A website has a test bank of questions. Students use the website to sharpen their skills. Teachers also use it to generate quizzes. Suppose the website generated n questions for Teacher Alice. It also provided her a size-n array T such that Ti] denotes the topic covered by question i. Teacher Alice wants to rearrange the questions so no two consecutive questions cover the same topic. That is, we say the questions are scrambled. For example, if T = [2, 3, 2, 2, 1, 3] then Teacher Alice can rcorder the questions as 1,2, 3, 5, 4, 6 so the new topic-array is [2,3, 2, 1, 2, 3]. Q ----> Assume the questions covers topics 1, 2, ..., ki, where k is some constant. Given a size-n array T, design an O(n)-time algorithm that outputs a scrambled ordering of the questions if it's possible and returns –1 otherwise. Again, justify the correctness of your algorithm and explain why it runs in lincar time. For exam- ple, if the input is T = [2, 3, 2, 2, 1, 3], your algorithm should output 1,2, 3, 5, 4, 6. On the other hand, if the input is T = [3,1, 1, 2, 1, 1], your algorithm outputs -1.

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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A website has a test bank of questions. Students usc the website to sharpen their
skills. Teachers also use it to gencrate quizzes. Suppose the website generated n
questions for Teacher Alice. It also provided her a size-n array T such that T[i]
denotes the topic covered by question i. Teacher Alice wants to rearrange the
questions so no two consecutive questions cover the same topic. That is, we say
the questions are scrambled. For example, if T = [2,3, 2, 2, 1, 3] then Teacher Alice
can reorder the questions as 1,2, 3, 5, 4, 6 so the new topic-array is [2,3, 2, 1, 2, 3].
Q ---> Assume the questions covers topics 1, 2,..., k, where k is some constant.
Given a size-n array T, design an O(n)-time algorithm that outputs a scrambled
ordering of the questions if it's possible and returns –1 otherwise. Again, justify
the correctness of your algorithm and explain why it runs in lincar time. For exam-
ple, if the input is T = [2, 3, 2,2, 1, 3], your algorithm should output 1,2,3, 5, 4, 6.
On the other hand, if the input is T = [3, 1, 1, 2, 1, 1], your algorithm outputs -1.
Transcribed Image Text:A website has a test bank of questions. Students usc the website to sharpen their skills. Teachers also use it to gencrate quizzes. Suppose the website generated n questions for Teacher Alice. It also provided her a size-n array T such that T[i] denotes the topic covered by question i. Teacher Alice wants to rearrange the questions so no two consecutive questions cover the same topic. That is, we say the questions are scrambled. For example, if T = [2,3, 2, 2, 1, 3] then Teacher Alice can reorder the questions as 1,2, 3, 5, 4, 6 so the new topic-array is [2,3, 2, 1, 2, 3]. Q ---> Assume the questions covers topics 1, 2,..., k, where k is some constant. Given a size-n array T, design an O(n)-time algorithm that outputs a scrambled ordering of the questions if it's possible and returns –1 otherwise. Again, justify the correctness of your algorithm and explain why it runs in lincar time. For exam- ple, if the input is T = [2, 3, 2,2, 1, 3], your algorithm should output 1,2,3, 5, 4, 6. On the other hand, if the input is T = [3, 1, 1, 2, 1, 1], your algorithm outputs -1.
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