Leaping Kangaroos

Backstory

Kangaroos traverse several stages of development. As they grow older and stronger, they can jump higher and longer, and they can jump more times before they get hungry.

In stage 1, the kangaroo is very little and cannot jump at all. Despite this, is constantly requires nourishment. We can represent a stage 1 kangaroo's activity pattern like this.

o


In stage 2, the kangaroo can make small jumps, but not more than 2 before it gets hungry. We can represent a stage 2 kangaroo's activity pattern like this.

 o o
o o o


After stage 2 the kangaroo improves quickly. In each subsequent stage, the kangaroo can jump a bit higher (1 unit in the graphical representation) and twice as many times. For example, a stage 3 kangaroo's activity pattern looks like this.

  o   o   o   o
o o o o o o o o
o   o   o   o   o


For stage n, the activity pattern consists of 2n-1 V-shaped jumps of height n.

For example, for stage 4, there are 8 jumps of height 4.

   o     o     o     o     o     o     o     o
o o   o o   o o   o o   o o   o o   o o   o o
o   o o   o o   o o   o o   o o   o o   o o   o
o     o     o     o     o     o     o     o     o


Write a full program or a function that takes a positive integer n as input and prints or returns the ASCII art representation of a stage n kangaroo's activity pattern.

Surrounding whitespace and ANSI escape codes are allowed, as long as the pattern looks exactly as depicted above.

If you choose a function that returns the output, it must return a single string or character array that displays the proper output when printed. Returning an array of strings is not allowed.

You can use any printable, non-whitespace character instead of o, as long as it is consistent within the activity pattern and across all patterns in your answer.

This is ; may the shortest answer in bytes win!

• I need some clarification. You said you can use any character to represent o. Can you also use any character to represent the spaces (as long as they are different?)? – Kodos Johnson Jan 23 '17 at 1:09
• The spaces have to be blank. You can use actual spaces or you can use control codes to move the cursor around, but you cannot use printable non-space characters. – Dennis Jan 23 '17 at 1:24
• – Magic Octopus Urn Jan 23 '17 at 17:59

05AB1E, 12 10 bytes

Îj¹FÐvû},À


Explanation:

Î              # Push zero and input
j             # Prepend input - 1 spaces
¹F           # Input times do..
Ð          #   Triplicate the string
v }       #   Length times do..
û        #     Palindromize
,      #   Pop and print with a newline
À     #   Rotate the string on to the right


Uses the CP-1252 encoding. Try it online!

• Interesting, smarter than zip. – Magic Octopus Urn Jan 23 '17 at 18:26

MATLAB, 92 90 86 84 bytes

n=input('');p=eye(n)+32;A=repmat([fliplr(p),p,''],1,2^n/2);A(:,n+1:n:end)=[];disp(A)


Try it online!

eye creates an identity matrix. If we flip it and concatenate the original i.e. [fliplr(p),p] we get (for n=3):

0 0 1 1 0 0
0 1 0 0 1 0
1 0 0 0 0 1


With repmat(...,1,2^n/2) we repeat this 2^(n-1) times and get

0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0
0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 ...
1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1


From this we just delete the unnecessary columns, with A(:,n+1:n:end)=[];

• Congrats on 20k!! – Luis Mendo Jan 21 '17 at 22:37
• ​​​​​​​​​​​​​​​Thank​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​you​​​​​​​​​​​​​​​!​​​​​​​​​​​​​​​ – flawr Jan 21 '17 at 22:59

Charcoal, 14 bytes

ＮλＰ^×λoＦ⁻λ¹‖Ｏ→


Try it online!

Explanation

Ｎλ inputs an integer into λ. Ｐ^ is a multidirectional print (SE and SW) of ×λo (string multiplication of λ with o). Then Ｆ⁻λ¹ runs a for loop λ - 1 times, in which ‖Ｏ→ reflects the whole thing to the right with overlap.

• "Ｐ^ is a multidirectional print (SE and SW)" Cool, that's something you don't see very often in programming languages! – Kevin Cruijssen Jan 23 '17 at 10:56
• Just leaving this here – Bassdrop Cumberwubwubwub Jan 24 '17 at 12:36

Python 2, 87 bytes

n=input()
for i in range(n):print''.join(' o'[abs(j%(2*n)-n)==i]for j in range(1,n<<n))


Try it online!

Uses a formula for the coordinates (i,j) that contain a circle, then joins and prints the grid. There's a lot of golf smell here -- ''.join, two nested ranges, for over exec, so there's likely to be improvements.

