[算法] Sequence Reconstruction

Question
Sequence Reconstruction

Question Description

Check whether the original sequence org can be uniquely reconstructed from the sequences in seqs. The org sequence is a permutation of the integers from 1 to n, with $1 \leq n \leq 10^4$. Reconstruction means building a shortest common supersequence of the sequences in seqs (i.e., a shortest sequence so that all sequences in seqs are subsequences of it). Determine whether there is only one sequence that can be reconstructed from seqs and it is the org sequence.

Example

Example 1:

Input:org = [1,2,3], seqs = [[1,2],[1,3]]
Output: false
Explanation:
[1,2,3] is not the only one sequence that can be reconstructed, because [1,3,2] is also a valid sequence that can be reconstructed.

Example 2:

Input: org = [1,2,3], seqs = [[1,2]]
Output: false
Explanation:
The reconstructed sequence can only be [1,2].

Example 3:

Input: org = [1,2,3], seqs = [[1,2],[1,3],[2,3]]
Output: true
Explanation:
The sequences [1,2], [1,3], and [2,3] can uniquely reconstruct the original sequence [1,2,3].

Language
Python 3

Data structure description
""" @param org: a permutation of the integers from 1 to n @param seqs: a list of sequences @return: true if it can be reconstructed only one or false """


Solution
class Solution: def sequenceReconstruction(self, org, seqs): graph = self.build_graph(seqs) topo_order = self.topo_sort(graph) return topo_order == org def build_graph(self, seqs): graph = {} for seq in seqs: for node in seq: if node not in graph: graph[node] = set() for seq in seqs: for i in range(1, len(seq)): graph[seq[i-1]].add(seq[i]) return graph def topo_sort(self, graph): inDegree = {node: 0 for node in graph} for node in graph: for edge in graph[node]: inDegree[edge] += 1 queue = collections.deque([]) for node in graph: if inDegree[node] == 0: queue.append(node) topo_order = [] while queue: if len(queue) > 1: return [] node = queue.popleft() topo_order.append(node) for edge in graph[node]: inDegree[edge] -= 1 if inDegree[edge] == 0: queue.append(edge) return topo_order

Reference Link
https://www.lintcode.com/problem/sequence-reconstruction/description