学步园

  很经典的一道题目，第K最短路，很多应用都会用到的一个小算法。然后解法也很多，这里用了Dijkstra+A*搜索，每次从最小堆中弹出"c[x]+f[x]"值最小的结点x来继续访问，其中c[x]为从起点访问到x点的距离，f[x]为从x点到终点的最短距离。

  不过为了AC这道题目，倒是犯了几个小错误：

  1：根据题目，就算给定的起点s==给定的终点t，那么必须也要走，最短路径不能为0，所以就有了讨论中很多人说的那句代码 if(s==t)k++;

  2：这个错误我也搞不清楚状况，主要是用Dijkstra计算所有点到终点的最短路径时候，我一开始的代码如下，一直是wrong answer。

		funcArr[beg-1] = 0;
		visFlag[beg-1] = true;
	
		PriorityQueue<HeapNode> queue = new PriorityQueue<HeapNode>(graph.size(),new Comp1());
		for(int i=0;i<graph.get(beg-1).lNodes.size();i++)
		{
		   LinkNode tlNode = graph.get(beg-1).lNodes.get(i);
		   funcArr[tlNode.lid-1] = tlNode.t;
		   queue.add(new HeapNode(tlNode.lid, funcArr[tlNode.lid-1]));
		}

  改为如下就AC了。难道是最近没有常写代码，都愚钝了。

		funcArr[beg-1] = 0;
	
		PriorityQueue<HeapNode> queue = new PriorityQueue<HeapNode>(graph.size(),new Comp1());
		queue.add(new HeapNode(beg, 0));

  最终AC的完整代码：

import java.util.*;

class Node
{
	public Node()
	{
		lNodes = new ArrayList<LinkNode>();
	}
	public ArrayList<LinkNode> lNodes;
}

class LinkNode
{
	public LinkNode()
	{
		lid = 0;
		t = 0;
	}
	
	public LinkNode(int linkId, int time)
	{
		lid = linkId;
		t = time;
	}
	
	public int lid;
	public int t;
}

class HeapNode
{
	public HeapNode(int nid,int cv)
	{
		this.nodeId = nid;
		this.cvalue = cv;
	}
	
	public HeapNode()
	{
		
	}
	
	public HeapNode(int nid, int cv, int fv)
	{
		nodeId = nid;
		cvalue = cv;
		fvalue = fv;
	}
	
	public int nodeId;
	public int cvalue;
	public int fvalue;
}

class Comp1 implements Comparator<HeapNode>
{
	public int compare(HeapNode arg0, HeapNode arg1) {
		return arg0.cvalue - arg1.cvalue;
	}
}

class Comp2 implements Comparator<HeapNode>
{
	public int compare(HeapNode arg0, HeapNode arg1)
	{
		return (arg0.cvalue + arg0.fvalue) - (arg1.cvalue + arg1.fvalue); 
	}
}

public class Main {
	final static int MAX = 1<<30;
	
	public static int[] Dijkstra(ArrayList<Node> graph, int beg)
	{
		int n = graph.size();
		
		int funcArr[] = new int[n];
		boolean visFlag[] = new boolean[n];
		
		for(int i=0;i<n;i++)
		{
			funcArr[i] = MAX;
			visFlag[i] = false;
		}
		
		funcArr[beg-1] = 0;
	
		PriorityQueue<HeapNode> queue = new PriorityQueue<HeapNode>(graph.size(),new Comp1());
		queue.add(new HeapNode(beg, 0));
		
		
		while(queue.isEmpty() == false)
		{
			HeapNode tnode = queue.poll();
			if(visFlag[tnode.nodeId-1] == true)
				continue;
			visFlag[tnode.nodeId-1] = true;
			
			for(int i=0;i<graph.get(tnode.nodeId - 1).lNodes.size();i++)
			{
				LinkNode tlnode = graph.get(tnode.nodeId-1).lNodes.get(i);
				if(funcArr[tnode.nodeId - 1] + tlnode.t < funcArr[tlnode.lid-1])
				{
					funcArr[tlnode.lid-1] = funcArr[tnode.nodeId - 1]  + tlnode.t;
					queue.add(new HeapNode(tlnode.lid, funcArr[tlnode.lid-1]));
				}
			}
		}
		
		return funcArr;
		
	}
	
	public static int AStartKShortestPath(ArrayList<Node> graph, int beg, int end,int k,int[] funcArr)
	{
		if(beg==end)k++;
		int dis = -1;
		int kcount = 0;
		int n = graph.size();
		
		PriorityQueue<HeapNode> queue = new PriorityQueue<HeapNode>(n,new Comp2());
	
		queue.add( new HeapNode(beg,0,funcArr[beg-1]));
		
		while(queue.isEmpty() == false)
		{
			HeapNode hNode= queue.poll();
			if(hNode.nodeId == end)kcount++;
			if(kcount == k)
			{
				//System.out.println(hNode.nodeId+":"+hNode.cvalue+","+hNode.fvalue);
				dis = hNode.cvalue + hNode.fvalue;
				break;
			}
			for(int i=0;i<graph.get(hNode.nodeId-1).lNodes.size();i++)
			{
				LinkNode tlNode = graph.get(hNode.nodeId-1).lNodes.get(i);
				
				if(funcArr[tlNode.lid-1] < MAX)
				{
				  HeapNode tmphnode = new HeapNode(tlNode.lid, hNode.cvalue + tlNode.t, funcArr[tlNode.lid-1]);
				  queue.add(tmphnode);
				}
			}
		}
		
		
		return dis;
	}
	
	public static void main(String[] args)
	{	
		
		//Initialize the graph and transpose graph//////////////////////
		Scanner scan = new Scanner(System.in);
		int n,m;
		n = scan.nextInt();
		m = scan.nextInt();
		
		
		ArrayList<Node> graph = new ArrayList<Node>(n);
		ArrayList<Node> tgraph = new ArrayList<Node>(n);
		
		for(int i=0;i<n;i++)
		{
			graph.add(new Node());
			tgraph.add(new Node());
		}
		
		for(int i=0;i<m;i++)
		{
			int b,e,t;
			b = scan.nextInt();
			e = scan.nextInt();
			t = scan.nextInt();
			
			//Graph
			LinkNode tn0 = new LinkNode(e,t);
			graph.get(b-1).lNodes.add(tn0);
			
			//Transpose graph
			LinkNode tn1 = new LinkNode(b,t);
			tgraph.get(e-1).lNodes.add(tn1);
		}
		
		int s,t,k;
		s = scan.nextInt();
		t = scan.nextInt();
		k = scan.nextInt();
		/////////////////////////////////////////////
		
		int[] funcArr = Dijkstra(tgraph, t);
		int dis = AStartKShortestPath(graph, s, t, k, funcArr);
		
		
		System.out.println(dis);
		

	}

}