Reconstructing Sequence

Prereq: Topological Sort

Check whether the original sequence original can be uniquely reconstructed from the sequences in seqs.

The original sequence is a permutation of the integers from 1 to n.

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 orginal sequence.

Parameters

• original: A list of integers of size n representing the original sequence.
• seqs: A list of sequences of size m representing the sequences to be reconstructed.

Result

• true or false, depending on whether the original sequence can be uniquely reconstructed.

Examples

Example 1:

Input: orgignal: [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: orgignal: [1,2,3], seqs: [[1,2]]

Output: false

Explanation:

The reconstructed sequence can only be [1,2].

Example 3:

Input: orginal: [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].

Example 4:

Input: orgignal: [4,1,5,2,6,3], seqs: [[5,2,6,3], [4,1,5,2]]

Output: true

Constraints

• 1 <= n <= 10^4
• 1 <= m <= 10^4
• 1 <= len(seqs[i]) <= n

Try it yourself

Solution