Dijkstra 算法 Python

Question

Given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph. Read more here -> Link

Please go through my code and help me out by pointing what's wrong with my logic.

My code:

from collections import defaultdict

global INT_MAX
INT_MAX = 3 ** 38


class Graph:
    def __init__(self, numofVertices):
        self.vertList = defaultdict(list)
        self.numofVertices = numofVertices

    def addEdge(self, u, v, cost):
        self.vertList[u].append((v, cost))
        self.vertList[v].append((u, cost))

    def minDist(self, dist, visited):
        
        for v in range(self.numofVertices):
            if dist[v] < INT_MAX and v not in visited:
                minIndex = v
        return minIndex

    def dijsktra(self, src):
        dist = [INT_MAX] * self.numofVertices
        dist[src] = 0
        visited = set()

        for _ in range(self.numofVertices):
            minVertex = self.minDist(dist, visited)

            visited.add(minVertex)

            for nbr, edgeCost in self.vertList[minVertex]:
                if dist[nbr] > dist[minVertex] + edgeCost and nbr not in visited:
                    dist[nbr] = dist[minVertex] + edgeCost
        return dist


g = Graph(9)
g.addEdge(0, 1, 4)
g.addEdge(0, 7, 8)
g.addEdge(1, 7, 11)
g.addEdge(7, 8, 7)
g.addEdge(7, 6, 1)
g.addEdge(7, 1, 11)
g.addEdge(1, 2, 8)
g.addEdge(2, 3, 7)
g.addEdge(2, 5, 4)
g.addEdge(2, 8, 2)
g.addEdge(6, 8, 6)
g.addEdge(6, 5, 2)
g.addEdge(5, 2, 4)
g.addEdge(5, 3, 14)
g.addEdge(5, 4, 10)
g.addEdge(3, 4, 9)
print(g.dijsktra(0))

Current Output:

[0, 4, 15, 25, 21, 11, 9, 8, 15] # Index represents the vertex

Expected Output

[0, 4, 12, 19, 21, 11, 9, 8 ,14]

Here's the graph we are solving:

Answer 1

The problem was with the function that checks the min distance, We need to update the current max so that we can compare it with other unvisited vertices and see if another vertex exists with a lesser value.

def minDist(self, dist, visited):
    max1 = 3 ** 38
    minIndex = 0
    for v in range(self.numofVertices):
        if dist[v] < max1 and v not in visited:
            max1 = dist[v]
            minIndex = v
    return minIndex

Answer 2

There is an error in minDist method. It returns the index of first adjacent index, not the one with minimal distance.

This function should look like:

def minDist(self, dist, visited):
    m = INT_MAX
    for v in range(self.numofVertices):
        if dist[v] < m and v not in visited:
            m = dist[v]
            minIndex = v 
    return minIndex

Also, I am not sure that you have to assign both vertList[u] and vertList[v] in addEdge .