[Hacker Rank] Interview Preparation Kit: Miscellaneous: Friend Circle…

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

src/hackerrank/interview_preparation_kit/miscellaneous/friend_circle_queries.test.ts

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+import { describe, expect, it } from '@jest/globals';
+import { logger as console } from '../../../logger';
+
+import { maxCircle } from './friend_circle_queries';
+import TEST_CASES from './friend_circle_queries.testcases.json';
+
+describe('friend_circle_queries', () => {
+  it('maxCircle test cases', () => {
+    expect.assertions(4);
+
+    TEST_CASES.forEach((test) => {
+      const answer = maxCircle(test.arr);
+
+      console.debug(`luckBalance(${test.arr}) solution found: ${answer}`);
+
+      expect(answer).toStrictEqual(test.expected);
+    });
+  });
+});

src/hackerrank/interview_preparation_kit/miscellaneous/friend_circle_queries.testcases.json

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+[
+    {
+        "title": "Sample Test case 0",
+        "arr": [[1, 2], [1, 3]],
+        "expected": [2, 3]
+    },
+    {
+        "title": "Sample Test case 0",
+        "arr": [[1, 2], [1, 3], [1, 2], [1, 3]],
+        "expected": [2, 3, 3, 3]
+    },
+    {
+        "title": "Sample Test case 1",
+        "arr": [
+            [1000000000, 23],
+            [11, 3778],
+            [7, 47],
+            [11, 1000000000]
+        ],
+        "expected": [2, 2, 2, 4]
+    },
+    {
+        "title": "Sample Test case 2",
+        "arr": [
+            [1, 2],
+            [3, 4],
+            [1, 3],
+            [5, 7],
+            [5, 6],
+            [7, 4]
+        ],
+        "expected": [2, 2, 4, 4, 4, 7]
+    }
+]

src/hackerrank/interview_preparation_kit/miscellaneous/friend_circle_queries.ts

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+/**
+ * @link Problem definition [[docs/hackerrank/interview_preparation_kit/miscellaneous/friend-circle-queries.md]]
+ */
+
+class GropingFriends {
+  _friendship: Record<number, number> = {};
+  _large_friendship: number = 0;
+
+  constructor() {
+    this._friendship = {};
+    this._large_friendship = 0;
+  }
+
+  add(point_a: number): void {
+    if (!this._friendship?.[point_a]) {
+      this._friendship[point_a] = -1;
+    }
+  }
+
+  find(point_a: number): number {
+    if (this._friendship[point_a] < 0) {
+      return point_a;
+    }
+    return this.find(this._friendship[point_a]);
+  }
+
+  unite(point_a: number, point_b: number): boolean {
+    this.add(point_a);
+    this.add(point_b);
+
+    let _a = this.find(point_a);
+    let _b = this.find(point_b);
+
+    if (_a == _b) {
+      return false;
+    }
+
+    if (_a > _b) {
+      [_a, _b] = [_b, _a];
+    }
+
+    this._friendship[_a] += this._friendship[_b];
+    this._friendship[_b] = _a;
+
+    // large group is the root node with "high" value
+    this._large_friendship = Math.max(
+      this._large_friendship,
+      -1 * this._friendship[_a]
+    );
+    return true;
+  }
+
+  count_groups(): number {
+    return this._large_friendship;
+  }
+}
+
+export function maxCircle(queries: number[][]): number[] {
+  const result: number[] = [];
+  const friends = new GropingFriends();
+
+  queries.forEach((query) => {
+    // Computing friendship
+    friends.unite(query[0], query[1]);
+
+    // Counting friends groups
+    result.push(friends.count_groups());
+  });
+
+  return result;
+}
+
+export default { maxCircle };