下面的代碼取自https://algorithms.tutorialhorizo??n.com/dijkstras-shortest-path-algorithm-spt-adjacency-list-and-min-heap-java-implementation/
它找到從給定源頂點到每個頂點的最短距離，但目前還沒有提供跟蹤所采用路徑的方法。有一個簡單的解決方法嗎？如果不是，我應該如何處理？
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.util.LinkedList;
import java.util.StringTokenizer;
public class DijkstraMinHeap {
static class Edge {
int source;
int destination;
int weight;
public Edge(int source, int destination, int weight) {
this.source = source;
this.destination = destination;
this.weight = weight;
}
}
static class HeapNode{
int vertex;
int distance;
}
static class Graph {
int vertices;
LinkedList<Edge>[] adjacencylist;
Graph(int vertices) {
this.vertices = vertices;
adjacencylist = new LinkedList[vertices];
for (int i = 0; i <vertices ; i ) {
adjacencylist[i] = new LinkedList<>();
}
}
public void addEdge(int source, int destination, int weight) {
Edge edge = new Edge(source, destination, weight);
adjacencylist[source].addFirst(edge);
/**edge = new Edge(destination, source, weight);
adjacencylist[destination].addFirst(edge); //for undirected graph*/
}
public void dijkstra_GetMinDistances(int sourceVertex){
int INFINITY = Integer.MAX_VALUE;
boolean[] SPT = new boolean[vertices];
// //create heapNode for all the vertices
HeapNode [] heapNodes = new HeapNode[vertices];
for (int i = 0; i <vertices ; i ) {
heapNodes[i] = new HeapNode();
heapNodes[i].vertex = i;
heapNodes[i].distance = INFINITY;
}
//decrease the distance for the first index
heapNodes[sourceVertex].distance = 0;
//add all the vertices to the DijkstraMinHeap.MinHeap
MinHeap minHeap = new MinHeap(vertices);
for (int i = 0; i <vertices ; i ) {
minHeap.insert(heapNodes[i]);
}
//while minHeap is not empty
while(!minHeap.isEmpty()){
//extract the min
HeapNode extractedNode = minHeap.extractMin();
//extracted vertex
int extractedVertex = extractedNode.vertex;
SPT[extractedVertex] = true;
//iterate through all the adjacent vertices
LinkedList<Edge> list = adjacencylist[extractedVertex];
for (int i = 0; i <list.size() ; i ) {
Edge edge = list.get(i);
int destination = edge.destination;
//only if destination vertex is not present in SPT
if(SPT[destination]==false ) {
///check if distance needs an update or not
//means check total weight from source to vertex_V is less than
//the current distance value, if yes then update the distance
int newKey = heapNodes[extractedVertex].distance edge.weight ;
int currentKey = heapNodes[destination].distance;
if(currentKey>newKey){
decreaseKey(minHeap, newKey, destination);
heapNodes[destination].distance = newKey;
}
}
}
}
//print SPT
printDijkstra(heapNodes, sourceVertex);
}
public void decreaseKey(MinHeap minHeap, int newKey, int vertex){
//get the index which distance's needs a decrease;
int index = minHeap.indexes[vertex];
//get the node and update its value
HeapNode node = minHeap.mH[index];
node.distance = newKey;
minHeap.bubbleUp(index);
}
public void printDijkstra(HeapNode[] resultSet, int sourceVertex){
System.out.println("Dijkstra's Algorithm: (using Adjacency List and Min Heap)");
for (int i = 0; i <vertices ; i ) {
String x = String.valueOf(resultSet[i].distance);
if(resultSet[i].distance == Integer.MAX_VALUE){
x = "unreachable";
}
System.out.println("Node: " i " | predecessor " resultSet[i].vertex
" | distance: " x);
}
}
}
public static void main(String[] args) throws IOException {
BufferedReader br = new BufferedReader(new FileReader("./vg1.txt"));
printResult(br);
}
public static void printResult(BufferedReader br) throws IOException {
