Answered: Definition: We define a path in a graph…

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

Section: Chapter Questions

Problem 1PE

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Definition: We define a path in a graph to be short if it contains ≤ 100 edges. Note that we are looking at the number of edges, not the number of vertices. The Problem:

•INPUT – An unweighted DAG G = (V, E)

– Two specific vertices s, t ∈V

•OUTPUT: the number of different short paths in G from s to t. You don’t have to output the actual paths; you just have to figure out how many of them there are.

Show a dynamic programming algorithm that solves the above problem in O(|E|) time.

You only need to write pseudocode, nothing else.

NOTE: a reminder that you can assume in this class that all arithmetic operations (multiplication, addition, etc.) take O(1) time, even if the numbers are very big.

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