0
In a particular social network friends are automatically allocated to users by the system and users cannot add friends of their choice on their own. There are currently N users on the social network, labeled from 2 to N + 1. For every i-th user (where i ranges from 2 to N + 1), the system allocated all the users labeled with multiples of i as the user's friends (if possible). One day, all users of the social network come together for a meeting and form groups such that each person in a group is a direct friend or a friend of friend of every other person of that group.
Answers
Explanation:
The given problem statement describes a social network where friends are allocated automatically by the system. The users cannot add friends of their choice, and the allocation is done based on the system's algorithm. Each user is allocated friends who are labeled with multiples of the user's label, from 2 to N + 1.
The problem requires us to form groups such that every person in a group is a direct friend or a friend of a friend of every other person of that group. Let's analyze the problem step by step to understand the solution.
First, we need to understand the concept of direct friends and friends of friends. Direct friends of a user are those who are allocated to the user by the system. Friends of friends are those who are not directly allocated to the user but are friends of the user's direct friends.
Let's take an example to understand this better. Suppose we have four users labeled as 2, 3, 4, and 5. The system allocated friends for each user as follows:
User 2: Friends are 4 and 6 (multiples of 2)
User 3: Friends are 6 and 9 (multiples of 3)
User 4: Friends are 8 (multiple of 4)
User 5: Friends are 10 (multiple of 5)
Now, let's identify the direct friends and friends of friends of each user.
User 2: Direct friends are 4 and 6. Friends of friends are 8 and 10.
User 3: Direct friends are 6 and 9. Friends of friends are 4 and 10.
User 4: Direct friend is 8. There are no friends of friends.
User 5: Direct friend is 10. There are no friends of friends.
Based on the above analysis, we can form two groups:
Group 1: Users 2, 4, and 6 (direct friends of each other)
Group 2: Users 3 and 9 (direct friends of each other)
Now, let's generalize the solution for any given value of N.
We start by allocating friends for each user based on the system's algorithm. Then, we identify the direct friends and friends of friends of each user. We create a list of groups, where each group contains users who are direct friends or friends of friends of every other person in the group.
To create the groups, we start with the first user (label 2) and add all its direct friends and friends of friends to the group. We repeat the process for each user until all users are included in a group. If a user is not included in any group, we create a new group with that user and its direct friends and friends of friends.
In the end, we will have a list of groups where each group contains users who are direct friends or friends of friends of every other person in the group.
In conclusion, we can form groups in the given social network by identifying the direct friends and friends of friends of each user and creating groups based on these connections. The solution requires analyzing the algorithm used by the system to allocate friends and creating groups based on these connections. The solution can be generalized for any value of N by following the above steps.