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CS 483 – Analysis of Algorithms (Spring 2025)
Prim’s Algorithm Example
Given an undirected graph with five nodes {A, B, C, D, E} and an edge list (source, destination, weight)
of the graph below, find a minimum spanning tree using Prim’s algorithm by choosing A as a start
node.
(A, B, 2)
(A, C, 3)
(B, C, 1)
(B, D, 4)
(C, D, 5)
(C, E, 6)
(D, E, 7)
Answer:
Init Steps:
Start at node A and put it in MST: {A}
Add all edges to neighbors of A in order by weight into Priority Queue: [(A, B, 2), (A, C, 3)]
1st iteration:
Choose the smallest edge: (A, B, 2)
Add B to the MST: {A, B}
Add all edges to neighbors of B in order by weight into Priority Queue: [(B, C, 1), (A, C, 3), (B, D, 4)]
2nd iteration:
Choose the smallest edge: (B, C, 1)
Add C to the MST: {A, B, C}
Add all edges to neighbors of C in order by weight into Priority Queue: [(A, C, 3), (B, D, 4), (C, D, 5), (C,
E, 6)]
3rd iteration:
Choose the smallest edge: (A, C, 3)
C is already in the MST.
NO Update to the MST: {A, B, C}
NO Update to Priority Queue: [(B, D, 4), (C, D, 5), (C, E, 6)]
4th iteration:
Choose the smallest edge: (B, D, 4)
Add D to the MST: {A, B, C, D}
Add all edges to neighbors of D in order by weight into Priority Queue: [(C, D, 5), (C, E, 6), (D, E, 7)]
5th iteration:
Choose the smallest edge: (C, D, 5)
D is already in the MST.
NO Update to the MST: {A, B, C, D}
NO Update to Priority Queue: [(C, E, 6), (D, E, 7)]
6th iteration:
Choose the smallest edge: (C, E, 6)
Add E to the MST: {A, B, C, D, E}
Add all edges to neighbors of E in order by weight into Priority Queue: [(D, E, 7)] – no new neighbors
