6174 is the Kaprekar constant. All natural numbers less than 10,000 (except some with same digits) can be reduced to 6174 in the following steps:
Order the digits of the number in descending and ascending order and compute the difference. Repeat the process till you get 6174.
Example
n = 2376
Digits in descending order = 7632
Digits in ascending order = 2367
Step1:
>> 7632 - 2367 ans = 5265
Step 2:
>> 6552 - 2556 ans = 3996
Step3:
>> 9963 - 3699 ans = 6264
Step4
>> 6642 - 2466 ans = 4176
Step5
>> 7641 - 1467 ans = 6174
Total number of steps = 5.
Your function should return the number of Kaprekar steps for a given input. Numbers such as 2222 will end in zero. These numbers will never result in 6174. They should return Inf.
The behavior at x=6174 is artifically set to 0, which taints the pure-recursive solution, but hey it was cool problem!
The K constant is 495 for 3 digits.
So the test with 691 is wrong.
Why tests with only one digit ?
Did I miss something ?
I don't understand the Test Suite for x = 3 and x = 1 too. what should I do in this case?
For x=3, the steps are 3000-0003=2997, 9972-2799=7173, etc.
Problem description is confusing as there are different Kaprekar constants depending on the number of digits. [0 9 495 6174 for 1, 2,3 4 digits respectively.
getting this error:
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Reference #3.c2c1ab8.1412090777.18623697
any ideas?
The problem should specify that any number with less than four digits should be filled up to four digits with leading zeros. (e.g. 3 -> 0003)
Very nice and interesting problem!
I like the recursion aspect of this problem.
There is a small correction needed in the problem statement. Not all natural numbers, but 4 digit numbers can be reduced to Kaprekar number by the mentioned method. Similarly 3 digit numbers can be reduced to 495
https://en.wikipedia.org/wiki/D._R._Kaprekar
How it works with x = 3, x = 691, x = 1?
This works for all but test 3 where it gives, in my opinion, the correct answer 8.
But zero is not sorted in this solution. You should get same answer for input x = 691 and 6910. (And then no need for abs())
1) 9610-0169=9441
2) 9441-1449=7992
3) 9972-2799=7173
4) 7731-1377=6354
5) 6543-3456=3087
6) 8730-0378=8352
7) 8532-2358=6174
This has been the lamest test so far. You need to pad the numbers with zeros to build it up to be a 4 digit number. Not explained in the rules.
Not all test cases seem to be correct. For example x=3 would imply that the next value should be x=3-3=0, so y_correct=Inf and not 6
An efficient lookup table solution
Interesting - a recursive approach
Could you stop doing this kind of thing? I think it would be a lot more fun if we could see the _actual_ best solution..
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