Java implementation of Dijkstra shortest path algorithm

　　

Algorithmic Thinking

　　Extends from the center of the starting point to the outer layer until it extends to the end point.

Algorithm main steps

　　1. Construct a two-dimensional array weight storage graph, weight[i][j] represents the weight of node I to node J, that is, the distance from node I to Node J (hereinafter denoted by Dij).

2. Build the array shortpath, store the starting node (0) to the minimum distance of each node , i.e. d0j (j for all nodes), initialize shortpath[0] = 0, and the other values are infinity.

3. Build the array visited to mark whether the nodes have been extended (assuming 0 is extended, 1 is extended), initialize visited[0] = 1, and the other values are zero.

4. Iterate the algorithm, traverse the two-dimensional array weight, select the unmarked node K, which is the shortest distance from the starting node, record the d0k to ShortPath, and Mark K as expanded.

The distance from the starting node to the other nodes is updated by K , if d0j > d0k + dkj, then d0j = d0k + dkj.

　　Code implementation

 Public Static  int[] Dijsktra (int[] weight,intstart) {                        intlength = Weight.length;//get the number of vertices                        int[] ShortPath =New int[Length];//Shortest Path Arrayshortpath[0] = 0;//string[] Path=NewString[length];//record the shortest path from the starting point to each point                         for(inti = 0; i < length; i++) {Path[i]= start + "+" +i; }                        int[] visited =New int[Length];//records whether the shortest path to the current vertex has been calculated, 1 indicates that                         for(inti = 0; i < length; i++) {Visited[i]= 0; } visited[0] = 1;//the shortest path to the starting point has been calculated                         for(intm = 1; m < length; M + +){                                intK =-1; intDMin =Integer.max_value; //Select an unlabeled vertex closest to the starting point, and the shortest path to the starting point is DMin                 for(intn = 0; n < length; n++){                                        if(Visited[n] = = 0 && Weight[start][n] <DMin) {DMin=Weight[start][n]; K=N; }} Shortpath[k]=DMin; VISITED[K]= 1; //To update the distance from the starting point to the other unlabeled points with K as the middle point                 for(intj = 0; J < length; J + +){                                        if(Visited[j] = = 0 && weight[k][j]! = Integer.max_value && weight[start][k] + Weight[k][j] <Weight[start][j]) {Weight[start][j]= Weight[start][k] +Weight[k][j]; PATH[J]= Path[k] + "+" +J; }                }            }                         for(inti = 1; i < length; i + +) {System.out.println ("Starting point to" + i + "Shortest path is:" + path[i] + "Distance:" +Shortpath[i]); }            returnShortPath; }

Declaring constants

 Public Static Final int MAX = Integer.max_value;

Code testing

 Public Static void Main (string[] args) {            int[] [] Weigth = {{0,50,70, Max,max},                              {50,0,15,30, MAX},                              {70,15,0,max,40},                              {MAX,30,max,0,20},                              {max,max,40,20,0}};                        Dijsktra (Weigth,0);        }

Run results

The shortest path from the starting point to 1 is: 0->1 Distance: 50
The shortest path from the starting point to 2 is: 0->1->2 Distance: 65
The shortest path from the starting point to 3 is: 0->1->3 Distance: 80
The shortest path from the starting point to 4 is: 0->1->3->4 Distance: 100

Java implementation of Dijkstra shortest path algorithm