Leetcode #444: Sequence Reconstruction
In this guide, we solve Leetcode #444 Sequence Reconstruction in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an integer array nums of length n where nums is a permutation of the integers in the range [1, n]. You are also given a 2D integer array sequences where sequences[i] is a subsequence of nums.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Graph, Topological Sort, Array
Intuition
The data forms a graph, so we should explore nodes and edges systematically.
A traversal ensures we visit each node once while maintaining the needed state.
Approach
Build an adjacency list and traverse with BFS or DFS.
Aggregate results as you visit nodes.
Steps:
- Build the graph.
- Traverse with BFS/DFS.
- Accumulate the required output.
Example
Input: nums = [1,2,3], sequences = [[1,2],[1,3]]
Output: false
Explanation: There are two possible supersequences: [1,2,3] and [1,3,2].
The sequence [1,2] is a subsequence of both: [1,2,3] and [1,3,2].
The sequence [1,3] is a subsequence of both: [1,2,3] and [1,3,2].
Since nums is not the only shortest supersequence, we return false.
Python Solution
class Solution:
def sequenceReconstruction(
self, nums: List[int], sequences: List[List[int]]
) -> bool:
n = len(nums)
g = [[] for _ in range(n)]
indeg = [0] * n
for seq in sequences:
for a, b in pairwise(seq):
a, b = a - 1, b - 1
g[a].append(b)
indeg[b] += 1
q = deque(i for i, x in enumerate(indeg) if x == 0)
while len(q) == 1:
i = q.popleft()
for j in g[i]:
indeg[j] -= 1
if indeg[j] == 0:
q.append(j)
return len(q) == 0
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.