Prims Minimum Spanning Tree Algorithm
A minimal spanning tree (MST) or minimal weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimal possible total edge weight. Currency is an acceptable unit for edge weight – there is no requirement for edge lengths to obey normal rules of geometry such as the triangle inequality.
#include <iostream>
using namespace std;
#define V 4
#define INFINITY 99999
int graph[V][V] = {
{0, 5, 1, 2},
{5, 0, 3, 3},
{1, 3, 0, 4},
{2, 3, 4, 0}};
struct mst
{
bool visited;
int key;
int near;
};
mst MST_Array[V];
void initilize()
{
for (int i = 0; i < V; i++)
{
MST_Array[i].visited = false;
MST_Array[i].key = INFINITY; // considering INFINITY as inifinity
MST_Array[i].near = i;
}
MST_Array[0].key = 0;
}
void updateNear()
{
for (int v = 0; v < V; v++)
{
int min = INFINITY;
int minIndex = 0;
for (int i = 0; i < V; i++)
{
if (MST_Array[i].key < min && MST_Array[i].visited == false && MST_Array[i].key != INFINITY)
{
min = MST_Array[i].key;
minIndex = i;
}
}
MST_Array[minIndex].visited = true;
for (int i = 0; i < V; i++)
{
if (graph[minIndex][i] != 0 && graph[minIndex][i] < INFINITY)
{
if (graph[minIndex][i] < MST_Array[i].key)
{
MST_Array[i].key = graph[minIndex][i];
MST_Array[i].near = minIndex;
}
}
}
}
}
void show()
{
for (int i = 0; i < V; i++)
{
cout << i << " - " << MST_Array[i].near << "\t" << graph[i][MST_Array[i].near] << "\n";
}
}
int main()
{
initilize();
updateNear();
show();
return 0;
}
