses a graph in a depthward motion and uses a stack to remember to get the next vertex to start a search when a dead end occurs in any iteration.

如上例所示，DFS 算法首先从 A 到 B 到 C 到 D，然后到 E，再到 F，最后到 G。它采用以下规则。

As in example given above, DFS algorithm traverses from A to B to C to D first then to E, then to F and lastly to G. It employs following rules.

Rule 1 − Visit adjacent unvisited vertex. Mark it visited. Display it. Push it in a stack.
Rule 2 − If no adjacent vertex found, pop up a vertex from stack. (It will pop up all the vertices from the stack which do not have adjacent vertices.)
Rule 3 − Repeat Rule 1 and Rule 2 until stack is empty.

public void depthFirstSearch(){
   //mark first node as visited
   lstVertices[0].visited = true;
   //display the vertex
   displayVertex(0);
   //push vertex index in stack
   stack.push(0);

   while(!stack.isEmpty()){
      //get the unvisited vertex of vertex which is at top of the stack
      int unvisitedVertex = getAdjUnvisitedVertex(stack.peek());
      //no adjacent vertex found
      if(unvisitedVertex == -1){
         stack.pop();
      }else{
         lstVertices[unvisitedVertex].visited = true;
         displayVertex(unvisitedVertex);
         stack.push(unvisitedVertex);
      }
   }

   //stack is empty, search is complete, reset the visited flag
   for(int i=0;i<vertexCount;i++){
      lstVertices[i].visited = false;
   }
}

Breadth First Search Algorithm

广度优先搜索算法 (BFS) 以广度方向遍历图并使用一个队列记住在任何迭代中发生死锁时获取下一个顶点以开始搜索。

Breadth First Search algorithm(BFS) traverses a graph in a breadthwards motion and uses a queue to remember to get the next vertex to start a search when a dead end occurs in any iteration.

如上例所示，BFS 算法首先从 A 到 B 到 E 到 F，然后到 C 和 G，最后到 D。它采用以下规则。

As in example given above, BFS algorithm traverses from A to B to E to F first then to C and G lastly to D. It employs following rules.

Rule 1 − Visit adjacent unvisited vertex. Mark it visited. Display it. Insert it in a queue.
Rule 2 − If no adjacent vertex found, remove the first vertex from queue.
Rule 3 − Repeat Rule 1 and Rule 2 until queue is empty.

public void breadthFirstSearch(){
   //mark first node as visited
   lstVertices[0].visited = true;
   //display the vertex
   displayVertex(0);
   //insert vertex index in queue
   queue.insert(0);

   int unvisitedVertex;
   while(!queue.isEmpty()){
      //get the unvisited vertex of vertex which is at front of the queue
      int tempVertex = queue.remove();
      //no adjacent vertex found
      while((unvisitedVertex=getAdjUnvisitedVertex(tempVertex)) != -1){
         lstVertices[unvisitedVertex].visited = true;
         displayVertex(unvisitedVertex);
         queue.insert(unvisitedVertex);
      }
   }

   //queue is empty, search is complete, reset the visited flag
   for(int i=0;i<vertexCount;i++){
      lstVertices[i].visited = false;
   }
}

Graph Implementation

Stack.java

package com.tutorialspoint.datastructure;

public class Stack {
   private int size;           // size of the stack
   private int[] intArray;     // stack storage
   private int top;            // top of the stack

   // Constructor
   public Stack(int size){
      this.size = size;
      intArray = new int[size];   //initialize array
      top = -1;                   //stack is initially empty
   }

   // Operation : Push
   // push item on the top of the stack
   public void push(int data) {

      if(!isFull()){
         // increment top by 1 and insert data
         intArray[++top] = data;
      }else{
         System.out.println("Cannot add data. Stack is full.");
      }
   }

   // Operation : Pop
   // pop item from the top of the stack
   public int pop() {
      //retrieve data and decrement the top by 1
      return intArray[top--];
   }

   // Operation : Peek
   // view the data at top of the stack
   public int peek() {
      //retrieve data from the top
      return intArray[top];
   }

   // Operation : isFull
   // return true if stack is full
   public boolean isFull(){
      return (top == size-1);
   }

   // Operation : isEmpty
   // return true if stack is empty
   public boolean isEmpty(){
      return (top == -1);
   }
}

Queue.java

package com.tutorialspoint.datastructure;

public class Queue {

   private final int MAX;
   private int[] intArray;
   private int front;
   private int rear;
   private int itemCount;

   public Queue(int size){
      MAX = size;
      intArray = new int[MAX];
      front = 0;
      rear = -1;
      itemCount = 0;
   }

   public void insert(int data){
      if(!isFull()){
         if(rear == MAX-1){
            rear = -1;
         }

         intArray[++rear] = data;
         itemCount++;
      }
   }

   public int remove(){
      int data = intArray[front++];
      if(front == MAX){
         front = 0;
      }
      itemCount--;
      return data;
   }

   public int peek(){
      return intArray[front];
   }

   public boolean isEmpty(){
      return itemCount == 0;
   }

   public boolean isFull(){
      return itemCount == MAX;
   }

   public int size(){
      return itemCount;
   }
}

Vertex.java

package com.tutorialspoint.datastructure;

public class Vertex {
   public char label;
   public boolean visited;

   public Vertex(char label){
      this.label = label;
      visited = false;
   }
}

