Node Way HomeWe have a directed graph G = EV Well define a meeting point as any node that is reachablefrom all other nodes in the graph In the graph below there are two meeting points 0 and 1Implement

code below.

To find the meeting point in a directed graph, we can use the Floyd-Warshall algorithm to find the shortest paths between all pairs of nodes. If there exists a node that is reachable from all other nodes and all other nodes are reachable from it, then that node is the meeting point.

Here's the Python code to implement this algorithm:

def find_meeting_point(graph):
    n = len(graph)
    dist = [[float('inf')] * n for _ in range(n)]
    for u in range(n):
        dist[u][u] = 0
        for v, w in graph[u]:
            dist[u][v] = w
    
    # Floyd-Warshall algorithm
    for k in range(n):
        for i in range(n):
            for j in range(n):
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
    
    # check for meeting point
    for u in range(n):
        if all(dist[u][v] < float('inf') for v in range(n)) and \
           all(dist[v][u] < float('inf') for v in range(n)):
            return u
    
    return None

The input graph is assumed to be a list of adjacency lists, where graph[u] is a list of tuples (v, w) representing edges from node u to node v with weight w.

For example, to find the meeting point in the graph given in the prompt:

graph = [
    [(1, 1), (2, 1)],
    [(2, 1)],
    [(3, 1)],
    [(0, 1)],
]
print(find_meeting_point(graph))  # output: 0 or 1

Note that there are two meeting points in this graph: nodes 0 and 1. The algorithm will return either one of them.