Comments on: Euler Problem 203

By: gruff999

gruff999 — Tue, 29 Sep 2009 12:59:00 +0000

fzz

I'm a 'hit it until it works' coder, rarely using subtleties of variable types - other than arrays. I wouldn't, for example, think to use dictionaries or collections, though obviously it looks like I should.

So when someone ReDims something other than an array it confuses me. Can you shed light on the internals of:

Dim pt As Variant
ReDim pt(1 To 51) As Double

gruff999

By: JoshG

JoshG — Mon, 28 Sep 2009 16:54:00 +0000

You guys and your collections / dictionaries. It makes things so...easy. My idea was to build the triangle, add each number to a list, sort the list, and then pull out the unique values for testing. It runs in a blink, but it's not nearly so neat and clean as fzz's. Well done.

-Josh

By: Michael

Michael — Mon, 28 Sep 2009 14:00:00 +0000

fzz -

Very nice. I particularly like doing the "heavy-lifting" in the dictionary keys, and having the item be a tiny boolean. That's a neat trick, and all that's required..

For those scoring at home, to use a dictionary object, you need to set a reference (via the Tools menu) to the Microsoft Scripting Runtime. One advantage of a dictionary over a collection is that a dictionary has an "exists" method (as fzz used). Takes the place of my IsIn(collection,key) function. Dictionaries are slower than collections, but you can't improve on fzz's zero seconds.

...mrt

By: fzz

fzz — Sun, 27 Sep 2009 07:26:00 +0000

Use the symmetry of Pascal's triangle (PT). If you index the 0th through 50th order rows 0..50 for rows and -50..50 for columns using the convention that even order rows use even column indices and odd order rows use odd column indices, PT(row, -col) = PT(row, col) for all row and col. You only need to fill out PT for nonnegative col.

Also, with only 4 squared primes to check, the Sieve of Eratosthenes is too much overhead.

The following runs a bit more than 10 times faster than your code, and it's all in one procedure (which is one of the reasons it's faster).

Function euler203fb()
Dim dn As New Dictionary
Dim pt As Variant, p As Double
Dim i As Long, j As Long

ReDim pt(1 To 51) As Double

pt(1) = 1
pt(2) = 1

dn.Add Key:=1, Item:=False

'use the symmetry of the triangle and don't do more than necessary
For i = 2 To 50
For j = i + 1 To i 2 + 1 Step -1
pt(j) = pt(j) + pt(j - 1)
p = pt(j)
'check if divisible by squared primes 2, 3, 5 or 7
If p / 4 - Int(p / 4) Then _
If p / 9 - Int(p / 9) Then _
If p / 25 - Int(p / 25) Then _
If p / 49 - Int(p / 49) Then _
If Not dn.Exists(p) Then dn.Add Key:=p, Item:=False
Next j
If i Mod 2 = 0 Then pt(j) = pt(j + 2)
Next i

Erase pt
pt = dn.Keys
dn.RemoveAll

For i = LBound(pt) To UBound(pt)
euler203fb = euler203fb + pt(i)
Next i

Erase pt

End Function

By: MaryP

MaryP — Sat, 26 Sep 2009 21:42:00 +0000

Whew; math. Nice job…I think.