minimum_spanning_tree_prims.py

import sys
from collections import defaultdict


def PrimsAlgorithm(l):

    nodePosition = []

    def getPosition(vertex):
        return nodePosition[vertex]

    def setPosition(vertex, pos):
        nodePosition[vertex] = pos

    def topToBottom(heap, start, size, positions):
        if start > size // 2 - 1:
            return
        else:
            if 2 * start + 2 >= size:
                m = 2 * start + 1
            else:
                if heap[2 * start + 1] < heap[2 * start + 2]:
                    m = 2 * start + 1
                else:
                    m = 2 * start + 2
            if heap[m] < heap[start]:
                temp, temp1 = heap[m], positions[m]
                heap[m], positions[m] = heap[start], positions[start]
                heap[start], positions[start] = temp, temp1

                temp = getPosition(positions[m])
                setPosition(positions[m], getPosition(positions[start]))
                setPosition(positions[start], temp)

                topToBottom(heap, m, size, positions)

    # Update function if value of any node in min-heap decreases
    def bottomToTop(val, index, heap, position):
        temp = position[index]

        while index != 0:
            if index % 2 == 0:
                parent = int((index - 2) / 2)
            else:
                parent = int((index - 1) / 2)

            if val < heap[parent]:
                heap[index] = heap[parent]
                position[index] = position[parent]
                setPosition(position[parent], index)
            else:
                heap[index] = val
                position[index] = temp
                setPosition(temp, index)
                break
            index = parent
        else:
            heap[0] = val
            position[0] = temp
            setPosition(temp, 0)

    def heapify(heap, positions):
        start = len(heap) // 2 - 1
        for i in range(start, -1, -1):
            topToBottom(heap, i, len(heap), positions)

    def deleteMinimum(heap, positions):
        temp = positions[0]
        heap[0] = sys.maxsize
        topToBottom(heap, 0, len(heap), positions)
        return temp

    visited = [0 for i in range(len(l))]
    Nbr_TV = [-1 for i in range(len(l))]  # Neighboring Tree Vertex of selected vertex
    # Minimum Distance of explored vertex with neighboring vertex of partial tree formed in graph
    Distance_TV = []  # Heap of Distance of vertices from their neighboring vertex
    Positions = []

    for x in range(len(l)):
        p = sys.maxsize
        Distance_TV.append(p)
        Positions.append(x)
        nodePosition.append(x)

    TreeEdges = []
    visited[0] = 1
    Distance_TV[0] = sys.maxsize
    for x in l[0]:
        Nbr_TV[x[0]] = 0
        Distance_TV[x[0]] = x[1]
    heapify(Distance_TV, Positions)

    for i in range(1, len(l)):
        vertex = deleteMinimum(Distance_TV, Positions)
        if visited[vertex] == 0:
            TreeEdges.append((Nbr_TV[vertex], vertex))
            visited[vertex] = 1
            for v in l[vertex]:
                if visited[v[0]] == 0 and v[1] < Distance_TV[getPosition(v[0])]:
                    Distance_TV[getPosition(v[0])] = v[1]
                    bottomToTop(v[1], getPosition(v[0]), Distance_TV, Positions)
                    Nbr_TV[v[0]] = vertex
    return TreeEdges


if __name__ == "__main__":
    # < --------- Prims Algorithm --------- >
    n = int(input("Enter number of vertices: ").strip())
    e = int(input("Enter number of edges: ").strip())
    adjlist = defaultdict(list)
    for x in range(e):
        l = [int(x) for x in input().strip().split()]
        adjlist[l[0]].append([l[1], l[2]])
        adjlist[l[1]].append([l[0], l[2]])
    print(PrimsAlgorithm(adjlist))