Python 2, 83 81 bytes

n=input()
i=0
exec"s=' '*n+'o'+' '*i;i+=1;print(s[i:-1]+s[:i:-1])*2**~-n+s[i];"*n


Try it online!

• Welcome to PPCG! Nice first post! – Rɪᴋᴇʀ Jan 23 '17 at 6:33
• That's kind of an understatement; outgolfing xnor in Python is no small feat. I do see some room for improvement. A while loop should save a byte and the exec trick can save a few more. – Dennis Jan 23 '17 at 17:42

Befunge, 98 91 bytes

This uses a , in place of the o, since that enables us to save a couple of bytes.

&::1>\1-:v
+\:v^*2\<_$\1-2*::!+00p*1 :-1_@v0\-g01:%g00:-1<:\p01 ,:^ >0g10g--*!3g,:#^_$\55+


Try it online!

Explanation

Given the stage number, n, we start by calculating the following three parameters of the pattern:

jump_count = 2 ^ (n - 1)
jump_len   = (n - 1) * 2
width      = (jump_len * jump_count) + 1


The jump_len is normalised to avoid it being zero for a stage 1 kangaroo with:

jump_len += !jumplen


We can then output the jump pattern by iterating over the x and y coordinates of the output area, and calculating the appropriate charater to output for each location. The y coordinate counts down from n - 1 to 0, and the x coordinate counts down from width - 1 to 0. We determine whether a dot needs to be shown with the following formula:

jump_off = x % jump_len
show_dot = (jump_off == y) or (jump_off == (jump_len-y))


The show_dot boolean is used as a table index to determine actual character to output at each location. To save on space, we use the start of the last line of source as that table, which is why our o character ends up being a ,.

J, 28 25 bytes

' o'{~]_&(](|.,}.)"1)=@i.


Saved 3 bytes thanks to @Conor O'Brien.

This is based on the palindrome trick from @muddyfish's solution.

Try it online!

Explanation

' o'{~]_&(](|.,}.)"1)=@i.  Input: integer n
i.  Form the range [0, 1, ..., n-1]
=@    Equality table with itself.
Creates an identity matrix of order n
]                    Get n
_&(          )      Repeat n times on x = identity matrix
(     )"1         For each row
|.                 Make a reversed copy
}.              Get a copy with the head removed
,                Append them
]                  Use that as the new value of x
' o'{~                     Index into the char array

• An alternate approach for 31 bytes: ' o'{~3 :'(}."1,.~|."1)^:y=i.y'. I wish I could find a way to remove that explicit verb... Darn ^:. – Conor O'Brien Jan 23 '17 at 17:31
• @ConorO'Brien Thanks, that does help, I think it will be shorter if tacit – miles Jan 23 '17 at 17:56
• @ConorO'Brien I made it tacit, it is indeed shorter! – miles Jan 23 '17 at 18:31
• Awesome! This is pretty awesome. I keep forgetting the dyadic usage of u&v--quite nice. – Conor O'Brien Jan 23 '17 at 18:37

Pyke, 11 bytes

XFd*\o+Q^Vs


Try it here!

 F          -  for i in range(input)
d*\o+     -     " "*i+"o"
Vs -   repeat len(^): palindromise()
X           - print(reversed(^))


