CANTON - Count on Cantor

no tags 

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

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.


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.


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.



TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
dr_br34k: 2017-06-27 14:58:37

Think of O(1) solution every ith new slant line is made of i elements.

anilkumar1998: 2017-06-09 19:44:47

Try to think of O(1) solution.

codervrinda: 2017-05-29 07:09:27

nice problem:) !

viratian_070: 2017-05-27 12:55:22

AC in one go!! took some time in finding the formula though!!

ramesh_961: 2017-05-26 07:25:31

AC in One Go!!Easy if you carefully observe the sequence!!

akhil9093: 2017-03-28 19:02:52

AC in one go..yipeee!!!!

caohoangtung: 2017-03-25 15:51:40

AC in 1 go :) Nice problem

vladimira: 2017-02-18 14:40:44

Hello everyone. I've written script in python 3. 13 lines of code: one range loop, one sqrt use, one ceil, some ariphmetic and one print. Why my solution uses 30 MB when all other people < 10MB?

Last edit: 2017-02-18 14:48:18
nilabja16180: 2017-02-09 21:57:48

AC in one Go, Triangular Number is the key!!

arindam1234: 2017-01-21 19:03:03

AC!!! My 100th on spoj.

Added by:Thanh-Vy Hua
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