Graph.java

package com.tutorialspoint.datastructure;

public class Graph {
   private final int MAX = 20;
   //array of vertices
   private Vertex lstVertices[];
   //adjacency matrix
   private int adjMatrix[][];
   //vertex count
   private int vertexCount;

   private Stack stack;
   private Queue queue;

   public Graph(){
      lstVertices = new Vertex[MAX];
      adjMatrix = new int[MAX][MAX];
      vertexCount = 0;
      stack = new Stack(MAX);
      queue = new Queue(MAX);
      for(int j=0; j<MAX; j++) // set adjacency
         for(int k=0; k<MAX; k++) // matrix to 0
            adjMatrix[j][k] = 0;
   }

   //add vertex to the vertex list
   public void addVertex(char label){
      lstVertices[vertexCount++] = new Vertex(label);
   }

   //add edge to edge array
   public void addEdge(int start,int end){
      adjMatrix[start][end] = 1;
      adjMatrix[end][start] = 1;
   }

   //display the vertex
   public void displayVertex(int vertexIndex){
      System.out.print(lstVertices[vertexIndex].label+" ");
   }

   //get the adjacent unvisited vertex
   public int getAdjUnvisitedVertex(int vertexIndex){
      for(int i=0; i<vertexCount; i++)
         if(adjMatrix[vertexIndex][i]==1 && lstVertices[i].visited==false)
            return i;
      return -1;
   }

   public void depthFirstSearch(){
      //mark first node as visited
      lstVertices[0].visited = true;
      //display the vertex
      displayVertex(0);
      //push vertex index in stack
      stack.push(0);

      while(!stack.isEmpty()){
         //get the unvisited vertex of vertex which is at top of the stack
         int unvisitedVertex = getAdjUnvisitedVertex(stack.peek());
         //no adjacent vertex found
         if(unvisitedVertex == -1){
            stack.pop();
         }else{
            lstVertices[unvisitedVertex].visited = true;
            displayVertex(unvisitedVertex);
            stack.push(unvisitedVertex);
         }
      }

      //stack is empty, search is complete, reset the visited flag
      for(int i=0;i<vertexCount;i++){
         lstVertices[i].visited = false;
      }
   }

   public void breadthFirstSearch(){
      //mark first node as visited
      lstVertices[0].visited = true;
      //display the vertex
      displayVertex(0);
      //insert vertex index in queue
      queue.insert(0);
      int unvisitedVertex;
      while(!queue.isEmpty()){
         //get the unvisited vertex of vertex which is at front of the queue
         int tempVertex = queue.remove();
         //no adjacent vertex found
         while((unvisitedVertex=getAdjUnvisitedVertex(tempVertex)) != -1){
            lstVertices[unvisitedVertex].visited = true;
            displayVertex(unvisitedVertex);
            queue.insert(unvisitedVertex);
         }
      }

      //queue is empty, search is complete, reset the visited flag
      for(int i=0;i<vertexCount;i++){
         lstVertices[i].visited = false;
      }
   }
}

Demo Program

GraphDemo.java

package com.tutorialspoint.datastructure;

public class GraphDemo {
   public static void main(String args[]){
      Graph graph = new Graph();

      graph.addVertex('A');   //0
      graph.addVertex('B');   //1
      graph.addVertex('C');   //2
      graph.addVertex('D');   //3
      graph.addVertex('E');   //4
      graph.addVertex('F');   //5
      graph.addVertex('G');   //6

      /*       1  2  3
       * 0  |--B--C--D
       * A--|
       * |
       * |     4
       * |-----E
       * |     5  6
       * |  |--F--G
       * |--|
       */
      graph.addEdge(0, 1);   //AB
      graph.addEdge(1, 2);   //BC
      graph.addEdge(2, 3);   //CD
      graph.addEdge(0, 4);   //AC
      graph.addEdge(0, 5);   //AF
      graph.addEdge(5, 6);   //FG
      System.out.print("Depth First Search: ");
      //A B C D E F G
      graph.depthFirstSearch();
      System.out.println("");
      System.out.print("Breadth First Search: ");
      //A B E F C G D
      graph.breadthFirstSearch();
   }
}

如果我们编译并运行上述程序，它将生成以下结果 -

If we compile and run the above program then it would produce following result −

Depth First Search: A B C D E F G
Breadth First Search: A B E F C G D