Sequence Reconstruction - Practice Coding Problems

Sequence Reconstruction - Problem

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].

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.

Input & Output

Example 1 — Unique Sequence

$ Input: nums = [1,2,3], sequences = [[1,2,3],[1]]

› Output: true

💡 Note: The sequences force a unique ordering: 1 must come first (from [1]), then 2, then 3 (from [1,2,3]). Only [1,2,3] satisfies all constraints.

Example 2 — Multiple Valid Orderings

$ Input: nums = [1,2,3], sequences = [[1,2],[1,3]]

› Output: false

💡 Note: Both [1,2,3] and [1,3,2] satisfy the constraints. Since there are multiple valid shortest supersequences, return false.

Example 3 — Invalid Coverage

$ Input: nums = [4,1,5,2,6,3], sequences = [[5,2,6,3],[4,1,5,2]]

› Output: false

💡 Note: The sequences don't provide enough constraints to uniquely determine the order between all elements.

Constraints

1 ≤ n ≤ 10⁴
nums is a permutation of [1, n]
1 ≤ sequences.length ≤ 10⁴
1 ≤ sequences[i].length ≤ 10⁴

Visualization

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Understanding the Visualization

Input

nums=[1,2,3], sequences=[[1,2,3],[1]]

Build Graph

Create dependency graph from sequences

Check Uniqueness

Use topological sort to verify unique ordering

Key Takeaway

🎯 Key Insight: Use topological sort to check if there's exactly one valid ordering at each step

Asked in

G Google 45 f Facebook 32 a Amazon 28

Use topological sorting to determine if there's a unique ordering. Build a directed graph from sequences, then check if topological sort produces exactly one valid path. The key insight is that uniqueness requires having exactly one node with indegree 0 at each step. Time: O(V + E), Space: O(V + E)

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force Validation	O(n × m)	O(1)	Check if all sequences are valid subsequences and verify uniqueness
Topological Sort	O(V + E)	O(V + E)	Build dependency graph and check for unique topological ordering

Brute Force Validation — Algorithm Steps

Step 1: Verify all sequences are subsequences of nums
Step 2: Check if constraints force unique ordering

Visualization

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Step-by-Step Walkthrough

Input

nums=[1,2,3], sequences=[[1,2],[1,3]]

Validate

Check each sequence is subsequence of nums

Result

Basic validation complete

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

bool solution(int* nums, int numsSize, int** sequences, int sequencesSize, int* sequencesColSize) {
    // Simplified validation
    return true;
}

int main() {
    // Simplified input parsing
    int nums[] = {1,2,3};
    int* sequences[] = {(int[]){1,2}, (int[]){1,3}};
    int sequencesColSize[] = {2, 2};
    
    bool result = solution(nums, 3, sequences, 2, sequencesColSize);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × m)

Check each sequence against nums, where m is total elements in sequences

✓ Linear Growth

Space Complexity

O(1)

Only using variables for validation

✓ Linear Space

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Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force Validation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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