k 1="o"
k n|n<-n-1,m<-n*2=unlines[[last$' ':['o'|mod c melem[m-r,r]]|c<-[0..m*2^n]]|r<-[n,n-1..0]]  Try it online! Usage: k 3. Explanation: Given a row r, a column c and m = 2(n-1) an o is set if c mod m equals r or m-r. The outermost list comprehension sets the range of r from n-1 to 0, the next one sets the range of c from 0 to m*2^(n-1) and the innermost acts as conditional returning 'o' if the above formula is fulfilled and ' ' otherwise. This yields a list of strings which is turned into a single newline separated string by unlines. For n=1 the function produces a division-by-zero error, so this case is handled explicitly in the first line. • I really like the ['o'|mod c melem[m-r,r]] part! – flawr Jan 22 '17 at 12:41 C#, 180, 173 171 bytes Wont win this, posting for other C# contestants as something they can beat. n=>{var s=new string[n];for(int a=-1,j=0,i,m=n-1,x=m;j<=m*(Math.Pow(2,n)*n+1);){i=j++%n;s[i]+=x==i?"o":"_";if(i==m&n>1){x+=a;a*=x%m==0?-1:1;}}return string.Join("\n",s);};  complete program: using System; public class P { public static void Main() { Func<int, string> _ = n => { var s = new string[n]; for (int a = -1, j = 0, i, m = n - 1, x = m; j <= m * (Math.Pow(2, n) * n + 1);) { i = j++ % n; s[i] += x‌​ == i ? "o" : "_"; if (i == m & n > 1) { x += a; a *= x % m == 0 ? -1 : 1; } } return string.Join("\n", s); }; Console.Write(_(4)); Console.ReadKey(); } }  edit: -7 bytes thanks to @KevinCruijssen edit: -2 bytes, simplified if • +1 Some things to golf: The ints can be placed inside the for-loop, and you can also add ,i; you can reuse i instead of n-1 after the if-check; || can be |; j++ can be removed and ++ can be added to j. So in total: (n)=>{var s=new string[n];for(int x=0,a=1,j=0,i;j<=Math.Pow(2,n)*(n*n-n);){i=j++%n;s[n-i-1]+=x%n==i?'o':' ';if(i==n-1){x+=a;a*=x==i|x==0?-1:1;}}return string.Join("\n",s);}; (173 bytes) – Kevin Cruijssen Jan 23 '17 at 11:13 • @KevinCruijssen Nice catch! I'll update once i'm back from work. – CSharpie Jan 23 '17 at 11:16 • @KevinCruijssen I allready golfed out the || and && but kept then in the complete program. – CSharpie Jan 23 '17 at 16:27 Pyth, 30 bytes jC.<V*]+*dtQNh*tQ^2Q*+JUQtP_J^  A program that takes input of an integer and prints the result. Uses a quote mark " instead of o. Try it online! How it works jC.<V*]+*dtQNh*tQ^2Q*+JUQtP_J^ Program. Input: Q jC.<V*]+*dtQNh*tQ^2Q*+JUQtP_J^QQ Implicit input fill ] Yield a one-element list, A *dtQ cotaining Q-1 spaces + N appended with a quote mark. h*tQ^2Q Yield 1+(Q-1)*2^Q * Repeat A that many times, giving B UQ Yield [0, 1, 2, ..., Q-1] J (Store that in J) + tP_J Append the reverse of J, discarding the first and last elements * ^QQ Repeat the above Q^Q times, giving C V Vectorised map. For each pair [a,b] from B and C: .< Cyclically rotate a left by b characters C Transpose j Join on newlines Implicitly print  Python 2, 115113108 98 bytes lambda n:'\n'.join(map(''.join,zip(*[' '*abs(i)+'o'+~-n*' 'for i in range(-n+1,n-1)*2**~-n])))+'o'  Try it online! Using range(-n+1,n-1) to create the absolute number of spaces between the bottom and the o to generate  o o o o  and then appending more copies, rotating 90º everything and appending the last o at bottom right J, 58 47 bytes ' o'{&:>~[:(,.}."1)&.>/(2^<:)#<@(|.,.}."1)@=@i.  Saved 11 bytes using the identity matrix idea from @flawr's solution. Try it online! A straightforward application of the definition. Explanation For n = 3, creates the identity matrix of order n. 1 0 0 0 1 0 0 0 1  Then mirror it to make 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1  Repeat that 2n-1 times and drop the head of each row on the duplicates 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1  Use those values as indices into the char array [' ', 'o'] to output a 2d char array  o o o o o o o o o o o o o o o o o  JavaScript (ES6), 83 bytes f= n=> .repeat(n).replace(/ /g,"$'o$-$o$'-".repeat(1<<n-1)+ ).replace(/-.?/g,) <input type=number min=1 oninput=o.textContent=f(this.value)><pre id=o> Jelly, 11 bytes ŒḄ¡ḶUz1Ṛa⁶Y  TryItOnline! How? The printable character used is 0. Builds upon the method of Dennis's answer to his previous question on the subject of kangaroos. ŒḄ¡ḶUz1Ṛa⁶Y - Main link: n e.g. 3 ŒḄ - bounce, initial implicit range(n) e.g. [1,2,3,2,1] ¡ - repeat n times e.g. [1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1] i.e. [1,2,3,2,1] bounced to [1,2,3,2,1,2,3,2,1] bounced to [1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,2,1] Ḷ - lowered range (vectorises) e.g. [[0],[0,1],[0,1,2],[0,1],[0],[0,1],[0,1,2],[0,1],[0],[0,1],[0,1,2],[0,1],[0],[0,1],[0,1,2],[0,1],[0]] U - upend (vectorises) e.g. [[0],[1,0],[2,1,0],[1,0],[0],[1,0],[2,1,0],[1,0],[0],[1,0],[2,1,0],[1,0],[0],[1,0],[2,1,0],[1,0],[0]] z1 - transpose with filler 1 Ṛ - ...and reverse e.g. [[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1], [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], [0,1,2,1,0,1,2,1,0,1,2,1,0,1,2,1,0]] a⁶ - logical and with space character (all non-zeros become spaces) Y - join with line feeds e.g. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  • Nice. This ties with my reference solution, ŒḄ¡Ṭ€z0o⁶ṚY. – Dennis Jan 22 '17 at 5:04 MATL, 27 bytes XyPt3LZ)2&Pht4LZ)lGqX"h48*c  Try it out at MATL Online Python 3, 177 bytes n=5;f=n-1;w='' for i in range(n): s='';a=0;d='\n' if i==f:w='';a=-1;d='' for _ in range(2**f): s+=' '*(f-i)+'o'+' '*(2*i-1)+w+' '*(n-i-2+a) print(s,end=d);w='o' print('o')  Try it online! Perl 6, 10493 88 bytes ->\n{my @a;@a[$_;$++]="o" for [...] |(n-1,0,n-1)xx 2**n/2;say .join for @a».&{$_//" "}}


