Fig Dijkstra Algorithm

The C language is implemented as follows: (using the adjacent matrix storage) # include <stdio. h> # include <malloc. h> # define VERTEXNUM 6 // edge element that stores the shortest path, typedef struct edge {int vertex; int value; struct edge * next;} st_edge; void createGraph (int (* edge) [VERTEXNUM], int start, int end, int value); void displayGraph (int (* edge) [VERTEXNUM]); void displayPath (st_edge ** path, int startVertex, int * shortestPath); void dijkstra (int (* edge) [VERTEXNUM], st_edge *** path, int ** ShortestPath, int startVertex, int * vertexStatusArr); int getDistance (int value, int startVertex, int start, int * shortestPath); void createPath (st_edge ** path, int startVertex, int start, int end, int edgeValue); int main (void) {// dynamically create a two-dimensional array int (* edge) for storing edges [VERTEXNUM] = (int (*) [VERTEXNUM]) malloc (sizeof (int) * VERTEXNUM); int I, j; for (I = 0; I <VERTEXNUM; I ++) {for (j = 0; j <VERTEXNUM; j ++) {edge [I] [J] = 0 ;}// stores the vertices traversal status, 0: not traversed, 1: traversed int * vertexStatusArr = (int *) malloc (sizeof (int) * VERTEXNUM); for (I = 0; I <VERTEXNUM; I ++) {vertexStatusArr [I] = 0;} printf ("after init: \ n "); displayGraph (edge); // create a graph createGraph (edge, 6); createGraph (edge, 5); createGraph (edge, 1); createGraph (edge, 1, 2, 5); createGraph (edge, 3); createGraph (edge, 2, 4, 6); createGraph (edge, 2, 3, 5); createGraph (edge, 2, 5, 4); c ReateGraph (edge, 3, 5, 2); createGraph (edge, 4, 5, 6); printf ("after create: \ n"); displayGraph (edge ); // Shortest path/* The storage structure is as follows: path [0]: edge0-> NULLpath [1]: edge1-> NULLpath [2]: edge1-> edge2-> NULLpath [3]: edge1-> edge2-> edge3-> NULLpath [4]: edge4-> NULL: the shortest path from vertex 0 to zero: from 0 to 0 the shortest path from vertex 0 to 1: from 0 to 1 the shortest path from vertex 0 to 2: from 0 to 1, starting from 1 to 2 ...... */st_edge ** path = NULL; // weight of the shortestPath stored/* shortestPath [0] = 0; shortestPath [1] = 8; shortestPath [2] = 12; from vertex 0 The path to 0 is 0. The path from vertex 0 to 1 is 8. The path from vertex 0 to 2 is 12 */int * shortestPath = NULL; // start from vertex 0 to find the shortest path int startVertex = 0; // shortestPath dijkstra (edge, & path, & shortestPath, startVertex, vertexStatusArr); printf ("the path is: \ n "); displayPath (path, startVertex, shortestPath); free (edge); free (path); return 0 ;}// create a diagram void createGraph (int (* edge) [VERTEXNUM], int start, int end, int value) {edge [start] [end] = value; edge [end] [start] = value;} // Print the stored graph void displayGraph (int (* edge) [VERTEXNUM]) {int I, j; for (I = 0; I <VERTEXNUM; I ++) {for (j = 0; j <VERTEXNUM; j ++) {printf ("% d", edge [I] [j]);} printf ("\ n") ;}// print the Shortest path void displayPath (st_edge ** path, int startVertex, int * shortestPath) {int I; st_edge * p; for (I = 0; I <VERTEXNUM; I ++) {printf ("Path from % d to % d:", startVertex, I ); p = * (path + I); while (p! = NULL) {printf ("% d (% d)", p-> vertex, p-> value); p = p-> next ;} printf ("\ n"); printf ("the count is: % d \ n", shortestPath [I]);} // shortestPath void dijkstra (int (* edge) [VERTEXNUM], st_edge *** path, int *** shortestPath, int startVertex, int * vertexStatusArr) {// initialize the shortest path * path = (st_edge **) malloc (sizeof (st_edge *) * VERTEXNUM); int I, j; for (I = 0; I <VERTEXNUM; I ++) {if (I = startVertex) {st_edge * e = (st_edge *) malloc (sizeof (st _ Edge); e-> vertex = startVertex; e-> value = 0; e-> next = NULL; (* path) [I] = e ;} else {(* path) [I] = NULL ;}// initialize the shortestPath value * shortestPath = (int *) malloc (sizeof (int) * VERTEXNUM ); for (I = 0; I <VERTEXNUM; I ++) {if (I = startVertex) {(* shortestPath) [I] = 0;} else {(* shortestPath) [I] =-1 ;}/// starting from vertex 0, vertex 0 is the accessed vertexStatusArr [startVertex] = 1; int shortest, distance, start, end, edgeValue, vNum = 1; // If the vertex has not been accessed, while (vNu M <VERTEXNUM) {shortest = 9999; for (I = 0; I <VERTEXNUM; I ++) {// select the accessed vertex if (vertexStatusArr [I] = 1) {for (j = 0; j <VERTEXNUM; j ++) {// select an unaccessed vertex if (vertexStatusArr [j] = 0) {// select an edge with the smallest value if (edge [I] [j]! = 0 & (distance = getDistance (edge [I] [j], startVertex, I, * shortestPath) <shortest) {shortest = distance; edgeValue = edge [I] [j]; <SPAN style = "WHITE-SPACE: pre"> </SPAN> start = I; end = j ;}}}}} vNum ++; // set the vertex to vertexStatusArr [end] = 1; // Save the shortestPath (* shortestPath) [end] = shortest; // Save the Shortest path createPath (* path, startVertex, start, end, edgeValue) ;}// returns the distance from startVertex to the new vertex int getDistance (int valu E, int startVertex, int start, int * shortestPath) {if (start = startVertex) {return value;} else {return shortestPath [start] + value ;}} // Save the Shortest path void createPath (st_edge ** path, int startVertex, int start, int end, int edgeValue) {if (start = startVertex) {st_edge * newEdge = (st_edge *) malloc (sizeof (st_edge); newEdge-> vertex = end; newEdge-> value = edgeValue; newEdge-> next = NULL; st_edge ** p = path + end; whil E (* p )! = NULL) {p = & (* p)-> next);} * p = newEdge;} else {st_edge ** pCopySrc = path + start; st_edge ** pCopyDes = path + end; st_edge * newEdge = NULL; while (* pCopySrc )! = NULL) {newEdge = (st_edge *) malloc (sizeof (st_edge); * newEdge = ** pCopySrc; newEdge-> next = NULL; * pCopyDes = newEdge; pCopySrc = & (* pCopySrc)-> next); pCopyDes = & (* pCopyDes)-> next);} newEdge = (st_edge *) malloc (sizeof (st_edge); newEdge-> vertex = end; newEdge-> value = edgeValue; newEdge-> next = NULL; * pCopyDes = newEdge ;}}

# Include <stdio. h> # include <malloc. h> # define VERTEXNUM 6 // elements in the vertex's adjacent table // The edge element typedef struct edge {int vertex; int value; struct edge * next;} st_edge; void createGraph (st_edge ** edge, int start, int end, int value); void displayGraph (st_edge ** edge); void delGraph (st_edge ** edge ); void dijkstra (st_edge ** edge, st_edge *** path, int ** shortestPath, int startVertex, int * vertexStatusArr); void displayPath (St_edge ** path, int startVertex, int * shortestPath); int getDistance (int value, int startVertex, int start, int * shortestPath); void createPath (st_edge ** path, int startVertex, int start, int end, int edgeValue); int main (void) {// dynamically create a pointer array st_edge ** edge = (st_edge **) for storing Edges **) malloc (sizeof (st_edge *) * VERTEXNUM); int I; for (I = 0; I <VERTEXNUM; I ++) {edge [I] = NULL ;} // store the vertex traversal status. values 0: not traversed; 1: vertexStatusArr = (int *) Malloc (sizeof (int) * VERTEXNUM); for (I = 0; I <VERTEXNUM; I ++) {vertexStatusArr [I] = 0;} printf ("after init: \ n "); displayGraph (edge); // create a graph createGraph (edge, 6); createGraph (edge, 5); createGraph (edge, 1); createGraph (edge, 5); createGraph (edge, 3); createGraph (edge, 6); createGraph (edge, 5 ); createGraph (edge, 2, 5, 4); createGraph (edge, 3, 5, 2); createGraph (edge, 4, 5, 6); printf ("after create: \ n"); displa YGraph (edge); // Shortest path/* The storage structure is as follows: path [0]: edge0-> NULLpath [1]: edge1-> NULLpath [2]: edge1-> edge2-> NULLpath [3]: edge1-> edge2-> edge3-> NULLpath [4]: edge4-> NULL: the shortest path from vertex 0 to zero: from 0 to 0 the shortest path from vertex 0 to 1: from 0 to 1 the shortest path from vertex 0 to 2: from 0 to 1, starting from 1 to 2 ...... */st_edge ** path = NULL; // weight of the shortestPath stored/* shortestPath [0] = 0; shortestPath [1] = 8; shortestPath [2] = 12; the path from vertex 0 to 0 is the path from vertex 0 to 1. The path from vertex 0 to 2 is 12 */int * shortestPath = NULL; int startVertex = 0; // The Shortest Path Path dijkstra (edge, & path, & shortestPath, startVertex, vertexStatusArr); printf ("the path is: \ n"); displayPath (path, startVertex, shortestPath ); delGraph (edge); edge = NULL; delGraph (path); path = NULL; if (vertexStatusArr! = NULL) {free (vertexStatusArr); vertexStatusArr = NULL;} if (shortestPath! = NULL) {free (shortestPath); shortestPath = NULL;} return 0;} // create a diagram void createGraph (st_edge ** edge, int start, int end, int value) {st_edge * newedge1 = (st_edge *) malloc (sizeof (st_edge); newedge1-> vertex = end; newedge1-> value = value; newedge1-> next = NULL; st_edge ** edge1 = edge + start; while (* edge1! = NULL) {edge1 = & (* edge1)-> next);} * edge1 = newedge1; st_edge * newedge2 = (st_edge *) malloc (sizeof (st_edge )); newedge2-> vertex = start; newedge2-> value = value; newedge2-> next = NULL; st_edge ** edge2 = edge + end; while (* edge2! = NULL) {edge2 = & (* edge2)-> next);} * edge2 = newedge2;} // print the stored figure void displayGraph (st_edge ** edge) {int I; st_edge * p; for (I = 0; I <VERTEXNUM; I ++) {printf ("% d:", I ); p = * (edge + I); while (p! = NULL) {printf ("% d (% d)", p-> vertex, p-> value); p = p-> next ;} printf ("\ n") ;}// print the Shortest path void displayPath (st_edge ** path, int startVertex, int * shortestPath) {int I; st_edge * p; for (I = 0; I <VERTEXNUM; I ++) {printf ("Path from % d to % d:", startVertex, I ); p = * (path + I); while (p! = NULL) {printf ("% d (% d)", p-> vertex, p-> value); p = p-> next ;} printf ("\ n"); printf ("the count is: % d \ n", shortestPath [I]);} // release the memory occupied by the neighboring table void delGraph (st_edge ** edge) {int I; st_edge * p; st_edge * del; for (I = 0; I <VERTEXNUM; I ++) {p = * (edge + I); while (p! = NULL) {del = p; p = p-> next; free (del);} edge [I] = NULL;} free (edge );} // dijkstra calculates the Shortest path void dijkstra (st_edge ** edge, st_edge *** path, int ** shortestPath, int startVertex, int * vertexStatusArr) {// initialize the shortest path * path = (st_edge **) malloc (sizeof (st_edge *) * VERTEXNUM); int I, j; for (I = 0; I <VERTEXNUM; I ++) {if (I = startVertex) {st_edge * e = (st_edge *) malloc (sizeof (st_edge); e-> vertex = startVertex; e-> value = 0; e-> Next = NULL; (* path) [I] = e;} else {(* path) [I] = NULL ;}} // initialize the shortestPath = (int *) malloc (sizeof (int) * VERTEXNUM); for (I = 0; I <VERTEXNUM; I ++) {if (I = startVertex) {(* shortestPath) [I] = 0;} else {(* shortestPath) [I] =-1 ;}} vertexStatusArr [startVertex] = 1; st_edge * p; int shortest, distance, edgeValue, start, end, vNum = 1; // If the while (vNum <VERTEXNUM) {shortest = 9999; for (I = 0; I <VERTEXNUM; I ++ ){/ /Select the accessed vertex if (vertexStatusArr [I] = 1) {for (j = 0; j <VERTEXNUM; j ++) {// select an unaccessed vertex if (vertexStatusArr [j] = 0) {p = * (edge + I); while (p! = NULL) {// if the distance from startVertex to j is less than shortestif (distance = getDistance (p-> value, startVertex, I, * shortestPath )) <shortest & p-> vertex = j) {shortest = distance; edgeValue = p-> value; start = I; end = j ;} p = p-> next ;}}}} vNum ++; vertexStatusArr [end] = 1; // Save the shortestPath weight (* shortestPath) [end] = shortest; // Save the shortest path createPath (* path, startVertex, start, end, edgeValue );}} // returns the distance from startVertex to the new vertex int getDistance (int val Ue, int startVertex, int start, int * shortestPath) {if (start = startVertex) {return value;} else {return value + shortestPath [start];} // Save the Shortest path void createPath (st_edge ** path, int startVertex, int start, int end, int edgeValue) {if (start = startVertex) {st_edge * newEdge = (st_edge *) malloc (sizeof (st_edge); newEdge-> vertex = end; newEdge-> value = edgeValue; newEdge-> next = NULL; st_edge ** p = path + end; whi Le (* p )! = NULL) {p = & (* p)-> next);} * p = newEdge;} else {st_edge ** pCopySrc = path + start; st_edge ** pCopyDes = path + end; st_edge * newEdge = NULL; while (* pCopySrc )! = NULL) {newEdge = (st_edge *) malloc (sizeof (st_edge); * newEdge = ** pCopySrc; newEdge-> next = NULL; * pCopyDes = newEdge; pCopySrc = & (* pCopySrc)-> next); pCopyDes = & (* pCopyDes)-> next);} newEdge = (st_edge *) malloc (sizeof (st_edge); newEdge-> vertex = end; newEdge-> value = edgeValue; newEdge-> next = NULL; * pCopyDes = newEdge ;}}