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An alternative minimum spanning tree algorithm is due to Prim [ 121. It works by growing a single tree in successive stages. Start by picking any node as the root. At the start of a stage, some nodes are part of the tree and the rest are not. In each stage, add the minimumcost edge that connects a tree node with a nontree node. An implementation of Prim's algorithm is essentially identical to Dijkstra's shortest-path algorithm given in Section 15.3, with an update rule: (instead of dw=min(dw, dv + cv.w)). Also, as the graph is undirected, each edge appears in two adjacency lists. Implement Prim's algorithm and compare its performance to that of Kruskal's algorithm.

An alternative minimum spanning tree algorithm is due to Prim [ 121. It works by growing a single tree in successive stages. Start by picking any node as the root. At the start of a stage, some nodes are part of the tree and the rest are not. In each stage, add the minimumcost edge that connects a tree node with a nontree node. An implementation of Prim's algorithm is essentially identical to Dijkstra's shortest-path algorithm given in Section 15.3, with an update rule:

(instead of dw=min(dw, dv + cv.w)). Also, as the graph is undirected, each edge appears in two adjacency lists. Implement Prim's algorithm and compare its performance to that of Kruskal's algorithm.

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