Answer
See the explanation
Work Step by Step
To check whether a route between two nodes exists in a directed graph, you can use a graph traversal algorithm such as Depth-First Search (DFS) or Breadth-First Search (BFS). Here's an algorithm using DFS:
1. Start with an empty visited set to keep track of visited nodes.
2. Create a function, let's call it `hasRoute`, that takes the following parameters:
- `graph`: The directed graph.
- `start`: The starting node.
- `end`: The target node.
- `visited`: The set of visited nodes.
3. If `start` is equal to `end`, return `True` as we have found a route.
4. Add `start` to the `visited` set.
5. For each neighbor `neighbor` of `start` in the graph:
- If `neighbor` is not in the `visited` set, recursively call `hasRoute` with `neighbor` as the new `start` node.
- If the recursive call returns `True`, return `True` as we have found a route.
6. If no route is found after iterating through all neighbors, return `False`.
Here's the implementation of the algorithm in Python:
```python
def hasRoute(graph, start, end, visited):
if start == end:
return True
visited.add(start)
for neighbor in graph[start]:
if neighbor not in visited:
if hasRoute(graph, neighbor, end, visited):
return True
return False
```
You can call the `hasRoute` function with the directed graph, starting node, target node, and an empty set as the visited set. If the function returns `True`, it means there is a route between the two nodes; otherwise, there is no route.
