Dijkstra演算法，可以從給定一個圖和圖中的源頂點src，找到從src到給定圖中所有頂點的最短路徑。但是圖不能包含負權重邊。時間複雜度O(n^2)。以下程式碼參考：https://blog.csdn.net/shui2104/article/details/107053966，與原文程式碼不同的是根據需要增加了最短路徑的計算。該博主把演算法的原理以及過程都解釋非常的詳細，具體演算法的過程詳解請參考https://blog.csdn.net/shui2104/article/details/107053966

package graph.dijkstra;
​
import java.util.Arrays;
​
public class ShortestPathOfDijkstra {
   private static final int MAX = 10000;
​
   /**
   * 接受一個有向圖的權重矩陣，和一個起點編號start（從0編號，頂點存在陣列中)
   *
   * @param graph      graph
   * @param startPointIndex startPointIndex
   * @return 返回一個int[] 陣列，表示從start到它的最短路徑長度
   */
   public static int[] dijsktra(int[][] graph, int startPointIndex) {
     int length = graph.length;
     //標記當前該頂點的最短路徑是否已經求出，true表示已經求出
     boolean[] visited = new boolean[length];
     //start點的最短距離已經求出
     for (int i = 0; i < graph.length; i++) {//初始化s集合，只有起始點
       if (i == startPointIndex) {
         visited[i] = true;
       } else {
         visited[i] = false;
       }
     }
​
     //存放從start到各個點的最短距離
     int[] shortDistance = new int[length];
​
     for (int i = 0; i < graph.length; i++) {//初始化，起始點到其他點的距離。
       shortDistance[i] = graph[startPointIndex][i];
     }
​
     //start到他本身的距離最短為0
     shortDistance[startPointIndex] = 0;
​
​
     //存放從start點到各點的最短路徑的字串表示
     String[] path = new String[length];
     for (int i = 0; i < length; i++) {
       path[i] = startPointIndex + "->" + i;
     }
​
     for (int count = 1; count < length; count++) {
       int k = -1;
       int dmin = MAX;
       for (int i = 0; i < length; i++) {
         if (!visited[i] && shortDistance[i] < dmin) {
           dmin = shortDistance[i];
           k = i;
         }
       }
       //選出一個距離start最近的未標記的頂點   將新選出的頂點標記為以求出最短路徑，且到start的最短路徑為dmin。
       shortDistance[k] = dmin;
       visited[k] = true;
       //以k為中間點，修正從start到未訪問各點的距離
       for (int i = 0; i < length; i++) {
         if (!visited[i] && shortDistance[k] + graph[k][i] < shortDistance[i]) {
           shortDistance[i] = shortDistance[k] + graph[k][i];
           path[i] = path[k] + "->" + i;
         }
       }
     }
     for (int i = 0; i < length; i++) {
       System.out.println("從" + startPointIndex + "出發到" + i + "的最短路徑為：" + path[i] + "=" + shortDistance[i]);
     }
     return shortDistance;
   }
​
   public static void main(String[] args) {
     int[][] graph = {
         {0, 4, 6, 6, MAX, MAX, MAX},
         {MAX, 0, 1, MAX, 7, MAX, MAX},
         {MAX, MAX, 0, MAX, 6, 4, MAX},
         {MAX, MAX, 2, 0, MAX, 5, MAX},
         {MAX, MAX, MAX, MAX, 0, MAX, 6},
         {MAX, MAX, MAX, MAX, 1, 0, 8},
         {MAX, MAX, MAX, MAX, MAX, MAX, MAX}};
     int start = 0;
     int[] dijsktra = dijsktra(graph, start);
     System.out.println(Arrays.toString(dijsktra));
   }
}