Problem Statement
A class has N number of students. When the students submit an assignment, they are assigned K peers to review their assignments and provide feedback such that 0 < K < N. Now, if given the input N and K, return a dict (Python) Object (JavaScript) or something equivalent in other languages in the format, student: [list of reviewers] adhering to the following rules:
- Each student should be assigned K reviewers.
- The student cannot review his/her own work.
- There shouldn’t be multiple reviews by the same person. Each reviewer assigned should be unique.
I should return 0/False if there is an error in the input conditions such K >= N
Example:
Input: N=3, K=1
Output:
{
0: [1],
1: [2],
2: [0]
}
Input: N=3, K=2
{
0: [1,2],
1: [2,0],
2: [0,1]
}
Solution
def generate_peer_pairs(N, K):
"""A function that provides unique peers for reviewing.
The generated matches follow the following rules:
1. The no.of reviews/rounds of review is less than total no.of users.
2. The user won't be reviewing his/her own work
3. All the reviewers assigned would be unique.
4. Each user will have equal no.of reviews to give and receive.
:param N: Total no.of student for whom the matching is to be done.
:param K: The no.of reviews each student is supposed to receive.
:returns: a dictionary of graders and their peers { grader_id: [peer_1, peer_2, ...]}
"""
if K >= N:
return False
available_offsets = list(range(1, N))
offsets = []
while len(offsets) < rounds:
offset = random.choice(available_offsets)
offsets.append(offset)
available_offsets.remove(offset)
students = list(range(N))
random.shuffle(students)
allocations = {}
for idx, student in enumerate(students):
allocations[student] = [students[(idx + offset) % N] for offset in offsets])
return allocations
Notes
The problem is an interesting one. I started out with the idea that the peers should be arranged in a random way and wrote an algorithm by selecting a random recipient while looping over each grader. It was completely non-roboust and failed to make the right pairs more times that it worked.
The solution if you had noticed, is completely a position shifting algorithm. What appears a non-repeating random order for the grader and the recipient is not really that random.