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/x=input();y=x-1;w=x+y;A=[];R=range;k,j,s,t=R(4) \
| for i in R(2,w*w): |
| A+=[(x,y)]*all(i%d for d in R(2,i)) |
| if i==s:j,k,s,t=k,-j,s+t/2,t+1 |
| x+=j;y+=k |
| for y in R(w):print"".join(" *"[(x,y)in A]for x in R(w)) |
\_________________________________________________________/
\ ^__^
\ (oo)\_______
(__)\ )\/\
||----w |
|| ||
x=input();y=x-1;w=x+y
A=[];R=range;k,j,s,t=R(4)
for i in R(2,w*w):
A+=[(x,y)]*all(i%d for d in R(2,i))
if i==s:j,k=k,-j;s,t=s+t/2,t+1
x+=j;y+=k
for y in R(w):print"".join(" *"[(x,y)in A]for x in R(w))
How it works
The idea is to fill A with x,y coords that need to be printed as '*'
The algorithm starts at the cell corresponding to 2, so the special case of testing 1 for primality is avoided.
x,y is the cell of interest
j,k keep track of whether we need to inc or dec x or y to get to the next cell
s is the value of i at the next corner
t keeps track of the increment to s
all(i%d for d in R(2,i)) does the primality check
The last line is rather clumsy. It iterates over all the cells and decides whether to place a space or an asterisk
MATLAB: 182 167 156 characters
Script ulam.m:
A=1;b=ones(1,4);for i=0:(input('')-2),c=b(4);b=b+i*8+(2:2:8);A=[b(2):-1:b(1);(b(2)+1:b(3)-1)' A (b(1)-1:-1:c+1)';b(3):b(4)];end;disp(char(isprime(A)*10+32))
And formatted a little nicer:
A = 1;
b = ones(1,4);
for i = 0:(input('')-2),
c = b(4);
b = b+i*8+(2:2:8);
A = [b(2):-1:b(1); (b(2)+1:b(3)-1)' A (b(1)-1:-1:c+1)'; b(3):b(4)];
end;
disp(char(isprime(A)*10+32))
Test cases:
>> ulam
2
* *
*
*
>> ulam
3
* *
* *
* **
*
*
>> ulam
5
* *
* *
* * *
* * *
* ** *
* *
* *
* *
* *
~.(:S+,:R{S\-:|;R{S-:$|>' *'1/[|$.|]2/@:d|~)$<!^=~:$;:y.*4*$-y-)2d*$y-*+:$,{)$\%!},,2==}%n}%
97 characters
~.(:S+,:R{S\-:|;R{S-:$|>' *'1/[|$.|]2/@:d|~)$<!^=~:$;:y.*4*$-y-)2d*$y-*+.1=3*+:$,2>{$\%!},!=}%n}%
99 characters
~.(:S+,{S-}%:R{~):|;R{:$|>' *'1/[|$.|]2/@:d|~)$<!^=~:$;:y.*4*$-y-)2d*$y-*+.1=3*+:$,2>{$\%!},!=}%n}%
100 characters
~:S.(+,{S(-}%:R{~):|;R{:$|>' *'1/[|$.|]2/@:d|~)$<!^=~:$;:y.*4*$-y-)2d*$y-*+.1=3*+:$,2>{$\%!},!=}%n}%
101 characters
~:S.(+,{S(-}%:R{~):v;R{:$v>:d;' *'1/[v$.v]2/v~)$<!d^=~:$;:y.*4*$-y-)2d*$y-*+.1=3*+:$,2>{$\%!},!=}%n}%
(if newlines are removed):
main(int u,char**b){
for(int v,x,y,S=v=**++b-48;--v>-S;putchar(10))
for(u=-S;++u<S;){
x=u;y=v;v>-u^v<u?:(x=v,y=u);
x=4*y*y-x-y+1+2*(v<u)*(x-y);
for(y=1;x%++y;);
putchar(y^x?32:42);}}
Compiled with
> gcc -std=c99 -o ulam ulam.c
Warning. This program is slow, because is does a trial division up to 2^31. But is does produce the required output:
* *
* *
* * *
* * *
* ** *
* *
* *
* *
* *
In nicely formatted C and with redundant #includes:
#include <stdio.h>
#include <stdlib.h>
int main(int argc, char** argv) {
int u,v,x,y,d,S = atoi(argv[1]);
/* v is the y coordinate of grid */
for (v=S; v>=-S; --v)
/* u is the x coordinate. The second operand (!putchar...) of the boolean or
* is only ececuted a a end of a x line and it prints a newline (10) */
for (u=-S; u<=S || !putchar(10); ++u) {
/* x,y are u,v after "normalizing" the coordintes to quadrant 0
normalizing is done with the two comparisions, swapping and and
an additional term later */
d = v<u;
x=u;
y=v;
if (v<=-u ^ d) {
x=v;
y=u;
}
/* reuse x, x is now the number at grid (u,v) */
x = 4*y*y -x-y+1 +2*d*(x-y);
/* primality test, y resused as loop variable, won't win a speed contest */
for (y=2; y<x && x%y; ++y)
;
putchar(y!=x?' ':'*');
}
}
It works by transforming the coordinates of the grid to the appropriate number and then performing the primality test, intead of drawing in a snake-like manner. The different equations for the four "quadrants" can be collapsed into one with swapping x and y and an additional term for "backward counting".
n=2*gets.to_i-1
r=n**2
l,c=[nil]*r,r/2
r.times{|i|l[c]=i+1;c=i==0||l[c-n]&&!l[c+1]?c+1:l[c-1]&&!l[c-n]?c-n:l[c+n]?c-1:c+n}
r.times{|i|print"1"*l[i]!~/^1?$|^(11+?)\1+$/?'*':' ',i%n==n-1?"\n":''}
For some reason, ruby1.9 wants another space on line 4:
r.times{|i|l[c]=i+1;c=i==0||l[c-n]&&!l[c+1]?c+1:l[c-1]&&!l[c-n]?c-n :l[c+n]?c-1:c+n}
drhirsch's C ported to python.
S=input();R=range(-S+1,S)
for w in R:
p="";v=-w
for u in R:d=v<u;x,y=[(u,v),(v,u)][(w>=u)^d];x=4*y*y-x-y+1+2*d*(x-y);p+=" *"[(x>1)*all(x%f for f in range(2,x))]
print p
echo 20 |python ulam.py
* * * * * *
* * * * * *
* * * * *
* * * * * *
* * * *
* * * * * *
* * * * * *
* * * * * * *
* * * * * * *
* * * * *
* * * * * * * *
* * * * * * *
* * * * *
* * * * * *
* * * * * * * * *
* * *
* * * * * * * * * *
* * * * * * * * * *
* * * *
* * ** * * * * * *
* * * *
* *
* * * * * * * * * * *
* * * * * * * *
* *
* * * * * * * *
* * * * * * *
* * * * *
* * * * * *
* * * * * * * * *
* * * *
* * * * * * * *
* * * * * *
* * * * * *
* * * * * *
* * * *
* * * * * *
* *
* * * * * *
based on @gnovice solution, improved by using MATLAB's spiral function :)
disp(char(isprime(flipud(spiral(2*input('')-1)))*10+32))
Test Cases:
>> disp(char(isprime(flipud(spiral(2*input('')-1)))*10+32))
2
* *
*
*
>> disp(char(isprime(flipud(spiral(2*input('')-1)))*10+32))
3
* *
* *
* **
*
*
>> disp(char(isprime(flipud(spiral(2*input('')-1)))*10+32))
5
* *
* *
* * *
* * *
* ** *
* *
* *
* *
* *
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