Which of the following statements are true ?Give reasons for your answers in the form of ashort proof or a counter-example.(i) All comparison based sorting algorithmshave the same worst case running time.(ii) A topological sort of a Directed AcyclicGraph (DAG) can be created by performinga depth-first-search on the DAG.(iii) o (p) = p\d primes p, where o is theEuler-phi function.(iv) There is a unique min binary heap on theset {1, 2,9}......(v) Two sequences can have several commonsubsequences of thelength.samemaximum

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Answered: (i) All comparison based sorting…

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(i) All comparison based sorting algorithms have the same worst case running time.

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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Concept explainers

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

Question

Which of the following statements are true ?
Give reasons for your answers in the form of a
short proof or a counter-example.
(i) All comparison based sorting algorithms
have the same worst case running time.
(ii) A topological sort of a Directed Acyclic
Graph (DAG) can be created by performing
a depth-first-search on the DAG.
(iii) o (p) = p\d primes p, where o is the
Euler-phi function.
(iv) There is a unique min binary heap on the
set {1, 2,
9}.
.....
(v) Two sequences can have several common
subsequences of the
length.
same
maximum

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