HackerRank Number Theory – Dancing in Pairs

Challenge: Dancing in Pairs

Subdomeniu: Number Theory (number-theory)

Scor cont: 40.0 / 40

Submission status: Accepted

Submission score: 1.0

Submission ID: 464729129

Limbaj: java8

Link challenge: https://www.hackerrank.com/challenges/dance-class/problem

Cerinta

Bob is a dance teacher and he started dance classes recently. He observes a strange attendance pattern among his students. Initially, there are no students. On day *i*, a new student starts attending the class. The student stops attending the class, if and only if he has attended the class for _i_ consecutive days. 
Also, the student resumes attending the class, if and only if he has not attended the class for _i_ consecutive days. 

We denote the student who starts coming on day *i* as student *i*.  
To mark attendance, `o` denotes present and `x` denotes absent.  

For example, the schedule for student 1 from day 1 is as follows:  
`oxoxoxoxoxoxoxoxoxox...`  

The schedule for the student 3 from day 1 is as follows:  

`xxoooxxxoooxxxoooxxx...`  
(Student 3 starts attending the class from day 3, and stops attending from day 6, and then starts attending from day 9, and so on. )  

The schedule for the student 5 from day 1 is as follows.
`xxxxoooooxxxxxoooooxxxxx...`

Bob wants his students to dance in pairs. However, if the number of students coming on day _i_ is odd, then there will be someone who can't find a partner. So Bob wants to know if the number of students coming on day i is even or odd. We denote the number of students coming on day _i_ as _N(i)_.  Please find out whether _N(i)_ is even or odd.


**Input format**  

The first line contains an integer, _T_, which denotes the number of test cases.  
For each test case, there is an integer _i_

**Output Format**  
For each test case, if _N(i)_ is even, then print `even`.  
If _N(i)_ is odd, then print one line `odd`.

**Constraints**  
1 ≤ *T* ≤ 100  
1 ≤ *i* ≤ 10<sup>18</sup>  

**Sample Input**

	4
	1
	2
	3
	4

**Sample Output**  

	odd
	odd
	odd
	even

**Explanation**  
The number of students coming on day 1 is 1: only student #1 attends the class. So N(1)=1 and it is odd.  
The number of students coming on day 2 is 1:  student #2, so n(2)=1 and it is odd.  
The number of students coming on day 3 is 3: student #1, student #2, and student #3. So N(3)=3 and it is odd.   
The number of students coming on day 4 is 2: student #3 and student #4. So N(4)=2 and it is even.

Cod sursa

import java.util.Scanner;

public class Solution {
  public static void main(final String[] args) {
    try (final Scanner in = new Scanner(System.in)) {
      for (int t = in.nextInt(); t > 0; t--) {
        final long i = in.nextLong() + 1;
        System.out.println(i == 2 || Math.ceil(Math.sqrt(i) - 1) % 2 == 1 ? "odd" : "even");
      }
    }
  }
}