大二暑假java培训第四天

2018.7.3 内容：dijstra的优化

   今天上课讲数据库Mysql和JDBC，然而我并不想听，于是选择了刷题。 又碰到了dijstra算法的运用变化，不禁感概，dijstra算法还真能出题。但是每次只有80分左右；然后网上查找了下资料 ，原来dijstra在搜寻当前最短权值还可以优化。就以CCF的201609-4交通规划为例：

这道题就是在dijstra的基础上，更新顶点权值时多加上一个相等的判断条件就可以。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
 static int N;
 static List> graph = new ArrayList<>();
 static List searchOrder = new ArrayList<>();
 static boolean[] visited;
 static int[] cost;
 static int[] path;
 
 public static void main(String[] args) {
  Scanner input = new Scanner(System.in);
   N = input.nextInt();
  int M = input.nextInt();
  for(int i = 0;i < N; i++){
   graph.add(new ArrayList<>());
   
  }
  
  for(int i = 0; i < M; i++){
   int firstVertex = input.nextInt();
   int nextVertex = input.nextInt();
   int weight = input.nextInt();
   graph.get(firstVertex - 1).add(new Edge(firstVertex - 1, nextVertex - 1, weight));
   graph.get(nextVertex - 1).add(new Edge(nextVertex - 1, firstVertex - 1, weight));
  }
   dijstra(0);
   int sum = 0;
   for(int i = 1; i < N; i++)
    sum += cost[i];
   System.out.println(sum);
  
 }
 private static void dijstra(int v) {
  path = new int[N];
  cost = new int[N];
  visited = new boolean[N];
  Arrays.fill(path, Integer.MAX_VALUE);
  Arrays.fill(visited, false);
  path[0] = 0;
  while(searchOrder.size() < N){
   int u = -1;
   int max = Integer.MAX_VALUE;
   for(int i = 0; i < N; i++){
    if(!visited[i] && path[i] < max){
     max = path[i];
     u = i;
    }
   }
   visited[u] = true;
   searchOrder.add(u);
   for(Edge edge: graph.get(u)){
    if(!visited[edge.nextVertex]){
     if(path[edge.nextVertex] > path[u] + edge.weight){
      path[edge.nextVertex] = path[u] + edge.weight;
      cost[edge.nextVertex] = edge.weight;
     }
      
     else  if(path[edge.nextVertex] == path[u] + edge.weight)
      cost[edge.nextVertex] = Math.min(cost[edge.nextVertex], edge.weight);
    }
     
   }
   
  }
  
 }
 public static class Edge{
  int firstVertex;
  int nextVertex;
  int weight;
  
  public Edge(int firstVertex, int nextVertex, int weight){
   this.firstVertex = firstVertex;
   this.nextVertex = nextVertex;
   this.weight = weight;
  }
 }

}

结果运行超时。。。

下面是用优先队列优化后的代码

package package1;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;

public class Main {
 static int N;
 static List> graph = new ArrayList<>();
 static int[] cost;
 static int[] path;
 static Queue searchOrder = new PriorityQueue<>();
   
   
 public static void main(String[] args) {
 Scanner input = new Scanner(System.in);
  N = input.nextInt();
 int M = input.nextInt();
 for(int i = 0;i < N; i++){
  graph.add(new ArrayList<>());
  
 }
 
 for(int i = 0; i < M; i++){
  int firstVertex = input.nextInt();
  int nextVertex = input.nextInt();
  int weight = input.nextInt();
  graph.get(firstVertex - 1).add(new Edge(nextVertex - 1, weight));
  graph.get(nextVertex - 1).add(new Edge(firstVertex - 1, weight));
 }
  dijstra(0);
  int sum = 0;
  for(int i = 1; i < N; i++)
   sum += cost[i];
  System.out.println(sum);
 }
 private static void dijstra(int n) {
  // TODO Auto-generated method stub
  cost = new int[N];
  path = new int[N];
  
  Arrays.fill(path, Integer.MAX_VALUE);
  path[0] = 0;
  searchOrder.offer(new Edge(0,0));
  while(!searchOrder.isEmpty()) {
   
   Edge edge = searchOrder.poll();
   int v = edge.firstVertex;
   if(path[v] < edge.weight){
    continue;
   }
   for(int i = 0; i < graph.get(v).size(); i++){
    Edge edge1 = graph.get(v).get(i);
    if(path[edge1.firstVertex] > edge1.weight + path[v]){
     path[edge1.firstVertex] = edge1.weight + path[v];
     searchOrder.offer(new Edge(edge1.firstVertex,path[edge1.firstVertex]));
     cost[edge1.firstVertex] = edge1.weight;
    
    }
    else if(path[edge1.firstVertex] == edge1.weight + path[v])
     cost[edge1.firstVertex] = Math.min(cost[edge1.firstVertex], edge1.weight);
     
   }
    
  }
  
 }
 public static class Edge implements Comparable{
  int firstVertex;
  
  int weight;
  
  public Edge(int firstVertex, int weight){
   this.firstVertex = firstVertex;
   
   this.weight = weight;
  }

  @Override
  public int compareTo(Edge edge) {
   if(this.weight > edge.weight)
    return 1;
   else if(this.weight < edge.weight)
    return -1;
   else
    return 0;
  }
 }

}

结果正确