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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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
How it works x = 1？？？？？
For those confused with test cases 2,3 and 5, like myself before, do conversion to 4-digit integer. Here is an example:
x = 1:
1000-0001 = 999
9990-0999 = 8991
9981-1899 = 8082
8820-0288 = 8532
8532-2358 = 6174
Therefore, y_correct = 5
Very nice. Took some few minutes to crack this.
What I did is to convert x into string and then use sort function.
I am used to program with C, could someone have a vectorization solution for this problem in MATLAB way?
function y = KaprekarSteps(x)
y = 0;
while ~(x == 6174 || x == 0)
x = step(x);
y = y + 1;
if x == 0
y = inf;
function x = step(x)
digits = getDigits(x);
gain = [1000 100 10 1]';
x_d = sort(digits,"descend")*gain;
x_a = sort(digits,"ascend")*gain;
x = x_d - x_a;
function digits = getDigits(x)
digits = [0 0 0 0];
for i = 1:4
digits(i) = fix(x/(10^(4-i)));
x = mod(x,10^(4-i));
The test suite doesn't match the problem description - how can the answer to test two be 5?
Cheated with 1...:
1000 - 0001 = 999.
999 - 999 = 0
y = inf;
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())
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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