Prim's Algorithm Time Complexity

Question

I was looking at the Wikipedia entry for Prim\'s algorithm and I noticed that its time complexity with an adjacency matrix is O(V^2) and its time complexity with a heap and

Answer 1

From the Introduction to Algorithms (Carmen)

Time= Θ(V)·T(EXTRACT-MIN) + Θ(E)·T(DECREASE-KEY)

                   T(EXTRACT-MIN)   T(DECREASE-KEY)   Total

1. array            O(V)             O(1)              O(V^2)
2. binary heap      O(lgV)           O(lgV)            O(E lgV)
3. Fibonacci heap   O(lgV)           O(1)              O(E + VlgV)

Using different data structures causes different time complexities.