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[Hacker Rank] Interview Preparation Kit: Miscellaneous: Friend Circle…
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‎docs/hackerrank/interview_preparation_kit/miscellaneous/friend-circle-queries.md

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# [Miscellaneous: Friend Circle Queries](https://www.hackerrank.com/challenges/friend-circle-queries)
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- Difficulty: `#medium`
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- Category: `#Miscellaneous`
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The population of HackerWorld is $ 10^9 $.
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Initially, none of the people are friends with each other.
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In order to start a friendship, two persons `a` and `b` have to shake hands,
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where $ 1 \leq a, b \leq 10^9 $.
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The friendship relation is transitive,
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that is if `a` and `b` shake hands with each other,
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`a` and friends of `b` become friends with `b` and friends of `b`.
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You will be given `q` queries. After each query,
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you need to report the size of the largest
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friend circle (the largest group of friends) formed after considering that query.
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For example, your list of queries is:
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```text
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1 2
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3 4
23+
2 3
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```
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First, `1` and `2` shake hands, forming a circle of `2`.
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Next, `3` and `4` do the same. Now there are two groups of `2` friends.
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When `2` and `3` become friends in the next query,
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both groups of friends are added together to make a circle of `4` friends.
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We would print
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```text
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2
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2
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4
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```
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## Function Description
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Complete the function maxCircle in the editor below.
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It must return an array of integers representing
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the size of the maximum circle of friends after each query.
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maxCircle has the following parameter(s):
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- `queries`: an array of integer arrays,
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each with two elements indicating a new friendship
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## Input Format
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The first line contains an integer, `q`, the number of queries to process.
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Each of the next `q` lines consists of two space-separated integers
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denoting the 2-D array `queries`.
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## Constraints
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- $ 1 \leq q \leq 10^5 $
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- $ 1
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\leq
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queries[i][0],queries[i][1]
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\leq 10^9
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$ for
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$ 0 \leq i < q $
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- $ queries[i][0] \not = queries[i][1] $
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## Output Format
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Return an integer array of size `q`,
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whose value at index is the size of
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largest group present after processing the $ i^{th}$ query.
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## Sample Input 0
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```text
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2
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1 2
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1 3
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```
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## Sample Output 0
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```text
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2
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3
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```
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## Explanation 0
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In the first query, `1` and `2` shake hands.
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So, the size of largest group of friends is `2` (as no other friendships exist).
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After the second query, `1`, `2` and `3` all become friends,
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as `1` shakes hand with `3`, `2` also become friends with `3`
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as he was already a friend of `1`.
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## Sample Input 1
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```text
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4
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1000000000 23
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11 3778
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7 47
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11 1000000000
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```
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## Sample Output 1
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```text
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2
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2
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2
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4
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```
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## Explanation 1
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After first query, person `1000000000` and person `23` become friends.
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So, the largest group size is `2`.
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After the second query, person `11` and person `3778` become friends.
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So, the largest group size is still .
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After the third query, person `7` and person `47` become friends.
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Answer is still `2`.
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After the last query, person `11` and person `1000000000` become friends,
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which means `23`, `11`, `1000000000` and `3778` all become friends.
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Hence, the answer now increased to `4`.
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## Sample Input 2
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```text
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6
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1 2
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3 4
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1 3
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5 7
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5 6
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7 4
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```
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## Sample Output 2
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```text
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2
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2
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4
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4
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4
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7
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```
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## Explanation 2
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Friend circles after each iteration:
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```text
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1 [1,2]
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2 [1,2],[3,4]
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3 [1,2,3,4]
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4 [1,2,3,4],[5,7]
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5 [1,2,3,4],[5,7,6]
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6 [1,2,3,4,5,6,7]
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```

‎docs/hackerrank/miscellaneous/friend-circle-queries.md

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# [Miscellaneous: Friend Circle Queries](https://www.hackerrank.com/challenges/friend-circle-queries)
2+
3+
- Difficulty: `#medium`
4+
- Category: `#Miscellaneous`
5+
6+
The population of HackerWorld is $ 10^9 $.
7+
Initially, none of the people are friends with each other.
8+
In order to start a friendship, two persons `a` and `b` have to shake hands,
9+
where $ 1 \leq a, b \leq 10^9 $.
10+
The friendship relation is transitive,
11+
that is if `a` and `b` shake hands with each other,
12+
`a` and friends of `b` become friends with `b` and friends of `b`.
13+
14+
You will be given `q` queries. After each query,
15+
you need to report the size of the largest
16+
friend circle (the largest group of friends) formed after considering that query.
17+
18+
For example, your list of queries is:
19+
20+
```text
21+
1 2
22+
3 4
23+
2 3
24+
```
25+
26+
First, `1` and `2` shake hands, forming a circle of `2`.
27+
Next, `3` and `4` do the same. Now there are two groups of `2` friends.
28+
When `2` and `3` become friends in the next query,
29+
both groups of friends are added together to make a circle of `4` friends.
30+
We would print
31+
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```text
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2
34+
2
35+
4
36+
```
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## Function Description
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Complete the function maxCircle in the editor below.
41+
It must return an array of integers representing
42+
the size of the maximum circle of friends after each query.
43+
44+
maxCircle has the following parameter(s):
45+
46+
- `queries`: an array of integer arrays,
47+
each with two elements indicating a new friendship
48+
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## Input Format
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The first line contains an integer, `q`, the number of queries to process.
52+
Each of the next `q` lines consists of two space-separated integers
53+
denoting the 2-D array `queries`.
54+
55+
## Constraints
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- $ 1 \leq q \leq 10^5 $
58+
- $ 1
59+
\leq
60+
queries[i][0],queries[i][1]
61+
\leq 10^9
62+
$ for
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$ 0 \leq i < q $
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- $ queries[i][0] \not = queries[i][1] $
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## Output Format
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Return an integer array of size `q`,
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whose value at index is the size of
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largest group present after processing the $ i^{th}$ query.
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## Sample Input 0
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```text
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2
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1 2
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1 3
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```
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## Sample Output 0
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```text
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2
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3
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```
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## Explanation 0
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In the first query, `1` and `2` shake hands.
90+
So, the size of largest group of friends is `2` (as no other friendships exist).
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After the second query, `1`, `2` and `3` all become friends,
92+
as `1` shakes hand with `3`, `2` also become friends with `3`
93+
as he was already a friend of `1`.
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## Sample Input 1
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```text
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4
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1000000000 23
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11 3778
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7 47
102+
11 1000000000
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```
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## Sample Output 1
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```text
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2
109+
2
110+
2
111+
4
112+
```
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## Explanation 1
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After first query, person `1000000000` and person `23` become friends.
117+
So, the largest group size is `2`.
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After the second query, person `11` and person `3778` become friends.
120+
So, the largest group size is still .
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After the third query, person `7` and person `47` become friends.
123+
Answer is still `2`.
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After the last query, person `11` and person `1000000000` become friends,
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which means `23`, `11`, `1000000000` and `3778` all become friends.
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Hence, the answer now increased to `4`.
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## Sample Input 2
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```text
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6
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1 2
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3 4
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1 3
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5 7
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5 6
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7 4
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```
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## Sample Output 2
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```text
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2
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2
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4
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4
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4
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7
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```
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## Explanation 2
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Friend circles after each iteration:
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```text
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1 [1,2]
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2 [1,2],[3,4]
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3 [1,2,3,4]
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4 [1,2,3,4],[5,7]
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5 [1,2,3,4],[5,7,6]
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6 [1,2,3,4,5,6,7]
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```

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