Hello all,
The output is almost perfect on a console, plus different fonts have
different widths for different numbers. So I guess the look of the
triangles will vary with email clients. I'd like to give credit to my
friend Fedor for coming up with much of the output equation. The
output works for any size output (notice how the spacing get smaller
toward the middle).
$ ./pp_pascal.rb 10
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
$ ./pp_pascal.rb 15
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55
11 1
1 12 66 220 495 792 924 792 495 220
66 12 1
1 13 78 286 715 1287 1716 1716 1287 715 286
78 13 1
1 14 91 364 1001 2002 3003 3432 3003 2002 1001
364 91 14 1
On an Athlon64 1.8 GHz
$ time ./pp_pascal.rb 666 > /dev/null
real 0m16.337s
user 0m16.147s
sys 0m0.185s
And finally the code:
#!/usr/bin/ruby
$factCache = [ 1 ]
def factorial(n)
return $factCache[n] if n <= $factCache.length
prod = $factCache.last
while $factCache.length <= n
$factCache.push(prod *= $factCache.length)
end
return prod
end
def pascalCombination(n, k)
return factorial(n) / (factorial(k) * factorial(n - k))
end
max = $*[0].to_i - 1
maxDigits = Math.log10(pascalCombination(max, max/2)).floor + 1
spaces = (maxDigits + maxDigits/2).ceil
for row in 0..max
print " " * ((max - row)*spaces/2)
for col in 0..row
combination = pascalCombination(row, col)
digitSpace = Math.log10(combination).floor + 1
digitSpace = 1 if digitSpace == 0
print " " * (spaces - digitSpace) + combination.to_s
end
print "\n"
end