Lecture Notes on 26 Apr 2013

Prim's Algorithm for Minimum Cost Spanning Tree

* Graph G = (V, E) is a connected graph with a set of vertices V
  and a set of edges E having non-negative weights.

* T is the set of edges in the minimum cost spanning tre.

* U is the set of vertices in the minimum cost spanning tree.

  /* to begin with the minimum cost spanning tree is empty */
  T = NULL

  /* set of edges E is ordered in increasing weight */

  /* start the tree from an arbitrary vertex */
  U = {1}

  /* maintain two arrays: closest[v] and lowcost[u, v] */

  while (U <= V)
  {
    /* find the least weight edge (u, v) such that u is in U and
    v is V - U */
    /* add edge to minimum cost spanning tree */
    Insert (T, u, v)
    /* add v to set of connected vertices */
    Insert (U, v)
  }