给定一个说明其已知顺序的元组列表，如何对 N 个元素进行排序？

Question

sorry for the complicated / confusing title.

Basically I'm trying to implement a system that helps with the sorting of documents with no known date of writing. It consists of two inputs:

Input 1: A tuple, where the first element is the number of documents, N . The second element is the number of pairs of documents with a known writing order, L . (First document was written before the second document).

Input 2 : A list of L tuples. Each tuple contains two elements (documents). The first document was written before the second document. Eg: (1 2), (3 4) means that document1 was written before document2 and document3 was written before document4 .

Next, the software must determine if there is a way of sorting all documents chronologically, there can be three outputs:

Inconclusive - Means that the temporal organization of the documents is inconsistent and there is no way of sorting them.

Incomplete - Means that information is lacking and the system can't find a way of sorting.

In case the information is enough, the system should output the order in which the documents have been written.

So far, I have managed to take both inputs, but I do not know where to start in terms of sorting the documents. Any suggestions?

Here's my code so far (Python3):

LN = tuple(int(x.strip()) for x in input("Number of docs. / Number of known pairs").split(' '))
print(LN)
if (LN[1]) > (LN[0]**2):
    print("Invalid number of pairs")
else:
    A = ['none'] * LN[0]
    for i in range(LN[0]):
        t = tuple(int(x.strip()) for x in input("Pair:").split(' '))
        A[i] = t
    print(A)

I appreciate all suggestions:)

Answer 1

Build a directed graph. The inputs are the edges. Check for cycles which would indicate inconsistent input. Find the "leftmost" node, that is the node that doesn't have any edge to it, meaning nothing to its left. Multiple that are leftmost? Incomplete. Then, for each node in the graph, assign the index that equals the length of the longest path from the leftmost node. As there are no (directed) cycles, you could probably just do BFS starting at the leftmost node and at each step assign to the node the maximum of its current value and its value given from its parent. Then iterate through all nodes, and put the numbers in their corresponding indices. Two nodes have the same index assigned? Incomplete.