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
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smso:
2023-09-21 16:49:30
similar to:
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dileep_32:
2021-03-19 04:01:11
GIVEN TEST CASE IS CORRECT |
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tejasreddyk:
2021-01-16 17:25:49
HHAHA AC in one go
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naveen1948:
2020-11-08 08:19:10
check the output format carefully orelse you will be doomed
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npoudel21:
2020-10-04 06:06:59
Isn't the sample answer wrong? Shouldn't the 14th term be 4/2
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saurabh_shinde:
2020-09-10 15:57:29
easy in concept. just slight tricky to implement |
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coolboy7:
2020-06-04 18:26:11
Hint if you are not able to solve the problem:
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manish_thakur:
2019-12-12 12:28:09
position(x,y) = (1/2)(x+y)(x+y+1) + y
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gak:
2019-10-28 10:53:57
Observe the pattern by summing numerator and denominator, after that it's a cakewalk. |
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saraswat000:
2019-08-27 21:08:22
AC in one go! |
| Added by: | Thanh-Vy Hua |
| Date: | 2005-02-27 |
| 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 |
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