Prim algorithm -- Minimum Spanning Tree

# Include <stdio. h> <br/> # define N 6 <br/> # define TRUE 1 <br/> # define FALSE 0 <br/> # define MAX_VALUE 9999 <br/> typedef struct edge {<br/> int from; <br/> int to; <br/> float weight; <br/>} edge; <br/> edge path [N]; // save steps 1st to N-1 <br/> float c [N + 1] [N + 1]; // Save the information of the adjacent matrix <br/> int closest [N + 1]; // ID of the vertex closest to j in S <br/> float lowcost [N + 1]; // lowcost [j] = c [j] [closest [j] is the distance from the closest vertex of j to S <br/> int s [N + 1]; // indicates whether a vertex is added. <Br/> void prim () {<br/> int I; <br/> s [1] = TRUE; // Add vertex 1 to the Minimum Spanning Tree <br/> for (I = 2; I <= N; I ++) {// initialization <br/> lowcost [I] = c [1] [I]; // minimum distance from any point to the S set, this is equivalent to the distance to vertex 1, because there is only one vertex in S <br/> closest [I] = 1; // any point is closest to vertex 1 in the S set (because only vertex 1 in the S set) <br/> s [I] = FALSE; // No vertex is added to the S collection <br/>}< br/> int pf = 1; <br/> for (I = 1; I <N; I ++) {<br/> float min = MAX_VALUE; <br/> int j = 1; <br/> for (int k = 2; k <= N; k ++) {// select a vertex that is not selected into the minimum spanning tree. Min distance from vertex in S <br/> if (lowcost [k] <min &&(! S [k]) {<br/> min = lowcost [k]; <br/> j = k; <br/>}< br/> printf ("% d, % d/n", j, closest [j]); <br/> path [pf]. from = j; <br/> path [pf]. to = closest [j]; <br/> path [pf]. weight = c [j] [closest [j]; <br/> pf ++; </p> <p> s [j] = TRUE; <br/> for (k = 2; k <= N; k ++) {// for all vertices that do not have the smallest Spanning Tree selected, update <br/> if (c [j] [k] <lowcost [k] & (! S [k]) {<br/> lowcost [k] = c [j] [k]; <br/> closest [k] = j; <br/>}</p> <p> void main () {<br/> c [1] [1] = MAX_VALUE; // vertex 1 <br/> c [1] [2] = 6; <br/> c [1] [3] = 1; <br/> c [1] [4] = 5; <br/> c [1] [5] = MAX_VALUE; <br/> c [1] [6] = MAX_VALUE; <br/> c [2] [1] = 6; // vertex 2 <br/> c [2] [2] = MAX_VALUE; <br/> c [2] [3] = 5; <br/> c [2] [4] = MAX_VALUE; <br/> c [2] [5] = 3; <br/> c [2] [6] = MAX_VALUE; <br/> c [3] [1] = 1; // vertex 3 <br/> c [3] [2] = 5; <br/> c [3] [3] = MAX_VALUE; <br/> c [3] [4] = 5; <br/> c [3] [5] = 6; <br/> c [3] [6] = 4; <br/> c [4] [1] = 5; // vertex 4 <br/> c [4] [2] = MAX_VALUE; <br/> c [4] [3] = 5; <br/> c [4] [4] = MAX_VALUE; <br/> c [4] [5] = MAX_VALUE; <br/> c [4] [6] = 2; <br/> c [5] [1] = MAX_VALUE; // vertex 5 <br/> c [5] [2] = 3; <br/> c [5] [3] = 6; <br/> c [5] [4] = MAX_VALUE; <br/> c [5] [5] = MAX_VALUE; <br/> c [5] [6] = 6; <br/> c [6] [1] = MAX_VALUE; // vertex 6 <br/> c [6] [2] = MAX_VALUE; <br/> c [6] [3] = 4; <br/> c [6] [4] = 2; <br/> c [6] [5] = 6; <br/> c [6] [6] = MAX_VALUE; </p> <p> prim (); </p> <p> printf ("-------------------------------------------/n"); <br/> printf ("The path is:/n "); <br/> for (int I = 1; I <N; I ++) {<br/> printf ("% d ---- % d Weigth: %. 2f/n ", path [I]. from, path [I]. to, path [I]. weight); <br/>}< br/>}