Add /r/dailyprogrammer Challenge #287 [Easy]
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# [[2016-10-10] Challenge #287 [Easy] Kaprekar's Routine](https://www.reddit.com/r/dailyprogrammer/comments/56tbds/20161010_challenge_287_easy_kaprekars_routine/)
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## Description
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Write a function that, given a 4-digit number, returns the largest digit in
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that number. Numbers between 0 and 999 are counted as 4-digit numbers with
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leading 0's.
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largest_digit(1234) -> 4
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largest_digit(3253) -> 5
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largest_digit(9800) -> 9
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largest_digit(3333) -> 3
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largest_digit(120) -> 2
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In the last example, given an input of `120`, we treat it as the 4-digit number
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`0120`.
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*Today's challenge is really more of a warmup for the bonuses. If you were able
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to complete it, I highly recommend giving the bonuses a shot!*
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## Bonus 1
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Write a function that, given a 4-digit number, performs the "descending digits"
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operation. This operation returns a number with the same 4 digits sorted in
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descending order.
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desc_digits(1234) -> 4321
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desc_digits(3253) -> 5332
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desc_digits(9800) -> 9800
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desc_digits(3333) -> 3333
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desc_digits(120) -> 2100
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## Bonus 2
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Write a function that counts the number of iterations in Kaprekar's Routine,
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which is as follows.
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Given a 4-digit number *that has at least two different digits*, take that
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number's descending digits, and subtract that number's ascending digits. For
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example, given `6589`, you should take `9865 - 5689`, which is `4176`. Repeat
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this process with `4176` and you'll get `7641 - 1467`, which is `6174`.
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Once you get to 6174 you'll stay there if you repeat the process. In this case
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we applied the process 2 times before reaching 6174, so our output for `6589`
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is `2`.
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kaprekar(6589) -> 2
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kaprekar(5455) -> 5
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kaprekar(6174) -> 0
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Numbers like 3333 would immediately go to 0 under this routine, but since we
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require at least two different digits in the input, all numbers will eventually
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reach 6174, which is known as Kaprekar's Constant. Watch
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[this video](https://www.youtube.com/watch?v=d8TRcZklX_Q) if you're still
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unclear on how Kaprekar's Routine works.
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What is the largest number of iterations for Kaprekar's Routine to reach 6174?
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That is, what's the largest possible output for your `kaprekar` function, given
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a valid input? Post the answer along with your solution.
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*Thanks to [/u/BinaryLinux](https://www.reddit.com/u/BinaryLinux) and
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[/u/Racoonie](https://www.reddit.com/u/Racoonie) for posting the idea behind
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this challenge in
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[/r/daliyprogrammer_ideas](https://www.reddit.com/r/daliyprogrammer_ideas)!*
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#include <stdio.h>
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char a[4];
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char largest_digit(short n)
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{
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char m = n / 1000;
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if (m < n % 1000 / 100)
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m = n % 1000 / 100;
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if (m < n % 100 / 10)
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m = n % 100 / 10;
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return (m < n % 10) ? n % 10 : m;
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}
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void sort_digits(short n)
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{
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char i, j;
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a[0] = n / 1000;
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a[1] = n % 1000 / 100;
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a[2] = n % 100 / 10;
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a[3] = n % 10;
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for (i = 0; i < 3; i++)
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for (j = i + 1; j < 4; j++)
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if (a[i] < a[j]) {
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a[i] += a[j];
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a[j] = a[i] - a[j];
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a[i] -= a[j];
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}
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}
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short desc_digits(short n)
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{
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sort_digits(n);
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return a[0] * 1000 + a[1] * 100 + a[2] * 10 + a[3];
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}
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short asc_digits(short n)
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{
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sort_digits(n);
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return a[3] * 1000 + a[2] * 100 + a[1] * 10 + a[0];
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}
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unsigned long long kaprekar(short n)
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{
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char i;
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for (i = 0; n ^ 6174; i++)
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n = desc_digits(n) - asc_digits(n);
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return i;
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}
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int main()
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{
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printf("largest_digit(1234) -> %hhd\n", largest_digit(1234));
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printf("largest_digit(3253) -> %hhd\n", largest_digit(3253));
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printf("largest_digit(9800) -> %hhd\n", largest_digit(9800));
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printf("largest_digit(3333) -> %hhd\n", largest_digit(3333));
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printf("largest_digit(120) -> %hhd\n\n", largest_digit(120));
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printf("desc_digits(1234) -> %hd\n", desc_digits(1234));
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printf("desc_digits(3253) -> %hd\n", desc_digits(3253));
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printf("desc_digits(9800) -> %hd\n", desc_digits(9800));
