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
coolboy7: 2020-06-04 18:26:11

Hint if you are not able to solve the problem:
Observe the pattern of numerator and denominator and also you need to apply the formula of first n terms;)

manish_thakur: 2019-12-12 12:28:09

position(x,y) = (1/2)(x+y)(x+y+1) + y

gak: 2019-10-28 10:53:57

Observe the pattern by summing numerator and denominator, after that it's a cakewalk.

saraswat000: 2019-08-27 21:08:22

AC in one go!

mriow: 2019-08-20 09:02:27

Solution can be achieved in O(1) for every Cantor's Term.


Use the formula for the Sum of the First n Terms of an Arithmetic Sequence.

jumaruba: 2019-08-01 19:28:34


Consider that it's a arithmetic progression second order.
0.0 second code

maverick080800: 2019-06-25 14:16:34

chaman chutiyo its so easy or sab ac in one go kr rhe ho . hurrrrr noobs

urjajn123: 2019-05-14 14:22:27

Last edit: 2019-05-15 11:59:29
aj_254: 2019-05-11 17:27:49

just obsever the pattern and apply stl binary search .. easy and solvable in python..

ashimk: 2019-03-18 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.
Just observe the pattern and BOOM!! A.C.

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