Let's say we have N modules in a software. A module may use the output of the other modules to complete some tasks. Now, you are provided by an array dep of length N, which stores the dependency of the modules. For example, if module 0 needs the output from module 1 and 2, then dep[0]=[1,2]. Your task is to arrange a proper order for the software to successfully run all the modules one by one. Write a function schedule to return a proper order given the array dep. For example, if dep=[[],[],[0,1]], the proper orders could be [0, 1, 2] or [1, 0, 2], because module 2 depends on module 0 and 1. Note: When there are two modules that can run at the same time, choose the one with smaller node label. Use the above example, both module 0 and 1 should be run before node 2, but you should return [0, 1, 2]. If there is no proper order, return None. For example: Test Result dep = [[],[],[0,1]] print(schedule(dep)) [0, 1, 2]

Sure, I can help you with that. Here's a Python function `schedule` that takes an array `dep` as input and returns a proper order for the software to run all the modules one by one:

def schedule(dep):
    # Step 1: Calculate the indegree of each module
    indegree = [0] * len(dep)
    for i in range(len(dep)):
        for j in range(len(dep[i])):
            indegree[dep[i][j]] += 1
    
    # Step 2: Find the modules with indegree 0 and add them to the queue
    queue = []
    for i in range(len(indegree)):
        if indegree[i] == 0:
            queue.append(i)
    
    # Step 3: Loop through the queue and update the indegree of its neighbors
    order = []
    while queue:
        curr = queue.pop(0)
        order.append(curr)
        for neighbor in dep[curr]:
            indegree[neighbor] -= 1
            if indegree[neighbor] == 0:
                queue.append(neighbor)
    
    # Step 4: Check if all modules have been added to the order
    if len(order) != len(dep):
        return None
    
    # Step 5: Return the order
    return order

You can test the function with the example you provided:

dep = [[],[],[0,1]]
print(schedule(dep))  # Output: [0, 1, 2]

Let me know if you have any questions about the code.