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# Prim's Algorithm For Finding Minimum Spanning Trees In C

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```The is a straight-forward implementation of Prim's Algorithm for finding the minimum spanning tree of a graph.

A detailed explanation is given here.

```
#include

/*
The input file (weight.txt) look something like this
4
0 0 0 21
0 0 8 17
0 8 0 16
21 17 16 0

The first line contains n, the number of nodes.
Next is an nxn matrix containg the distances between the nodes
NOTE: The distance between a node and itself should be 0
*/

int n; /* The number of nodes in the graph */

int weight[100][100]; /* weight[i][j] is the distance between node i and node j;
if there is no path between i and j, weight[i][j] should
be 0 */

char inTree[100]; /* inTree[i] is 1 if the node i is already in the minimum
spanning tree; 0 otherwise*/

int d[100]; /* d[i] is the distance between node i and the minimum spanning
tree; this is initially infinity (100000); if i is already in
the tree, then d[i] is undefined;
this is just a temporary variable. It's not necessary but speeds
up execution considerably (by a factor of n) */

int whoTo[100]; /* whoTo[i] holds the index of the node i would have to be
linked to in order to get a distance of d[i] */

/* updateDistances(int target)
should be called immediately after target is added to the tree;
updates d so that the values are correct (goes through target's
neighbours making sure that the distances between them and the tree
are indeed minimum)
*/
void updateDistances(int target) {
int i;
for (i = 0; i < n; ++i)
if ((weight[target][i] != 0) && (d[i] > weight[target][i])) {
d[i] = weight[target][i];
whoTo[i] = target;
}
}

int main(int argc, char *argv[]) {
FILE *f = fopen("dist.txt", "r");
fscanf(f, "%d", &n);
int i, j;
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
fscanf(f, "%d", &weight[i][j]);
fclose(f);

/* Initialise d with infinity */
for (i = 0; i < n; ++i)
d[i] = 100000;

/* Mark all nodes as NOT beeing in the minimum spanning tree */
for (i = 0; i < n; ++i)
inTree[i] = 0;

/* Add the first node to the tree */
printf("Adding node %c\n", 0 + 'A');
inTree[0] = 1;
updateDistances(0);

int total = 0;
int treeSize;
for (treeSize = 1; treeSize < n; ++treeSize) {
/* Find the node with the smallest distance to the tree */
int min = -1;
for (i = 0; i < n; ++i)
if (!inTree[i])
if ((min == -1) || (d[min] > d[i]))
min = i;

printf("Adding edge %c-%c\n", whoTo[min] + 'A', min + 'A');
inTree[min] = 1;
total += d[min];

updateDistances(min);
}

printf("Total distance: %d\n", total);

return 0;
}

``````
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