Prim Minimum Spanning Tree

Problem

Given n nodes and undirected weighted edges as [u, v, w] triples, return the total weight of a minimum spanning tree, or -1 if the graph is disconnected.

Grow the tree from node 0 using a min-heap of candidate edges, skipping nodes already in the tree. A single node has weight 0.

Hint

The starting node is free; every later pop adds one new node and its cheapest connecting edge.

Test cases

case 1

in: [4,[[0,1,1],[0,2,4],[1,2,2],[1,3,5],[2,3,3]]]

expected: 6

case 2

in: [1,[]]

expected: 0

case 3

in: [3,[[0,1,1]]]

expected: -1

case 4

in: [5,[[0,1,2],[0,2,3],[1,2,1],[2,3,4],[3,4,5],[2,4,6]]]

expected: 12

case 5

in: [2,[[0,1,7]]]

expected: 7

Starter codePython

def prim_mst(n, edges):
    # Your code here
    pass

5 test cases · run your code against them in the editor