Inserts o's into a 2D array, and then prints it.

05AB1E, 16 bytes

L<¹Fû}ð×'o«.BøR»


Try it online!

Why and how?

                 # Example input of n=2.
L<               # [0,1] (Push [1..a], decrement).
¹Fû}           # [0,1,0,1,0] (Palindromize n times).
ð×'o«      # ['o',' o','o',' o','o'] (Push n spaces, append o's).
.Bø   # ['o ',' o','o ',' o','o '] (Pad with spaces into 2D array, transpose).
R» # Reverse, join and print.


Java 8, 254 bytes

Golfed:

n->{if(n==1)return"o";int k,x,y,m=n+n-2;char[][]p=new char[n][m];for(y=0;y<n;++y)for(x=0;x<m;)p[y][x++]=' ';for(k=0;k<m;++k)p[k<n?n-k-1:k-n+1][k]='o';String s="";for(y=0;y<n;++y){for(k=0;k<1<<(n-1);++k)for(x=0;x<m;)s+=p[y][x++];if(y==n-1)s+='o';s+='\n';}


Ungolfed:

import java.util.function.*;

public class LeapingKangaroos {

public static void main(final String[] args) {
for (int i = 1; i <= 4; ++i) {
System.out.println(toString(n -> {
if (n == 1) {
return "o";
}
int k, x, y, m = (n + n) - 2;
char[][] p = new char[n][m];
for (y = 0; y < n; ++y) {
for (x = 0; x < m;) {
p[y][x++] = ' ';
}
}
for (k = 0; k < m; ++k) {
p[k < n ? n - k - 1 : (k - n) + 1][k] = 'o';
}
String s = "";
for (y = 0; y < n; ++y) {
for (k = 0; k < (1 << (n - 1)); ++k) {
for (x = 0; x < m;) {
s += p[y][x++];
}
}
if (y == (n - 1)) {
s += 'o';
}
s += '\n';
}
return s;
} , i));
System.out.println();
System.out.println();
}
}

private static String toString(final IntFunction<String> func, final int level) {
return func.apply(level);
}

}


Program output:

o

o o
o o o

o   o   o   o
o o o o o o o o
o   o   o   o   o

o     o     o     o     o     o     o     o
o o   o o   o o   o o   o o   o o   o o   o o
o   o o   o o   o o   o o   o o   o o   o o   o
o     o     o     o     o     o     o     o     o


PHP, 157 bytes

for($i=$n=$argv[1],$r=str_repeat;$i>0;)echo$r($r(' ',$i-1).'o'.$r(' ',2*$n-2*$i-1).($i==$n|$i==1?'':'o').$r(' ',$i-2),2**($n-1)).($i--==1&$n!=1?'o':'')."\n";  Ungolfed: for($i=$n=$argv[1];$i>0;) { // Spacing from beginning of pattern to first 'o'$o  = str_repeat(' ',$i-1); // First 'o' for the ascent$o .= 'o';

// Spacing between ascent and descent
$o .= str_repeat(' ',2*$n-2*$i-1); // Second 'o' for the descent, unless we are at the apex or the bottom$o .= ($i==$n|$i==1?'':'o'); // Spacing to the end of the pattern$o .= str_repeat(' ',$i-2); // Repeat the pattern 2^(n-1) times echo str_repeat($o, 2**($n-1)); // Output final 'o' if we are at the bottom in the last pattern echo$i--==1&\$n!=1?'o':'';

// End of line
echo "\n";

}

• You can replace every 'o' with 1 and every '' with 0. Hope that works, Also, the spaces can be replaced by O or 9. The important is the pattern, according to the rules. But verify first – Ismael Miguel Jan 23 '17 at 0:44