# ASCII Ice Cream

Write a program or function that takes in a positive integer N, and prints or returns an N×N ASCII art string whose top half is a semicircle made of ('s and whose bottom half is a downward-pointing triangle made of V's, with spaces used as padding.

In other words, make an ASCII ice cream cone: (output for N = 17)

      (((((
(((((((((
(((((((((((((
(((((((((((((
(((((((((((((((
(((((((((((((((
(((((((((((((((((
(((((((((((((((((
VVVVVVVVVVVVVVVVV
VVVVVVVVVVVVVVV
VVVVVVVVVVVVV
VVVVVVVVVVV
VVVVVVVVV
VVVVVVV
VVVVV
VVV
V


# Examples

Here are the outputs for N = 1 to 5. Note that for odd N, the triangle always must be the larger half.

V

((
VV

(((
VVV
V

((
((((
VVVV
VV

(((
(((((
VVVVV
VVV
V


And here's an ungolfed Python 3 reference implementation:

N = int(input())
ic = [[' '] * N for _ in range(N)]
for y in range(N//2):
for x in range(N):
if (x - (N - 1) / 2)**2 + (y - (N - 1) / 2)**2 < (N / 2)**2:
ic[y][x] = '('
for y in range(N//2, N):
for x in range(y - N//2, N - (y - N//2)):
ic[y][x] = 'V'
for line in ic:
print(''.join(line))


# Details

• Take input from stdin, command line, or as function argument. Output to stdout or similar, or you may return the string if you write a function.
• The cone portion should exactly match the reference implementation for all N.
• The ice cream portion does not need to exactly match the reference implementation as long as it is clearly in the shape of a semicircle for all N. (This is so you don't have to worry about slight differences in the semicircle due to roundoff errors.)
• There should not be any unnecessary leading spaces but there may be superfluous trailing spaces.
• The output may optionally contain a trailing newline.
• You may optionally use any 3 other distinct printable ASCII characters in place of (, V, and space.

# Scoring

The shortest submission in bytes wins. Tiebreaker goes to the oldest submission.

• Am I the only one who thought "IceCII ASCream" when I read the title? – Sp3000 Mar 2 '15 at 17:19
• @Sp3000 Jeez, I hope so... – Calvin's Hobbies Mar 2 '15 at 17:21

# CJam, 46 bytes

Try it online.

{:Z{Z{Z(2./:R-zYR<):P#YR-zP#+Z2./P#>SP?}/N}fY}


I believe this currently mimics the original specification exactly, which was required when I started producing this answer. There may be potential to save a few bytes by making the math less accurate to the original specification, but until I see a way to save more than one or two bytes doing so, I'll leave it as-is.

### Explanation

{               "Begin block";
:Z{             "For each y from 0 to input-1";
Z{              "For each x from 0 to input-1";
Z(2./:R         "Calculate the radius as (input-1)/2.0";
-z              "Calculate the horizontal distance from the center";
YR<):P          "Calculate the power to raise distances to: (y<radius)+1
(This results in Euclidean distance being calculated for
the ice cream and Manhattan distance being calculated
for the cone)";
#               "Raise the horizontal distance to the determined power";
YR-zP#          "Calculate the vertical distance from the center and
raise it to the determined power";
+               "Add the horizontal and vertical distances";
Z2./P#          "Calculate the solid distance threshold and raise it to
the determined power";
>SP?            "If the solid threshold is exceeded, produce a space;
otherwise, produce the determined power digit
(This results in ice cream being represented by the
digit '2' and the cone by the digit '1')";
}/              "End x loop";
N               "Produce a new line";
}fY             "End y loop";
}               "End block";

• This appears to use 2's and 1's instead of ('s and V's ? – Mark Reed Mar 2 '15 at 22:54
• @MarkReed This is allowed. Last line in the details section. – Jakube Mar 2 '15 at 23:01

## inca2129123121111 107

This mostly uses the formulas from the python example, but using jot-dots and iotas instead of double-looping. The i function performs the circular test for the j function which invokes jot-dot upon it. And the k function performs the triangle test for the l function. The c function catenates the results of j and l and reshapes it to N×N.

edit: -6 combine 2 maps into 1.
edit: -2 remove useless ravels.
edit: nicer typescript.
edit: -10 apply repeated expression array-wise.
edit: -4 factor out repeated expression as a function.
edit: line-by-line commentary.

