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Coding & Algorithms questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master coding & algorithms interviews.

What difficulty level is this interview question?

This is a medium difficulty Coding & Algorithms question, commonly asked during Take-home Project rounds at Codeium.

What role is this question designed for?

This question is commonly asked for Software Engineer candidates at Codeium during technical interviews.

Validate whether a given sequence is a Hamiltonian path

Quick Overview

This question evaluates understanding of graph theory concepts—specifically Hamiltonian paths, graph representation parsing, and sequential edge validation— within the Coding & Algorithms domain and emphasizes practical application of graph traversal and validation rather than purely theoretical proofs.

You are given strArr, an array of three strings describing an undirected graph and a proposed vertex visit order:

strArr[0] : a comma-separated list of vertices in parentheses, e.g. "(A,B,C)"
strArr[1] : a comma-separated list of undirected edges in parentheses, e.g. "(A-B,C-D)"
strArr[2] : a comma-separated list of vertices representing the proposed path order, e.g. "(C,A,B)"

Task:

Determine whether the proposed order is a Hamiltonian path : it must visit every vertex in the graph exactly once , and every consecutive pair in the order must be connected by an edge.

Output:

Return "yes" if the order forms a Hamiltonian path.
Otherwise, return the first vertex in the given order where the path fails , meaning the earliest vertex order[i] such that either:
- order[i] is not a vertex in the graph, or
- order[i] has already appeared earlier in the order, or
- there is no edge between order[i-1] and order[i] (for i > 0 ).

Assumptions/constraints:

The graph has at least 2 vertices and is connected.
Vertices are represented by single tokens like A , B , X , etc.

Examples:

Input: ["(A,B,C)", "(B-A,C-B)", "(C,A,B)"] → Output: "yes"
Input: ["(X,Y,Z,Q)", "(X-Y,Y-Q,Y-Z)", "(Z,Y,Q,X)"] → Output: "Q" (because there is no edge between Q and X )

Quick Overview

You are given strArr, an array of three strings describing an undirected graph and a proposed vertex visit order:

strArr[0] : a comma-separated list of vertices in parentheses, e.g. "(A,B,C)"
strArr[1] : a comma-separated list of undirected edges in parentheses, e.g. "(A-B,C-D)"
strArr[2] : a comma-separated list of vertices representing the proposed path order, e.g. "(C,A,B)"

Task:

Determine whether the proposed order is a Hamiltonian path : it must visit every vertex in the graph exactly once , and every consecutive pair in the order must be connected by an edge.

Output:

Return "yes" if the order forms a Hamiltonian path.
Otherwise, return the first vertex in the given order where the path fails , meaning the earliest vertex order[i] such that either:
- order[i] is not a vertex in the graph, or
- order[i] has already appeared earlier in the order, or
- there is no edge between order[i-1] and order[i] (for i > 0 ).

Assumptions/constraints:

The graph has at least 2 vertices and is connected.
Vertices are represented by single tokens like A , B , X , etc.

Examples:

Input: ["(A,B,C)", "(B-A,C-B)", "(C,A,B)"] → Output: "yes"
Input: ["(X,Y,Z,Q)", "(X-Y,Y-Q,Y-Z)", "(Z,Y,Q,X)"] → Output: "Q" (because there is no edge between Q and X )

Validate whether a given sequence is a Hamiltonian path

Quick Overview

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Validate whether a given sequence is a Hamiltonian path

Quick Overview

Submit Your Answer