Comments on: Euler Problem 76

By: Michael

Michael — Wed, 23 Sep 2009 19:27:00 +0000

Hi Tim -

Prime is an array of Booleans. In the above, it keeps getting Re-Dimmed to a larger array.

Sift() is a functional implementation (it's above) of the Sieve of Eratosthenes (see http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes). It very quickly assigns TRUE to the boolean if the index is a prime number. So you can find if a number is prime by "If Prime(n)" returns true. To make this work, you have to have set the boundaries above the n you are interested in.

So my "Sift Sieve:=Prime" is a VBA play on words ("sifting the prime sieve" )to create the proper boolean array. Works very well. It can be made faster by being TRUE if a number is NOT PRIME, but I like the logic better this way.

...mrt

By: Tim Martin

Tim Martin — Wed, 23 Sep 2009 16:59:00 +0000

Hi Michael,

Can you explain what the line of code in your post on August 05, 2009 at 2:26 pm does?

It is inside your prime sieve.

Sift Sieve:=Prime

I have not seen/used this before.

-Tim

By: Michael

Michael — Fri, 07 Aug 2009 00:32:00 +0000

Hi Josh -

I just did 131 exactly that way. Double ugly. Then in the forum found a 4-liner solution once the arrays are populated. Some times I have the math insight, but most often not. For 131 I was sort of half-math

Not sure what’s next…I sort of do them in difficulty order picking one that I think understand on page 3 when the problems are sorted in ascending order of difficulty.

#205 goes up Saturday. I found an approach that took me from 385 seconds to about 0.6 seconds.

…mrt

By: JoshG

JoshG — Thu, 06 Aug 2009 17:07:00 +0000

Michael,
Glad to help.

That's a pretty sweet machine for sure.

What problem are you working on next? This latest collection of partition problems, especially #76, is one of the reasons I love PE. I can often hack my way to a solution, sometimes in Euler time and sometimes not, and then visit the forums and get blown away by something I've never heard of before. The flip side of this is that many times it seems that if you don't know the right algorithm / equation, the problem is nearly impossible to solve. #233 for example seems to fall in this class. It can be really frustrating. I think I've found the right approach, but it took quite a while to find it and even longer to understand how to use it. Now, I just need to figure out how to program it...

-Josh

By: Michael

Michael — Wed, 05 Aug 2009 22:05:00 +0000

Hi Josh -

Victory! 0.5625 seconds. Thank you.

Per the System Properties/General: Intel(R) Core(TM)2 Duo CPU E8400 @3.00GHz 1.97GHz, 3.46GB of RAM

It's my tech refresh hot rod. Now on to the next one.

...mrt

By: JoshG

JoshG — Wed, 05 Aug 2009 21:48:00 +0000

Michael,
Your new code runs in 2.5 seconds for me. You must have a fast machine indeed!

Suggestion: in the findsum function argument list, change the line from
ByRef PrimeArr as Variant
to
ByRef PrimeArr() as Long

Cuts the time to ~0.75 seconds for me.

I try not to use globals much, but I make an exception for the primes array. They get used and passed between procedures so often that it's easier for me to just let them go everywhere on their own.

-Josh

By: Michael

Michael — Wed, 05 Aug 2009 21:26:00 +0000

Josh -

Oh. Haven't got the hang of it yet. My old code did run in 3.5 seconds. New arrayed code in 1.5. Something eludes my grasp here about ref to arrays. No globals any more.

Sub Euler77()
Dim MaxNum As Long, T As Single, i As Long, j As Long
Dim Item As Long, Key As String, T1 As Single
Dim Prime() As Boolean, PrimeArr(1 To 100) As Long

T = Timer

MaxNum = 1
j = 0
Do
MaxNum = MaxNum + 1
ReDim Prime(1 To MaxNum) As Boolean
Sift Sieve:=Prime
If Prime(MaxNum) Then
j = j + 1
PrimeArr(j) = MaxNum
End If
Loop Until findsum(MaxNum, 1, PrimeArr, j) > 5000

Debug.Print MaxNum, Timer - T
End Sub
Function findsum(money As Long, maxcoin As Long, ByRef PrimeArr As Variant, j As Long) As Long
Dim sum As Long, i As Long

sum = 0

If maxcoin = j Then
findsum = 1
Exit Function
End If

For i = maxcoin To j
If money - PrimeArr(i) = 0 Then sum = sum + 1
If money - PrimeArr(i) > 0 Then sum = sum + findsum(money - PrimeArr(i), i, PrimeArr, j)
Next i

findsum = sum
End Function

Same number of trips. No surprise there. j is the pointer to the last added prime. Was the collection count before.

...mrt

By: JoshG

JoshG — Wed, 05 Aug 2009 19:06:00 +0000

Hi Michael,
Your code as posted takes about 6 seconds on my machine. I think I found the slowdown though - it's the collection object. You're only adding a few numbers to the collection, but by my count you're extracting a number about 15 million times! For comparison I decided to get a list of the first few primes, store them in a collection, and then time how long it took to extract the same number 15 million times. I then stored the numbers as Longs in an array and timed how long it took to extract the same number 15 million times.
Extract from collection: 3.6 seconds
Extract from array: 0.5 seconds

I modified your code to use an array rather than a collection and consistently got around 1 second. Hope this helps.

-Josh

By: Michael

Michael — Wed, 05 Aug 2009 17:56:00 +0000

At the top, it's

If PrimeCol.Count != to 0 then

...mrt

By: Michael

Michael — Wed, 05 Aug 2009 17:50:00 +0000

Hi Josh - FWIW

Private PrimeCol As New Collection, Num As Long
Sub Euler77()
Dim MaxNum As Long, T As Single
Dim Prime() As Boolean

T = Timer
Num = 0

If PrimeCol.Count 0 Then
Do
PrimeCol.Remove (PrimeCol.Count)
Loop Until PrimeCol.Count = 0
End If

MaxNum = 1
Do
MaxNum = MaxNum + 1
ReDim Prime(1 To MaxNum) As Boolean
Sift Sieve:=Prime
If Prime(MaxNum) Then PrimeCol.Add Item:=MaxNum, Key:=CStr(MaxNum)
Loop Until findsum(MaxNum, 1) > 5000

Debug.Print MaxNum, Timer - T, Num
End Sub
Function findsum(money As Long, maxcoin As Long) As Long
Dim sum As Long, i As Long
Num = Num + 1
sum = 0

If maxcoin = PrimeCol.Count Then
findsum = 1
Exit Function
End If

For i = maxcoin To PrimeCol.Count
If money - PrimeCol(i) = 0 Then sum = sum + 1
If money - PrimeCol(i) > 0 Then sum = sum + findsum(money - PrimeCol(i), i)
Next i

findsum = sum

End Function
Function Sift(ByRef Sieve As Variant) As Variant
'Sets Sieve(N) TRUE if prime
Dim Limit As Long, BreakPT As Long
Dim N As Long, M As Long, Count As Long

Limit = UBound(Sieve)
BreakPT = Int(Sqr(Limit))

Sieve(1) = False
Sieve(2) = True

For N = 3 To Limit
Sieve(N) = True
If N Mod 2 = 0 Then Sieve(N) = False
Next N

For N = 3 To BreakPT Step 2
If Sieve(N) Then
For M = N * N To Limit Step 2 * N
Sieve(M) = False
Next M
End If
Next N

End Function

...mrt