CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
ashimk:
20190318 20:26:34
Submitted after making a table upto the maximum value of number i.e 10^7 but got R.E(which was obvious though) . Then generated the number for every n.


newbie_127:
20190312 17:49:42
Use std :: lower_bound( ) . AC in 1 go :) 

anant6025:
20190205 22:02:11
***Hints Below***


cypher33:
20181227 06:15:56
@abhinav__ your comment made my day lmao 

adipat:
20181012 19:55:37
This was how I solved it. First identify the diagonal pattern. A diagonal k has k terms and the total terms upto that diagonal will be (1+2+...+k). Using this property, locate the diagonal in which n will lie. From there the exact row and column of the nth term can be found by iterating through the diagonal up or down depending on whether it's an odd or even diagonal. 

rajat_enzyme:
20180820 19:58:32
Last edit: 20180820 20:01:19 

quannguyenlhp:
20180818 06:27:54
AC in 1000000th go, 5 sec Last edit: 20180818 06:28:15 

harsh771:
20180708 19:02:48
Easy to solve once you observe the pattern! 

vritta:
20180618 13:16:25
1/1 1/2 1/3 1/4 1/5 ...


itachi_2016:
20180612 10:57:50
Last edit: 20180612 10:59:06 
Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM South Eastern European Region 2004 