Code Golf: Leibniz formula for Pi

Asked 2009-01-02T17:42:45.507

I recently posted one of my favourite interview whiteboard coding questions in "What's your more controversial programming opinion", which is to write a function that computes Pi using the Leibniz formula.

It can be approached in a number of different ways, and the exit condition takes a bit of thought, so I thought it might make an interesting code golf question. Shortest code wins!

Given that Pi can be estimated using the function 4 * (1 - 1/3 + 1/5 - 1/7 + ...) with more terms giving greater accuracy, write a function that calculates Pi to within 0.00001.

Edit: 3 Jan 2008

As suggested in the comments I changed the exit condition to be within 0.00001 as that's what I really meant (an accuracy 5 decimal places is much harder due to rounding and so I wouldn't want to ask that in an interview, whereas within 0.00001 is an easier to understand and implement exit condition).

Also, to answer the comments, I guess my intention was that the solution should compute the number of iterations, or check when it had done enough, but there's nothing to prevent you from pre-computing the number of iterations and using that number. I really asked the question out of interest to see what people would come up with.

code-golf rosetta-stone

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5 Answers

F#:

Attempt #1:

let pi = 3.14159

Cheating? No, its winning with style!

Attempt #2:


let pi =
    seq { 0 .. 100 }
    |> Seq.map (fun x -> float x)
    |> Seq.fold (fun x y -> x + (Math.Pow(-1.0, y)/(2.0 * y + 1.0))) 0.0
    |> (fun x -> x * 4.0)

Its not as compact as it could possibly get, but pretty idiomatic F#.

answered 2009-01-02T18:44:42.327

Javascript:

a=0,b=-1,d=-4,c=1e6;while(c--)a+=(d=-d)/(b+=2)

In javascript. 51 characters. Obviously not going to win but eh. :P

Edit -- updated to be 46 characters now, thanks to Strager. :)

UPDATE (March 30 2010)

A faster (precise only to 5 decimal places) 43 character version by David Murdoch

for(a=0,b=1,d=4,c=~4e5;++c;d=-d)a-=d/(b-=2)

answered 2009-01-03T02:27:13.483

C# using iterator block:

static IEnumerable<double> Pi()
{
    double i = 4, j = 1, k = 4;
    for (;;)
    {
        yield return k;
        k += (i *= -1) / (j += 2);
    }
}

answered 2009-01-03T09:00:31.660

VB 117 chars:

Function Pi()
  Dim t = 0D
  For n = 0 To 1000000
    t += Math.Pow(-1, n) / (2 * n + 1)
  Next
  Return 4 * t
End Function

VB LINQ 115 chars (omitting the unnecessary line continuation):

Function Pi()
  Return 4 * Enumerable.Range(0, 1000000) _
             .Sum(Function(n) Math.Pow(-1, n) / (2 * n + 1))
End Function

And then call:

Sub Main()
  Console.WriteLine("{0:n5}", Pi)
End Sub

answered 2009-01-03T04:23:32.187

Lua, 46 characters

p=4 for i=3,9^6,4 do p=p-8/i/(i+2)end print(p)

answered 2010-02-16T17:47:31.780

Code Golf: Leibniz formula for Pi

5 Answers

Lua, 46 characters

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