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printf("desc_digits(3333) -> %hd\n", desc_digits(3333));
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printf("desc_digits(120) -> %hd\n\n", desc_digits(120));
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printf("kaprekar(6589) -> %lld\n", kaprekar(6589));
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printf("kaprekar(5455) -> %lld\n", kaprekar(5455));
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printf("kaprekar(6174) -> %lld\n", kaprekar(6174));
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return 0;
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}
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type
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aos = array[0 .. 3] of shortint;
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function largest_digit(n: smallint): shortint;
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var
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m: shortint;
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begin
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m := n div 1000;
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if m < n mod 1000 div 100 then
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m := n mod 1000 div 100;
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if m < n mod 100 div 10 then
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m := n mod 100 div 10;
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if m < n mod 10 then
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exit(n mod 10)
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else
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exit(m)
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end;
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function sorted_digits(n: smallint): aos;
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var
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a: aos;
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i, j: shortint;
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begin
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a[0] := n div 1000;
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a[1] := n mod 1000 div 100;
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a[2] := n mod 100 div 10;
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a[3] := n mod 10;
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for i := 0 to 2 do
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for j := i + 1 to 3 do
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if a[i] < a[j] then
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begin
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inc(a[i], a[j]);
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a[j] := a[i] - a[j];
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dec(a[i], a[j])
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end;
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exit(a)
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end;
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function desc_digits(n: smallint): smallint;
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var
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a: aos;
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begin
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a := sorted_digits(n);
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exit(a[0] * 1000 + a[1] * 100 + a[2] * 10 + a[3])
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end;
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function asc_digits(n: smallint): smallint;
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var
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a: aos;
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begin
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a := sorted_digits(n);
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exit(a[3] * 1000 + a[2] * 100 + a[1] * 10 + a[0])
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end;
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function kaprekar(n: smallint): qword;
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var
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i: shortint = 0;
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begin
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while n <> 6174 do
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begin
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n := desc_digits(n) - asc_digits(n);
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inc(i)
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end;
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exit(i)
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end;
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begin
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writeln('largest_digit(1234) -> ', largest_digit(1234));
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writeln('largest_digit(3253) -> ', largest_digit(3253));
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writeln('largest_digit(9800) -> ', largest_digit(9800));
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writeln('largest_digit(3333) -> ', largest_digit(3333));
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writeln('largest_digit(120) -> ', largest_digit(120));
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writeln;
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writeln('desc_digits(1234) -> ', desc_digits(1234));
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writeln('desc_digits(3253) -> ', desc_digits(3253));
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writeln('desc_digits(9800) -> ', desc_digits(9800));
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writeln('desc_digits(3333) -> ', desc_digits(3333));
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writeln('desc_digits(120) -> ', desc_digits(120));
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writeln;
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writeln('kaprekar(6589) -> ', kaprekar(6589));
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writeln('kaprekar(5455) -> ', kaprekar(5455));
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writeln('kaprekar(6174) -> ', kaprekar(6174))
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end.
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#!/usr/bin/env python3
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def largest_digit(n):
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return int(max(str(n)))
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def desc_digits(n):
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return int(''.join(sorted('{:04}'.format(n), reverse=True)))
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def asc_digits(n):
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return int(''.join(sorted('{:04}'.format(n))))
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def kaprekar(n):
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i = 0
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while n != 6174:
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n = desc_digits(n) - asc_digits(n)
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i += 1
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return i
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if __name__ == '__main__':
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print('largest_digit(1234) -> {}'.format(largest_digit(1234)))
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print('largest_digit(3253) -> {}'.format(largest_digit(3253)))
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print('largest_digit(9800) -> {}'.format(largest_digit(9800)))
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print('largest_digit(3333) -> {}'.format(largest_digit(3333)))
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print('largest_digit(120) -> {}\n'.format(largest_digit(120)))
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print('desc_digits(1234) -> {}'.format(desc_digits(1234)))
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print('desc_digits(3253) -> {}'.format(desc_digits(3253)))
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print('desc_digits(9800) -> {}'.format(desc_digits(9800)))
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print('desc_digits(3333) -> {}'.format(desc_digits(3333)))
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print('desc_digits(120) -> {}\n'.format(desc_digits(120)))
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print('kaprekar(6589) -> {}'.format(kaprekar(6589)))
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print('kaprekar(5455) -> {}'.format(kaprekar(5455)))
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print('kaprekar(6174) -> {}'.format(kaprekar(6174)))
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