StringTokenizer st = new StringTokenizer((br.readLine()));
int vertices = Integer.parseInt(st.nextToken());
Graph graph = new Graph(vertices);
int K = Integer.parseInt((st.nextToken()));
for (int i = 0; i < K; i ) {
st = new StringTokenizer(br.readLine());
int from = Integer.parseInt(st.nextToken());
int to = Integer.parseInt(st.nextToken());
int weight = Integer.parseInt(st.nextToken());
graph.addEdge(from, to, weight);
}
int source_vertex = 1;
graph.dijkstra_GetMinDistances(source_vertex);
}
static class MinHeap {
int capacity;
int currentSize;
HeapNode[] mH;
int[] indexes; //will be used to decrease the distance
public MinHeap(int capacity) {
this.capacity = capacity;
mH = new HeapNode[capacity 1];
indexes = new int[capacity];
mH[0] = new HeapNode();
mH[0].distance = Integer.MIN_VALUE;
mH[0].vertex = -1;
currentSize = 0;
}
public void display() {
for (int i = 0; i <= currentSize; i ) {
System.out.println(" " mH[i].vertex " distance " mH[i].distance);
}
System.out.println("________________________");
}
public void insert(HeapNode x) {
currentSize ;
int idx = currentSize;
mH[idx] = x;
indexes[x.vertex] = idx;
bubbleUp(idx);
}
public void bubbleUp(int pos) {
int parentIdx = pos / 2;
int currentIdx = pos;
while (currentIdx > 0 && mH[parentIdx].distance > mH[currentIdx].distance) {
HeapNode currentNode = mH[currentIdx];
HeapNode parentNode = mH[parentIdx];
//swap the positions
indexes[currentNode.vertex] = parentIdx;
indexes[parentNode.vertex] = currentIdx;
swap(currentIdx, parentIdx);
currentIdx = parentIdx;
parentIdx = parentIdx / 2;
}
}
public HeapNode extractMin() {
HeapNode min = mH[1];
HeapNode lastNode = mH[currentSize];
// update the indexes[] and move the last node to the top
indexes[lastNode.vertex] = 1;
mH[1] = lastNode;
mH[currentSize] = null;
sinkDown(1);
currentSize--;
return min;
}
public void sinkDown(int k) {
int smallest = k;
int leftChildIdx = 2 * k;
int rightChildIdx = 2 * k 1;
if (leftChildIdx < heapSize() && mH[smallest].distance > mH[leftChildIdx].distance) {
smallest = leftChildIdx;
}
if (rightChildIdx < heapSize() && mH[smallest].distance > mH[rightChildIdx].distance) {
smallest = rightChildIdx;
}
if (smallest != k) {
HeapNode smallestNode = mH[smallest];
HeapNode kNode = mH[k];
//swap the positions
indexes[smallestNode.vertex] = k;
indexes[kNode.vertex] = smallest;
swap(k, smallest);
sinkDown(smallest);
}
}
public void swap(int a, int b) {
HeapNode temp = mH[a];
mH[a] = mH[b];
mH[b] = temp;
}
public boolean isEmpty() {
return currentSize == 0;
}
public int heapSize() {
return currentSize;
}
}
}
uj5u.com熱心網友回復：
嘗試添加 Edge[] edgeTo 陣列，該陣列將跟蹤您用于到達特定頂點的邊。
例如
edgeTo[0] = null
edgeTo[1] = Edge( 0 -> 1 )
edgeto[2] = Edge( 1 -> 2 )
There is the path 0 -> 1 -> 2 and you can find it by traversing backwards.
您可以通過更改以下行來創建這樣的陣列結構：
public void dijkstra_GetMinDistances(int sourceVertex){
int INFINITY = Integer.MAX_VALUE;
boolean[] SPT = new boolean[vertices];
Edge[] edgeTo = new Edge[vertices];
...
并且您將在 if 陳述句中更新此edgeTo陣列，您可以在其中找到較短的距離：
if(currentKey>newKey){
edgeTo[destination] = edge;
decreaseKey(minHeap, newKey, destination);
heapNodes[destination].distance = newKey;
}
最后，將最短部分回傳source_vertex到 any_other_的方法vertex是：
public List<Edge> pathTo(int vertex) {
List<Edge> path = new LinkedList<>();
for (Edge e = edgeTo[vertex]; e != null; e = edgeTo[e.source]) {
path.addFirst(e);
}
return path;
}
所有學分都用于好書和在線課程https://algs4.cs.princeton.edu/home/
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