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Question 3 (Group discussion) A lecture hall with n people indexed from 1 to n. Each people either has no mentor or exactly one mentor, who is another person with a different index. A person X is considered as the supervisor of another person Y if at least one of the following is true: (1) Person X is the mentor of person Y. (2) Person Y has a mentor person Z such that person X is the supervisor of person Z. People in hall will not form a cycle, i.e., there will not exist a person who is the supervisor of his own mentor. You need to divide n people in the lecture hall into several groups for discussion as required: (1) each person belongs to exactly one group; (2) Within any group, there must not be two people X and Y such that X is the supervisor of Y. Please tell us the minimum number of groups must be formed. Examples: Input with n+1 lines. The first line contains an integer n (1sns2000), referring to the number of people. Each of the next n lines contains an integer m (1sm;sn or m;=-1). Every m¡ represents the mentor for the ith person. If m; equals to -1, it means that the įth person does not have a mentor. We assume that no person will be the mentor of himself (m; + i). Output the minimal number of the groups that must be formed. Input: 5 -1 1 1 -1 Output: 3 Explanation: There are five persons in total. The (1), (2,4), (3,5) persons can form three groups as required.

Question 3 (Group discussion) A lecture hall with n people indexed from 1 to n. Each people either has no mentor or exactly one mentor, who is another person with a different index. A person X is considered as the supervisor of another person Y if at least one of the following is true: (1) Person X is the mentor of person Y. (2) Person Y has a mentor person Z such that person X is the supervisor of person Z. People in hall will not form a cycle, i.e., there will not exist a person who is the supervisor of his own mentor. You need to divide n people in the lecture hall into several groups for discussion as required: (1) each person belongs to exactly one group; (2) Within any group, there must not be two people X and Y such that X is the supervisor of Y. Please tell us the minimum number of groups must be formed. Examples: Input with n+1 lines. The first line contains an integer n (1sns2000), referring to the number of people. Each of the next n lines contains an integer m (1sm;sn or m;=-1). Every m¡ represents the mentor for the ith person. If m; equals to -1, it means that the įth person does not have a mentor. We assume that no person will be the mentor of himself (m; + i). Output the minimal number of the groups that must be formed. Input: 5 -1 1 1 -1 Output: 3 Explanation: There are five persons in total. The (1), (2,4), (3,5) persons can form three groups as required.

Database System Concepts
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
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Question 3 (Group discussion) A lecture hall with n people indexed from 1 to n. Each people either has no mentor or exactly one mentor, who is another person with a different index. A person X is considered as the supervisor of another person Y if at least one of the following is true: (1) Person X is the mentor of person Y. (2) Person Y has a mentor person Z such that person X is the supervisor of person Z. People in hall will not form a cycle, i.e., there will not exist a person who is the supervisor of his own mentor. You need to divide n people in the lecture hall into several groups for discussion as required: (1) each person belongs to exactly one group; (2) Within any group, there must not be two people X and Y such that X is the supervisor of Y. Please tell us the minimum number of groups must be formed. Examples: Input with n+1 lines. The first line contains an integer n (1sns2000), referring to the number of people. Each of the next n lines contains an integer m (1sm;Sn or m=-1). Every m¡ represents the mentor for the ith person. If m¡ equals to -1, it means that the ith person does not have a mentor. We assume that no person will be the mentor of himself (m; ± i). Output the minimal number of the groups that must be formed. Input: -1 1 2 1 -1 Output: 3 Explanation: There are five persons in total. The (1), (2,4), (3,5) persons can form three groups as required.
Transcribed Image Text:Question 3 (Group discussion) A lecture hall with n people indexed from 1 to n. Each people either has no mentor or exactly one mentor, who is another person with a different index. A person X is considered as the supervisor of another person Y if at least one of the following is true: (1) Person X is the mentor of person Y. (2) Person Y has a mentor person Z such that person X is the supervisor of person Z. People in hall will not form a cycle, i.e., there will not exist a person who is the supervisor of his own mentor. You need to divide n people in the lecture hall into several groups for discussion as required: (1) each person belongs to exactly one group; (2) Within any group, there must not be two people X and Y such that X is the supervisor of Y. Please tell us the minimum number of groups must be formed. Examples: Input with n+1 lines. The first line contains an integer n (1sns2000), referring to the number of people. Each of the next n lines contains an integer m (1sm;Sn or m=-1). Every m¡ represents the mentor for the ith person. If m¡ equals to -1, it means that the ith person does not have a mentor. We assume that no person will be the mentor of himself (m; ± i). Output the minimal number of the groups that must be formed. Input: -1 1 2 1 -1 Output: 3 Explanation: There are five persons in total. The (1), (2,4), (3,5) persons can form three groups as required.
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