In a program, a dictionary contains lists of students and their courses. The teacher is interested to have a dictionary that has the courses as key and the students enrolled in each course as values. Each key has three different values. To address this requirement, write a function to invert the dictionary and implement a solution that satisfies the teacher’s need. In particular, the function will need to turn each of the list items into separate keys in the inverted dictionary. Also provide a technical explanation for the code and its output in minimum 200 words.

Sure, here is a Python function that inverts a dictionary where each key has a list of values:

def invert_dict(d):
    inverted_dict = {}
    for student, courses in d.items():
        for course in courses:
            if course not in inverted_dict:
                inverted_dict[course] = [student]
            else:
                inverted_dict[course].append(student)
    return inverted_dict

This function takes a dictionary d as input, where the keys are students and the values are lists of courses. It initializes an empty dictionary inverted_dict to store the inverted dictionary.

The function then iterates over each key-value pair in the input dictionary. For each student and their list of courses, it iterates over each course. If the course is not already a key in inverted_dict, it adds the course as a key with the student as the value in a list. If the course is already a key in inverted_dict, it appends the student to the list of students for that course.

The function finally returns the inverted_dict, which is a dictionary where the keys are courses and the values are lists of students enrolled in each course.

This function effectively inverts the input dictionary, turning each item in the value lists into separate keys in the inverted dictionary. It satisfies the teacher's need by providing a dictionary that maps each course to the students enrolled in it.

The output of this function will be a dictionary where each key is a course and each value is a list of students. For example, if the input dictionary is {'Alice': ['Math', 'English'], 'Bob': ['Math', 'Science']}, the output will be {'Math': ['Alice', 'Bob'], 'English': ['Alice'], 'Science': ['Bob']}.