444. Sequence Reconstruction

Description

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.

Check if nums is the shortest possible and the only supersequence. The shortest supersequence is a sequence with the shortest length and has all sequences[i] as subsequences. There could be multiple valid supersequences for the given array sequences.

  • For example, for sequences = [[1,2],[1,3]], there are two shortest supersequences, [1,2,3] and [1,3,2].
  • While for sequences = [[1,2],[1,3],[1,2,3]], the only shortest supersequence possible is [1,2,3]. [1,2,3,4] is a possible supersequence but not the shortest.

Return true if nums is the only shortest supersequence for sequences, or false otherwise.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

 

Example 1:

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.

Example 2:

Input: nums = [1,2,3], sequences = [[1,2]]
Output: false
Explanation: The shortest possible supersequence is [1,2].
The sequence [1,2] is a subsequence of it: [1,2].
Since nums is not the shortest supersequence, we return false.

Example 3:

Input: nums = [1,2,3], sequences = [[1,2],[1,3],[2,3]]
Output: true
Explanation: The shortest possible supersequence is [1,2,3].
The sequence [1,2] is a subsequence of it: [1,2,3].
The sequence [1,3] is a subsequence of it: [1,2,3].
The sequence [2,3] is a subsequence of it: [1,2,3].
Since nums is the only shortest supersequence, we return true.

 

Constraints:

  • n == nums.length
  • 1 <= n <= 104
  • nums is a permutation of all the integers in the range [1, n].
  • 1 <= sequences.length <= 104
  • 1 <= sequences[i].length <= 104
  • 1 <= sum(sequences[i].length) <= 105
  • 1 <= sequences[i][j] <= n
  • All the arrays of sequences are unique.
  • sequences[i] is a subsequence of nums.

Solutions

Solution 1

Python Code
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class Solution:
    def sequenceReconstruction(
        self, nums: List[int], sequences: List[List[int]]
    ) -> bool:
        g = defaultdict(list)
        indeg = [0] * len(nums)
        for seq in sequences:
            for a, b in pairwise(seq):
                g[a - 1].append(b - 1)
                indeg[b - 1] += 1
        q = deque(i for i, v in enumerate(indeg) if v == 0)
        while q:
            if len(q) > 1:
                return False
            i = q.popleft()
            for j in g[i]:
                indeg[j] -= 1
                if indeg[j] == 0:
                    q.append(j)
        return True

Java Code
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class Solution {
    public boolean sequenceReconstruction(int[] nums, List<List<Integer>> sequences) {
        int n = nums.length;
        int[] indeg = new int[n];
        List<Integer>[] g = new List[n];
        Arrays.setAll(g, k -> new ArrayList<>());
        for (var seq : sequences) {
            for (int i = 1; i < seq.size(); ++i) {
                int a = seq.get(i - 1) - 1, b = seq.get(i) - 1;
                g[a].add(b);
                indeg[b]++;
            }
        }
        Deque<Integer> q = new ArrayDeque<>();
        for (int i = 0; i < n; ++i) {
            if (indeg[i] == 0) {
                q.offer(i);
            }
        }
        while (!q.isEmpty()) {
            if (q.size() > 1) {
                return false;
            }
            int i = q.poll();
            for (int j : g[i]) {
                if (--indeg[j] == 0) {
                    q.offer(j);
                }
            }
        }
        return true;
    }
}

C++ Code
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class Solution {
public:
    bool sequenceReconstruction(vector<int>& nums, vector<vector<int>>& sequences) {
        int n = nums.size();
        vector<vector<int>> g(n);
        vector<int> indeg(n);
        for (auto& seq : sequences) {
            for (int i = 1; i < seq.size(); ++i) {
                int a = seq[i - 1] - 1, b = seq[i] - 1;
                g[a].push_back(b);
                ++indeg[b];
            }
        }
        queue<int> q;
        for (int i = 0; i < n; ++i)
            if (indeg[i] == 0) q.push(i);
        while (!q.empty()) {
            if (q.size() > 1) return false;
            int i = q.front();
            q.pop();
            for (int j : g[i])
                if (--indeg[j] == 0) q.push(j);
        }
        return true;
    }
};

Go Code
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func sequenceReconstruction(nums []int, sequences [][]int) bool {
	n := len(nums)
	g := make([][]int, n)
	indeg := make([]int, n)
	for _, seq := range sequences {
		for i := 1; i < len(seq); i++ {
			a, b := seq[i-1]-1, seq[i]-1
			g[a] = append(g[a], b)
			indeg[b]++
		}
	}
	q := []int{}
	for i, v := range indeg {
		if v == 0 {
			q = append(q, i)
		}
	}
	for len(q) > 0 {
		if len(q) > 1 {
			return false
		}
		i := q[0]
		q = q[1:]
		for _, j := range g[i] {
			indeg[j]--
			if indeg[j] == 0 {
				q = append(q, j)
			}
		}
	}
	return true
}