# Algorithm: Prim's Algorithm
# Type: Minimum Spanning Tree, Greedy
# Time Complexity: O(E log V) with a priority queue
# Space Complexity: O(V + E)

function Prim(graph, start):
    create a priority queue Q
    create a set MST to store MST edges
    create a distance array dist initialized with infinity
    dist[start] = 0
    add start vertex to Q with priority 0

    while Q is not empty:
        u = vertex in Q with smallest dist
        remove u from Q
        add u to MST

        for each neighbor v of u:
            if v not in MST and weight(u, v) < dist[v]:
                dist[v] = weight(u, v)
                update priority of v in Q to dist[v]

    return MST edges