I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n+m) as stated in the question. Problem 1. A walk in a directed graph G = (V, E) from a vertex s to a vertex t, is a sequence of verticesV₁, V2, ..., Uk where v₁ = s and vk = t such that for any i < k, (vį, Vi+1) is an edge in G. The length of a walkis defined as the number of vertices inside it minus one, i.e., the number of edges (so the walk V₁, V2, ..., Ukhas length k-1).Note that the only difference of a walk with a path we defined in the course is that a walk can contain thesame vertex (or edge) more than once, while a path consists of only distinct vertices and edges.Design and analyze an O(n + m) time algorithm that given a directed graph G = (V, E) and two vertices sand t, outputs Yes if there is a walk from s to t in G whose length is even, and No otherwise.

An algorithm is a set of precise and well-defined instructions that are used to solve a problem or…

Answered: Problem 1. A walk in a directed graph G…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

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I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n+m) as stated in the question.

Problem 1. A walk in a directed graph G = (V, E) from a vertex s to a vertex t, is a sequence of vertices
V₁, V2, ..., Uk where v₁ = s and vk = t such that for any i < k, (vį, Vi+1) is an edge in G. The length of a walk
is defined as the number of vertices inside it minus one, i.e., the number of edges (so the walk V₁, V2, ..., Uk
has length k-1).
Note that the only difference of a walk with a path we defined in the course is that a walk can contain the
same vertex (or edge) more than once, while a path consists of only distinct vertices and edges.
Design and analyze an O(n + m) time algorithm that given a directed graph G = (V, E) and two vertices s
and t, outputs Yes if there is a walk from s to t in G whose length is even, and No otherwise.

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I needed the algorithm for G whose length is even. You can read it in the last line of the question. I don't know where the divisible by 5 part came from. Please solve the question again.

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