1: Dijkstra algorithm
The algorithm can be realized greedy algorithm, by starting from the starting point to find the shortest distance from other points, find the vertex of the shortest distance, and then in the vertex as a transit point, to find
Starting with transit point to other vertices closer distance, in order to find the optimal path step by step through choice!
2: algorithmic process
As shown in FIG flow, the distance to other vertex v0 is set to an array path [0,1,5,65535,65535,65535,65535,65535,65535] where v0 65535 substituting the distance between the point to be infinite. First, find the nearest one vertex in the path to v1, v1 then we as a transit point to update the array, how to update Nepal? V0 to v1 through joining path and reaches the other vertex v0 is smaller than the path directly to the other vertex, instead of directly using the values in the array smaller path. In turn continue the cycle come and find v0 to v2, to v3, to v4, to v5, to v6, to v7, v8 of the distance. On it.
3: Code Example
package nearstWay; import sun.security.util.Length; /** * @Author: dazhu * @date ：Created in 2020/3/18 11:37 * @Description: Shortest Path * @modified By： * @version: $ * / Public class the Main { public static void main (String [] args) { // create a vertex array, the adjacency matrix int INF = 65535 ; Vertex[] vertexList = new Vertex[]{ new Vertex("v0"), new Vertex("v1"), new Vertex("v2"), new Vertex("v3"), new Vertex("v4"), new Vertex("v5"), new Vertex("v6"), new Vertex("v7"), new Vertex("v8") }; int[][] adjMat = new int[][]{ { 0 , 1 , 5 , inf inf inf inf inf inf}, { 1 , 0 , 3 , 7 , 5 , inf inf inf inf}, { 5 , 3 , 0 , inf, 1 , 7 , inf inf inf}, {inf, 7 , inf, 0 , 2 , inf, 3 , inf inf}, {inf, 5 , 1 , 2 , 0 , 3 , 6 , 9 , inf}, {inf inf, 7 , inf, 3 , 0 , inf, 5 , inf}, {inf inf inf, 3 , 6 , inf, 0 , 2 , 7 }, {inf inf inf inf, 9 , 5 , 2 , 0 , 4 }, {inf inf inf inf inf inf, 7 , 4 , 0 }, }; Graph g = new Graph(vertexList,adjMat); Dijkstra djk = new Dijkstra(g); djk.findNearestWay(0); } } class the Dijkstra { public Graph G = null ; public int nVertex; public int [] pathMatirx; // for the shortest path table storing array public int [] shortPathTable; // weight value for storing shortest path points public int [] markArr; // markArr [K] = v0. 1 representative of the shortest path to obtain vk of the public the Dijkstra (Graph G) { the this .g = G; the this .nVertex = g.vertexList.length; // the output initialize the array to the number of vertices graph the this .pathMatirx = new new int[nVertex]; this.shortPathTable = new int[nVertex]; this.markArr = new int[nVertex]; } public void findNearestWay ( int V0) { int V = 0 , W = 0 , K = 0 ; int min; // initialize the data for ( int I = 0 ; I <nVertex; I ++ ) { the this .markArr [I] = 0 ; // initializes to shotPathTable other vertex v0 is the distance the this .shortPathTable [I] = g.adjMat [v0] [I]; // initialize array of paths is 0 the this .pathMatirx [I] = 0 ; } // do not need to claim on behalf of a path between v0 to v0! ! the this .markArr [ 0 ] = . 1 ; // start the main loop, each cycle of v0 to find the shortest path between a vertex v, until all of the vertices are seeking! ! ! for (V = . 1 ; V <nVertex; V ++ ) { min = 65535 ; // current knowledge of the distance from the nearest v0, initialized to a suitable value larger // Find the nearest vertex v0 in for (W = 0 ; W <nVertex; W ++ ) { // if and only if the point and find the shortest path is not less than min the path IF ((markArr [W] == 0 ) && shortPathTable [W] < min) { // save the shortest path to the vertex K K = W; // be replaced by the min the shortest path min = shortPathTable [W]; } } // to find the nearest vertex currently set to 1, vk to v0 represents the shortest path has been found the this .markArr [K] = 1 ; // correction of the current route and the shortest distance! ! // If v0 through the previously determined distance reaches another vertex vk, v0 is smaller than the distance from the other straight lines in vertex // update shortPathTable v0 in [] is the shortest distance for (W = 0 ; W <nVertex; W ++ ) { IF ( markArr [W] == 0 && g.adjMat + min [K] [W] < shortPathTable [W]) { short path table [w] = min + g.adjMat [k] [w]; pathMatirx [i] = k; } } } } } class Graph{ public Vertex[] vertexList; public int adjMat[][]; public int nVerts; public Graph (Vertex [] VertexList, int [] [] adjMat) { // initialization, the vertex array the this .vertexList = VertexList; // Create the matrix side the this .adjMat = adjMat; // initial vertex ordering the this .nVerts = 0 ; } // added vertex to the vertex array public void addVertex (String Lab) { vertexList[nVerts++] = new Vertex(lab); } // add edge to edge matrix // weight 0: a weight of 0 are connected // weight k: k is connected to the right // weight infinity: not connected to public void addEdge ( int Start, int End, int weight) { adjMat[start][end] = weight; adjMat[end][start] = weight; } // display all vertices public void showVertexs () { for ( int I = 0 ; I <vertexList.length; I ++ ) { System.out.println(vertexList[i]); } } // print the specified vertices public void printVertex ( int V) { System.out.println(vertexList[v].label); } } // structure vertex class // vertex can be present in the array, denoted by index, // course also be present in the list class Vertex { public String label; // label public Boolean wasVisited; // if traversed indicia. public Vertex (String label) { the this .label = label; wasVisited = false; } }