CANTON - Count on Cantor

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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

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dileep_32: 2021-03-19 04:01:11


tejasreddyk: 2021-01-16 17:25:49

HHAHA AC in one go

naveen1948: 2020-11-08 08:19:10

check the output format carefully orelse you will be doomed

npoudel21: 2020-10-04 06:06:59

Isn't the sample answer wrong? Shouldn't the 14th term be 4/2
edit: My bad, I was mistaken on how the numbers are arranged in the list

Last edit: 2020-10-06 22:13:08
saurabh_shinde: 2020-09-10 15:57:29

easy in concept. just slight tricky to implement

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.

Added by:Thanh-Vy Hua
Time limit:5s
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