Goldbach's comet: Difference between revisions
Nim solution.
(Nim solution.) |
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[graphical object showing Goldbach's comet]</pre>
=={{header|Nim}}==
{{libheader|nim-plotly}}
{{libheader|chroma}}
To display the Golbach’s comet, we use a library providing a Nim interface to “plotly”. The graph is displayed into a browser.
<syntaxhighlight lang="Nim">import std/[math, strformat, strutils, sugar]
import chroma, plotly
const
N1 = 100 # For part 1 of task.
N2 = 1_000_000 # For part 2 of task.
N3 = 2000 # For stretch part.
# Erathostenes sieve.
var isPrime: array[1..N1, bool]
for i in 2..N1: isPrime[i] = true
for n in 2..sqrt(N1.toFloat).int:
for k in countup(n * n, N1, n):
isPrime[k] = false
proc g(n: int): int =
## Goldbach function.
assert n > 2 and n mod 2 == 0, "“n” must be even and greater than 2."
for i in 1..(n div 2):
if isPrime[i] and isPrime[n - i]:
inc result
# Part 1.
echo &"First {N1} G numbers:"
var col = 1
for n in 2..N1:
stdout.write align($g( 2 * n), 3)
stdout.write if col mod 10 == 0: '\n' else: ' '
inc col
# Part 2.
echo &"\nG({N2}) = ", g(N2)
# Stretch part.
const Colors = collect(for name in ["red", "blue", "green"]: name.parseHtmlName())
var x, y: seq[float]
var colors: seq[Color]
for n in 2..N3:
x.add n.toFloat
y.add g(2 * n).toFloat
colors.add Colors[n mod 3]
let trace = Trace[float](type: Scatter, mode: Markers, marker: Marker[float](color: colors), xs: x, ys: y)
let layout = Layout(title: "Goldbach’s comet", width: 1200, height: 400)
Plot[float64](layout: layout, traces: @[trace]).show(removeTempFile = true)
</syntaxhighlight>
{{out}}
<pre>First 100 G numbers:
1 1 1 2 1 2 2 2 2 3
3 3 2 3 2 4 4 2 3 4
3 4 5 4 3 5 3 4 6 3
5 6 2 5 6 5 5 7 4 5
8 5 4 9 4 5 7 3 6 8
5 6 8 6 7 10 6 6 12 4
5 10 3 7 9 6 5 8 7 8
11 6 5 12 4 8 11 5 8 10
5 6 13 9 6 11 7 7 14 6
8 13 5 8 11 7 9 13 8 9
G(1000000) = 5402
</pre>
=={{header|Perl}}==
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