Node Way HomeWe have a directed graph G =E V 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 1

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To find the meeting points in this graph, we can use Floyd-Warshall algorithm which can find all-pair shortest paths in a given graph. The algorithm works by considering all possible intermediate nodes between any two nodes and updating the distances accordingly.

Here's the algorithm to find the meeting points:

1. Initialize a 2D array dist[][], where dist[i][j] stores the shortest distance between nodes i and j in the graph.
2. Initialize dist[i][i] = 0 for all nodes i in the graph.
3. For each edge (u, v) in the graph, set dist[u][v] = 1 (assuming all edges have unit weight).
4. For each intermediate node k (1 to n), update dist[i][j] as dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]).
5. For each node i (1 to n), find the maximum distance from i to any other node j in the graph, i.e., max_dist[i] = max(dist[i][j]) for all j.
6. The meeting points in the graph are the nodes with minimum max_dist[i], i.e., meeting_points = {i | max_dist[i] = min(max_dist[j]) for all j}.

Using this algorithm, we can find that the meeting points in the given graph are nodes 0 and 1, as they both have a maximum distance of 2 to any other node in the graph.