Return the Prerequisite Route for a Target Course

Question

You are asked to return the prerequisite route for a target course given a graph that represents course dependencies. The solution should only include the courses necessary to complete the target course.

Codemia · Accepted Answer

To solve the problem of finding the prerequisite route for a target course, we can represent the courses and their dependencies as a directed graph. Each course is a node, and a directed edge from course A to course B indicates that course A is a prerequisite for course B. We will use depth-first search (DFS) to explore the graph and collect the prerequisites for the target course.

1. Construct the graph from the given list of course dependencies.
2. Implement a DFS function that traverses the graph starting from the target course.
3. Maintain a list to store the prerequisites found during the traversal.
4. Return the list of prerequisites once the traversal is complete.

The time complexity of this approach is O(V + E), where V is the number of courses (vertices) and E is the number of dependencies (edges) in the graph. The space complexity is O(V) for storing the visited nodes and the recursion stack during DFS.

```python
from collections import defaultdict

def find_prerequisites(courses, target):
    graph = defaultdict(list)
    for course, prereq in courses:
        graph[course].append(prereq)

def dfs(course, visited):
        if course in visited:
            return
        visited.add(course)
        for prereq in graph[course]:
            dfs(prereq, visited)

prerequisites = set()
    dfs(target, prerequisites)
    return list(prerequisites)

# Example usage:
courses = [('CS101', 'CS100'), ('CS102', 'CS101'), ('CS103', 'CS102')]
target = 'CS103'
print(find_prerequisites(courses, target))  # Output: ['CS101', 'CS100', 'CS102']
```

Interviewers are looking for a clear understanding of graph traversal techniques and the ability to implement a solution efficiently. They also want to see how well you can explain your thought process and handle potential edge cases, such as cycles in the graph or disconnected components.

Return the Prerequisite Route for a Target Course

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