（Java数据结构和算法）最短路径---Dijkstra+Floyd

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参考博文

Floyd算法和Dijkstra算法都不能针对带有负权边的图，否则一直走负权边，没有最小，只有更小！！

Floyd算法

import java.util.Scanner;

//Floyd算法

class Graph{
	public int[][] adjacencyMatrix;
	public int vertexNumber;
	public int arcNumber;

	public static final int INF = 1000000;//这个值要设置的刚刚好，后面存在加运算，以防溢出

	public void createGraph(){
		Scanner scan = new Scanner(System.in);
		System.out.print("请输入图的顶点数：");
		vertexNumber = scan.nextInt();	
		System.out.print("请输入图的边数：");
		arcNumber = scan.nextInt();
		
		adjacencyMatrix = new int[vertexNumber][vertexNumber];
		
		for(int i = 0; i < vertexNumber; i++){
			for(int j = 0; j < vertexNumber; j++){
				adjacencyMatrix[i][j] = Graph.INF;
			}
		}
		for(int i = 0; i < vertexNumber; i++){
			adjacencyMatrix[i][i] = 0;
		}
	
		System.out.println("请输入各条边（顶点+空格+顶点+边权）：");
		for(int i = 0; i < arcNumber; i++){
			int x = scan.nextInt();
			int y = scan.nextInt();
			int w = scan.nextInt();
			adjacencyMatrix[x-1][y-1] = adjacencyMatrix[y-1][x-1] = w;
		}
	}

	public void floyd(){
		for(int k = 0; k < vertexNumber; k++){
			for(int i = 0; i < vertexNumber; i++){
				for(int j = 0; j < vertexNumber; j++){
					if(adjacencyMatrix[i][k] + adjacencyMatrix[k][j] < adjacencyMatrix[i][j]){
						adjacencyMatrix[i][j] = adjacencyMatrix[i][k] + adjacencyMatrix[k][j];
					}
				}
			}
		}
	}
}

public class Main {

	public static void main(String[] args){
		Graph g = new Graph();
		g.createGraph();
		g.floyd();
		for(int i = 0; i < g.vertexNumber; i++){
			System.out.print(g.adjacencyMatrix[0][i]+" ");
		}
		System.out.println();
		
	}
}

Dijkstra算法

import java.util.Scanner;

//Floyd算法

class Graph{
	public int[][] adjacencyMatrix;
	public int vertexNumber;
	public int arcNumber;
	public boolean[] visited;	
	public int[] distance;
	public int[] pre;//记录路径

	public static final int INF = 1000000;//这个值要设置的刚刚好，后面存在加运算，以防溢出

	public void createGraph(){
		Scanner scan = new Scanner(System.in);
		System.out.print("请输入图的顶点数：");
		vertexNumber = scan.nextInt();	
		System.out.print("请输入图的边数：");
		arcNumber = scan.nextInt();
		
		adjacencyMatrix = new int[vertexNumber][vertexNumber];
		visited = new boolean[vertexNumber];
		distance = new int[vertexNumber];			
		pre = new int[vertexNumber];

		for(int i = 0; i < vertexNumber; i++){
			for(int j = 0; j < vertexNumber; j++){
				adjacencyMatrix[i][j] = Graph.INF;
			}
		}
		for(int i = 0; i < vertexNumber; i++){
			adjacencyMatrix[i][i] = 0;
			distance[i] = Graph.INF;
			visited[i] = false;
			pre[i] = -1;
		}
	
		
		System.out.println("请输入各条边（顶点+空格+顶点+边权）：");
		for(int i = 0; i < arcNumber; i++){
			int x = scan.nextInt();
			int y = scan.nextInt();
			int w = scan.nextInt();
			adjacencyMatrix[x-1][y-1] = adjacencyMatrix[y-1][x-1] = w;
		}
	}

	public void dijkstra(int st){
		distance[st] = 0;
		
		for(int i = 0; i < vertexNumber; i++){
			int pos = st;
			int min = Graph.INF;
			//找到一个向外扩展的顶点
			for(int j = 0; j < vertexNumber; j++){
				if(visited[j] == false && distance[j] < min){
					pos = j;
					min = distance[j];
				}
			}
			if(min == Graph.INF){//说明后继没有相连顶点了
				break;
			}
			visited[pos] = true;
			for(int j = 0; j < vertexNumber; j++){
				if(visited[j]==false && distance[pos] + adjacencyMatrix[pos][j] < distance[j] ){
					distance[j] = distance[pos] + adjacencyMatrix[pos][j];
					pre[j] = pos;
				}
			}
		}
		//打印st到各个顶点的最短路径及距离
		for(int i = 0; i < vertexNumber; i++){
			print(pre[i]);
			System.out.println(i+1);
			System.out.println("distance: "+distance[i]);
		}
	}

	public void print(int en){
		if(en == -1){
			return;
		}
		print(pre[en]);
		System.out.print((en+1)+"->");
	}
}

public class Main {

	public static void main(String[] args){
		Graph g = new Graph();
		g.createGraph();
		g.dijkstra(0);	
	}
}