I'm having trouble with a coding question. I have attempted a solution (see below), but am stuck on one part and would like suggestions.
Question: Consider an academic program that consists of N courses. Some courses have others as prerequisites. For example, if course 2 is a prerequisite of course 3 you must finish course 2 before enrolling in course 3. You can attend only a single course at a time. Build a schedule to complete all courses in a linear sequence and to satisfy all prerequisites for every course. If more than one variant of possible schedule exists, use the schedule where courses with smaller indices are finished first.
For example:
4
1 0
2 0
3 1 2
The first row means that there are 4 courses in the academic program. The second and third rows define that course 0 must be taken before courses 1 and 2. And the fourth row defines that courses 1 and 2 must be taken before course 3.
Output: A schedule containing a space-delimited list of courses, in the order of their attendance. For example:
0 1 2 3
For this example, another schedule exists 0 2 1 3. But we must select the variant 0 1 2 3 where course 1 (with a smaller index) is attended before the course 2 (with a greater index).
Test 1
Test Input
4
1 0
2 0
3 1 2
Expected Output
0 1 2 3
Test 2
Test Input
7
0 1 2
1 3
2 3
3 4 5
4 6
5 6
Expected Output
6 4 5 3 1 2 0
Test 3
Test Input
8
4 0 2
0 1 6
2 3 7
1 5
6 5
3 5
7 5
Expected Output
5 1 3 6 0 7 2 4
Solution Attempt:
I recognized this as just performing BFS on an undirected graph with the courses and prerequisites as edges connected to each other.
import collections
graph = collections.defaultdict(set)
def add_edge_undirected(graph, u, v):
if not (u in graph and v in graph[u]) or not (v in graph and u in graph[v]):
graph[u].add(v)
graph[v].add(u)
def bfs(graph, root, ans):
visited, queue = set(), collections.deque([root])
visited.add(root)
while queue:
print(queue)
vertex = queue.popleft()
ans.append(vertex)
for neighbour in graph[vertex]:
if neighbour not in visited:
visited.add(neighbour)
queue.append(neighbour)
def main():
inputs = [[4, 0, 2], [0, 1, 6], [2, 3, 7], [1, 5], [6, 5], [3, 5], [7, 5]] # test case 3
start = 5 # we are starting from vertex 5 because that is the first course in the entire sequence
for prereq in inputs:
for i in range(1, len(prereq)):
add_edge_undirected(graph, prereq[0], prereq[i])
ans = []
bfs(graph, start, ans)
print(ans)
main()
Sample Input: Test case 3. Terminal Output: [5, 1, 3, 6, 7, 0, 2, 4] Expected Output: [5, 1, 3, 6, 0, 7, 2, 4]
Here are the issues I am having. (1) The bfs doesn't take into account the order (priority) of courses that should be taken. Any suggestions on how to take into account the priority? (2) How do I figure out the start vertex for bfs? I can tell from drawing the graph but how can I tell from the input?
Any suggestions would be appreciated