q:y-(n-1)%2
i:[((n%2)^2)>+/(qx y)^2
j:(~[y%2)i.(~y)
k:2*[x>[|qy
l:(@1+~]y%2)k.(~y)
c:y y#((jn<y),ly){' (V'


In more detail, the entry-point is the c function which takes one argument implicitly named y.

c:y y#((jn<y),ly){' (V'
n<y            } assign y to 'n'
jn<y            } call j(y)
ly        } call l(y)
((    ),  )       } catenate the results
(         ){' (V' } map 0 1 2 to ' ' '(' 'V'
y y#                  } reshape to NxN


The j function receives the same input value as its y parameter.

j:(~[y%2)i.(~y)
y%2         } y divided by 2
[            } floor
~             } iota. this generates the row indices 0..y/2
~y   } iota y. this generates the column indices 0..y
(     )i.(  )  } jot-dot with the function i


The jot-dot here does the double-loop. It calls the i function with every combination of elements from the left and right arrays (0..n/2 and 0..n). So the i function receives as x the y index of the table, and it receives as y the x index. The names got a little backwards here :).

i:[((n%2)^2)>+/(qx y)^2
n%2                 } n divided by 2
(n%2)^2              } squared
x y     } make a 2-element array (x,y)
qx y     } call q on this array


where q does

q:y-(n-1)%2
n-1    } n minus 1
%2 } divided by 2
y-        } y minus that


back to i

i:[((n%2)^2)>+/(qx y)^2
(    )^2  } square the result from q(x,y)
+/          } sum the two numbers
>            } compare the left side (above) with the right (=> 0/1)
[                      } floor


The floor should not be necessary. But apparently there's a bug in the interpreter.

The l function works similarly to the j function, using a jot-dot.

l:(@1+~]y%2)k.(~y)
y%2         } y divided by 2
]            } ceiling
~             } iota 0..ceil(y/2)-1
1+              } add 1 => 1..ceil(y/2)
@                } reverse => ceil(y/2)..1
~y   } iota y  0..y-1
(        )k.(  )  } jot-dot using k


The k function yields a boolean scaled by 2 so the values can be distinguished from the ice cream values later on, in the mapping.

k:2*[x>[|qy
x       } k's left arg
qy  } y-(n-1)%2
|    } abs
[     } floor
x       } left-hand-side again
>      } compare
[        } floor (should be unnecessary)
2*         } scale by 2


In action (piping through tr to remove tab chars which are the REPL's prompt):

josh@Z1 ~/inca
$./inca2 <icecream | tr -d '\t' c1 V c2 (( VV c3 ((( VVV V c4 (( (((( VVVV VV c5 ((( ((((( VVVVV VVV V josh@Z1 ~/inca$


# Python 2, 193 192

Does not use strings, only math

N=input()
R=(N+1)/2;r=range(R)
s=lambda L,U:(10**U-10**L)/9
f=lambda N,m:s(0,N)+s(m,N-m)
g=lambda N,m:s(0,N)+s(m,N-m)*6
for i in r[1:]:print f(N,int(R-(2*R*i-i*i)**.5))
for i in r:print g(N,i)


s(L,U) returns a number of the form "U-digits with the rightmost L zeros and the rest ones"
f(N,m) returns an N-digit number with the inner section of 2 and an m-wide border of 1on each side
g(N,m) does the same, but using 7 for the 'colour' of the inner section since it matches the texture of the cone more closely

Output

N=8         N=9
11122111    112222211
12222221    122222221
22222222    222222222
22222222    222222222
77777777    777777777
17777771    177777771
11777711    117777711
11177111    111777111
111171111

• Very unique way to do it :) – Calvin's Hobbies Mar 4 '15 at 14:13
• If only we can see the ice cream too :P – Optimizer Mar 4 '15 at 14:22

# Perl 6, 175

Pretty straightforward implementation without much golfing, just extraneous whitespace/punctuation elimination:

sub MAIN($d){my$r=($d/2).Int;for 1..$r ->$n {my$y=$n-$r;my$h=sqrt($r*$r-$y*$y).Int;my$w=2*$h+$d%2;say
' 'x($r-$h)~'('x$w};for 1..($d-$r) ->$y {say ' 'x($y-1)~'V'x($d-2*\$y+2)}}