I have seen many varients of complexities using diferent data structures in implementing Prims Agorithm. Can you pls post standard algorithm and tells me in details how to derive the complexities. Please also mention the variations possibles when data structure changes and How will effect the complexity taking Best case and Worst case senarios .

Consider the following graph and Assume node ‘P’ as the starting vertex for Prim’s algorithm. Which of the following can be the correct order of edges in which they are added to construct Minimum Spanning Tree (MST)? P-Q, P-X, X-V, V-U, U-R, R-S, R-W, S-T P-Q, P-X, X-V, V-U, U-R, R-W, R-S, S-T P-Q, Q-R, R-W, W-V, V-X, V-U, R-S, S-T P-Q, Q-R, R-W, R-S, V-X, V-U, W-V, S-T

Assuming that the graph can contain repeated edge weights, we have a single tree at any instance when applying Prim's algorithm. Justify this statement.