Java single source shortest path (shortest path,sssp problem) Dijkstra algorithm solution

title: Given a weighted graph, and then given a vertex (source point) in the graph, the shortest distance to all other points, called single source shortest path problem.

For example, find the shortest distance from point 1 to other points

Preparation: The following data is required for the problem

int N; Save Vertex count

int M; Save the number of edges

int Max; Used to set a value that is greater than the weight of all sides to indicate that there is no connection between two points

Int[] Visit; To find the shortest distance of a vertex, set it to 1, which defaults to 0 (not found yet)

Int[][] distance; Saves the values of the edges in the graph, and the infinity between two points is set to Max

Int[] Bestmin; Save the shortest distance from the source point to other points for the final output

string[] path; Some topics will require the output path, save the output path

Algorithm steps:

① find the point that is the shortest distance from the source point, that is, traverse distance[1][1],distance[1][2],..... Distance[1][n] The minimum value, such as the title:

The distance from source point 1 to 2,4,5 is 10, 30,100, respectively. 3 cannot be reached directly at this time distance[1][3] = max. So the point of this step is to find

Vertex 2. At this point, distance[1][2] is the shortest distance from source point 1 to Vertex 2. Set visit[2] to 1 (vertex 2 complete).

② Relaxation operation,

Points identified by ① as the center point (vertex 2 at this point), to traverse Visit[i] to 0 points, if distance[1][2] + Distance[2][i] < Distance[1][i]

The new shorter path is assigned to it, i.e. distance[1][i] = distance[1][2] + distance[2][i],

Vertex 2 can reach at this point only Vertex 3, and distance[1][3] = max, so the value of update distance[1][3] is distance[1][2] + distance[2][3] = 60

After completing the two steps above, go back to step ①, which is a loop, each time the loop can find a minimum distance point and update other points, so the loop will traverse

The shortest distance of all points can be found N-1 times, the approximate process is as follows:

for (int i = 2; I <= N; i++) {

Step ① (Find the shortest distance within a loop)

Step ② (centered on the point found by ①, updating all Visit[i] points to the source point through a loop)

}

The complete code is as follows:

 Packagealgorithm;ImportJava.util.Scanner; Public classDijkstra__single_source_shortest_path {Private Static intN; Private Static intM; Private Static intMax; Private Static int[] visit; Private Static int[] distance; Private Static int[] bestmin; Private Staticstring[] path;  Public Static voidDijkstra () {visit[1] = 1; bestmin[1] = 0; //The Big cycle (this is done here even if the algorithm, the back of the output what can not see)         for(intL = 2; L <= N; l++) {            intDtemp =Max; intK =-1; //Step ①             for(inti = 2; I <= N; i++) {                if(Visit[i] = = 0 && Distance[1][i] <dtemp) {Dtemp= Distance[1][i]; K=i; }} Visit[k]= 1; BESTMIN[K]=dtemp; //Step ②             for(inti = 2; I <= N; i++) {                if(Visit[i] = = 0 && (distance[1][k] + distance[k][i]) < distance[1][i]) {distance[1][i] = Distance[1][k] +Distance[k][i]; Path[i]= Path[k] + "--" +i; }            }        }                //Output Path         for(inti=1;i<=n;i++) {System.out.println (The shortest path from "+1+" to "+i+" is: "+Path[i]); } System.out.println ("=====================================");  for(inti = 1; I <= N; i++) {System.out.println (The shortest distance from 1 to "+ i +" points is: "+Bestmin[i]); }    }     Public Static voidMain (string[] args) {//TODO auto-generated Method StubScanner Input=NewScanner (system.in); System.out.print ("Please enter the number of nodes N, total number of paths m:"); N=Input.nextint (); M=Input.nextint (); Max= 10000; Bestmin=New int[N+1]; Distance=New int[N+1] [N+1]; Visit=New int[N+1]; Path=NewString[n+1];  for(inti = 1; I <= N; i++) {             for(intj = 1; J <= N; J + +) {                if(i = =j) {Distance[i][j]= 0; }Else{Distance[i][j]=Max; }} Bestmin[i]=Max; Path[i]=NewString ("1-->" +i); } System.out.println ("Please enter the" + M + "strip data x, Y, Z (the distance to the Y point from the point of origin is *):");  for(inti = 1; I <= M; i++) {            intx =Input.nextint (); inty =Input.nextint (); intz =Input.nextint (); Distance[x][y]=Z;                } input.close ();    Dijkstra (); }}

The results of the operation are as follows:

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Java single source shortest path (shortest path,sssp problem) Dijkstra algorithm solution