Dimensional countdown

Question

Write a function f(n,k) that displays the k-dimensional countdown from n.

A 1-dimensional countdown from 5 looks like

 54321

A 2-dimensional countdown from 5 looks like

 54321
 4321
 321
 21
 1

Finally, a 3-dimensional countdown from 5 looks like

 54321
 4321
 321
 21
 1
 4321
 321
 21
 1
 321
 21
 1
 21
 1
 1

Formal definition

The 1-dimensional countdown from any n is a single line with the digits n, n-1,...,1 concatenated (followed by a newline).

For any k, the k-dimensional countdown from 1 is the single line

 1

For n > 1 and k > 1, a k-dimensional countdown from n is a (k-1)-dimensional countdown from n followed by a k-dimensional countdown from n-1.

Input

Two positive integers k and n <= 9, in any format you choose.

Output

The k-dimensional countdown from n, with a newline after each 1-dimensional countdown. Extra newlines are permitted in the output.

Scoring

Standard golf scoring.

Bonus example

Here's an example with k > n, a 4-dimensional countdown from 3 (with extra comments that are not to be included in actual solutions):

 -- 3-dimensional countdown from 3
 321
 21
 1
 21
 1
 1
 -- 4-dimensional countdown from 2:
 ---- 3-dimensional countdown from 2:
 21
 1
 1
 ---- 4-dimensional countdown from 1:
 1  

Clarifications:

Digits on a line do not need to be adjacent, but they must be evenly-spaced.

You may write a full program instead of just a function, if you prefer.

Answer 1

Python, 60 bytes

f=lambda n,k:n>1<k and f(n,k-1)+f(n-1,k)or'987654321\n'[~n:]

Test it on Ideone.

How it works

The k-dimensional countdown from n can be defined with a single base case:

If n = 1 or k = 1, the output is n || n-1 || ... || 1 || ¶, where || indicates concatenation.

Using the recursive definition from the question, f(n,k) returns f(n,k-1)+f(n-1,k) if n > 1 and k > 1; otherwise it returns the last n + 1 characters from '987654321\n'.

Answer 2

Jelly, 8 bytes

R¡UḌFṚp⁷

This is a full program that expects n and k as command-line arguments.

Try it online!

How it works

R¡UḌFṚp⁷  Main link. Left argument: n. Right argument: k

 ¡        Repeat the link to the left k times.
R           Range; map each integer j in the previous return value to [1, ..., j].
  U       Upend; reverse each 1-dimensional array in the result.
   Ḍ      Undecimal; convert each 1-dimensional array from base 10 to integer.
    F     Flatten the resulting array.
     Ṛ    Reverse the result.
      p⁷  Cartesian product with '\n'. (Join is weird for singleton arrays.)

Answer 3

Javascript, 40 38 37 bytes

Saved 1 bytes thanks to @edc65:

f=(n,k)=>k*n?f(n,k-1)+f(n-1,k):n||`
`

Previous answers

38 bytes thanks to @Neil:

f=(n,k)=>k&&n?f(n,k-1)+f(n-1,k):n||`
`

40 bytes:

f=(n,k)=>k&&n?f(n,k-1)+f(n-1,k):n?n:'\n'

Answer 4

Python, 76 75 bytes

-1 byte thanks to @Sp3000

c=lambda n,k:k>1and'\n'.join(c(n-i,k-1)for i in range(n))or'987654321'[-n:]

Caries out the procedure as described in the OP: joins the decreasing n results for k-1 on newlines with a base of the recursion of the 'n...1' string when k is 1 (k not greater than 1 since we are guaranteed positive k input).

Test cases on ideone

Answer 5

Python, 86 81 80 bytes

o=lambda d,n:"987654321"[-n:]if d<2else"\n".join([o(d-1,n-x) for x in range(n)])

d is the number of dimensions, n is the countdown number.

Will post an explanation soon.

EDIT #1: Changed it to lambda.

EDIT #2: Saved 1 byte thanks to @DestructibleWatermelon.

Answer 6

Haskell, 57 bytes

n#1='\n':(show=<<[n,n-1..1])
1#_=1#1
n#k=n#(k-1)++(n-1)#k

Usage example: 5 # 3 -> "\n54321\n4321\n321\n21\n1\n4321\n321\n21\n1\n321\n21\n1\n21\n1\n1".

A direct implementation of the definition.

Answer 7

Racket 215 bytes

(define(g n k(s(number->string n)))(cond [(< k 2) n]
[else(define o(for/list((i(string-length s)))
(string->number(substring s i))))(for/list((x o))(g x(- k 1)))])) 
(define(f n k)(for-each println(flatten(g n k))))

Testing:

(f 54321 3)

54321
4321
321
21
1
4321
321
21
1
321
21
1
21
1
1

Answer 8

J, 38 37 32 bytes

a:":@>@-.~&,0<@-."1~0&(](-i.)"0)

This is a function that takes k on the LHS and n on the RHS.

Saved 5 bytes with ideas from @Adám.

Usage

   f =: a:":@>@-.~&,0<@-."1~0&(](-i.)"0)
   3 f 5
5 4 3 2 1
4 3 2 1  
3 2 1    
2 1      
1        
4 3 2 1  
3 2 1    
2 1      
1        
3 2 1    
2 1      
1        
2 1      
1        
1

Explanation

a:":@>@-.~&,0<@-."1~0&(](-i.)"0)  Input: k on LHS, n on RHS
                    0&(        )  Repeat k times on initial value n
                        (   )"0   For each value x
                          i.        Make the range [0, x)
                         -          Subtract x from each to make the range [x, 1]
                       ]            Return the array of ranges
            0  -."1~              Remove the zeros from each row
             <@                   Box each row
          &,                      Flatten the array of boxes
a:     -.~                        Remove the empty boxes
     >@                           Unbox each
  ":@                             Convert it into a string and return

Answer 9

Dyalog APL, 18 bytes

Prompts for n, then for k.

~∘'0'⍤1⍕(⌽⍳)⍤0⍣⎕⊢⎕

~∘'0'⍤1 remove (~) the (∘) zeros ('0') from the rows (⍤1) (padding with spaces as needed) of

⍕ the character representation of

(⌽⍳)⍤0⍣⎕ the reversed (⌽) count until (⍳) each scalar (⍤0), repeated (⍣) input (⎕) times

⊢ on

⎕ numeric input

TryAPL online!

Answer 10

C 93 Bytes

Iterative implementation.

m,i,j;f(n,k){for(;m<k+2;m++)for(j=0;j<n;j++){for(i=m;i<n-j;i++)printf("%d",n-j-i);puts("");}}

C 67 65 61 56 52 Bytes

Recursive implementation

f(n,k){n*k?f(n,k-1)+f(n-1,k):puts("987654321"+9-n);}

Answer 11

Batch, 117 bytes

@setlocal
@set/an=%1-1,k=%2-1,p=n*k,s=987654321
@if %p%==0 (call echo %%s:~-%1%%)else call %0 %1 %k%&call %0 %n% %2

Port of Dennis♦'s Python answer.

Answer 12

Ruby, 56 bytes

f=->n,k{n>1&&k>1?[f[n,k-1],f[n-1,k]]:[*1..n].reverse*""}

Usage

When you display any solutions, you should use "Kernel#puts".

Example:

puts f[9,3]