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Make an algorithm that, given a bunch of (n) random INTEGERs and two inputted (sp??) LONGs, where the sum of the LONGs equals the sum of the integers,
finds the combination of INTEGERs for each LONG that most closely approximate (or exactly equal) the LONG's individual values.
Example:
INTEGERS: 5 4 2 3 = 14
LONGs: 6 8
Solution:
4 2, 5 3
Most efficient (or, the one that actually works, if there is only one that works..) algorithm wins...
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let's say the two longs = 10, 8
and the integers are 7, 2, and 9
both sets sum 18
would you want the program to say "7+2, 9" or "9+2, 7"? Both return answers (9, 9) or (11, 7) that are one away from correct.
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Meg.
p.s. cool challenge
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heh. Good question.
Just any equivalent answer will do.
You could just display all equivalent answers. That would be even cooler.
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*swats the flies and gets rid of the giant dust balls*
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Quote:*swats the flies and gets rid of the giant dust balls*
Need some help there? I've got a vacuum
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Aga, I had such a question on a programming tournament (olympiad) once, and the answer is just like:
Code: [pseudocode]
do
do
give highest number from the stack
loop all groups
do
give lowest number from the stack
loop all groups
loop all available 'stacknumbers'
[/pseudocode]
I got many points on that question
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I don't get it.
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First you divide all highest numbers to all groups, then you divide all lowest numbers to each group. That should give a good answer. This is a global algorithm, there could be better answers, but take a look:
LONGs: 8, 6
INTs: 5, 4, 3, 2
My algo: 5 + 2 = 7 and 4 + 3 = 7
Oneofatime algo: 5 + 3 = 8, 4 + 2 = 6
But take a look: average of my algo is 7, the one of a time algo is 7 as well.
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How would it work with this:
100 500
200 100 195 15
?
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This is my shot at it. It's probably not optimized, but it seems to work. My strategy is to only try to fit the smaller of the two longs, and I start with the biggest integers first.
If you want to try it with your own numbers, call GroupAddends with the longs in SUM(), the integers in Choices() (starting with Choices(1)), and the number of integers in n. The output is in Groups(), with the number of integers for the jth long in Groups(j, 0), and the integers starting from Groups(j, 1).
Code: DEFINT AZ
DECLARE SUB Sort (Array%(), n%)
DECLARE SUB GroupAddends (Sum() AS LONG, Choices%(), n%, Groups%(), Errr%)
DECLARE SUB FindAddends (Chcs%(), n%, BYVAL Total AS LONG, Sum AS LONG, Addends%(), Errr%)
DIM Sum(1) AS LONG, Total AS LONG
n = 14
DIM Choices(n), Groups(1, n)
CLS
RANDOMIZE TIMER
' Generate & Display Numbers 
Adds0 = INT(RND * (n  1) + 1)
FOR j = 1 TO n
Choices(j) = INT(RND * 1000 + .5)
PRINT Choices(j);
IF j <= Adds0 THEN
Sum(0) = Sum(0) + Choices(j)
IF j < Adds0 THEN
PRINT "+";
ELSE
PRINT "="; Sum(0)
END IF
ELSE
Sum(1) = Sum(1) + Choices(j)
IF j < n THEN
PRINT "+";
ELSE
PRINT "="; Sum(1)
END IF
END IF
NEXT
PRINT
' End of Genrate & Display Numbers 
GroupAddends Sum(), Choices(), n, Groups(), Errr
' Display Results 
FOR i = 0 TO 1
Total = 0
FOR j = 1 TO Groups(i, 0)  1
Total = Total + Groups(i, j)
PRINT Groups(i, j); "+";
NEXT
Total = Total + Groups(i, j)
PRINT Groups(i, j); "="; Total
NEXT
PRINT "Error ="; Errr
' End of Display results 
SUB FindAddends (Chcs(), n, BYVAL Total AS LONG, Sum AS LONG, Addends(), Errr)
DIM Adds(n)
Errr = 10000
j = n
DO
IF Total <= Sum THEN
IF Sum  Total < Errr THEN
Errr = Sum  Total
Addends(0) = j
FOR i = 1 TO j
Addends(i) = Chcs(i)
NEXT
END IF
EXIT SUB
ELSE
Total = Total  Chcs(j)
IF Chcs(j) < Sum THEN
FindAddends Chcs(), j  1, Total, Sum  Chcs(j), Adds(), NewEr
IF Sum  Chcs(j) < NewEr THEN
IF Sum  Chcs(j) < Errr THEN
Addends(0) = 1
Addends(1) = Chcs(j)
Errr = Sum  Chcs(j)
END IF
ELSEIF NewEr < Errr THEN
Errr = NewEr
Addends(0) = Adds(0) + 1
FOR i = 1 TO Adds(0)
Addends(i) = Adds(i)
NEXT
Addends(Addends(0)) = Chcs(j)
IF NewEr = 0 THEN EXIT SUB
END IF
ELSE
IF Chcs(j)  Sum < Errr THEN
Errr = Chcs(j)  Sum
Addends(0) = 1
Addends(1) = Chcs(j)
END IF
IF Chcs(j) = Sum THEN EXIT SUB
END IF
END IF
j = j  1
LOOP WHILE j > 0
END SUB
SUB GroupAddends (Sum() AS LONG, Choices(), n, Groups(), Errr)
DIM Addends(n), Total AS LONG
Sort Choices(), n
Smaller = (Sum(1) < Sum(0))
Total = Sum(0) + Sum(1)
FindAddends Choices(), n, Total, Sum(Smaller), Addends(), Errr
CIndex = 1
GIndex = 0
Groups(Smaller, 0) = Addends(0)
Groups(1  Smaller, 0) = n  Addends(0)
FOR j = 1 TO Addends(0)
WHILE Addends(j) > Choices(CIndex)
GIndex = GIndex + 1
Groups(1  Smaller, GIndex) = Choices(CIndex)
CIndex = CIndex + 1
WEND
Groups(Smaller, j) = Addends(j)
CIndex = CIndex + 1
NEXT
IF CIndex <= n THEN
FOR j = CIndex TO n
GIndex = GIndex + 1
Groups(1  Smaller, GIndex) = Choices(j)
NEXT
END IF
END SUB
SUB Sort (Array(), n)
DO
Changes = 0
FOR j = 0 TO n  1
IF Array(j) > Array(j + 1) THEN
SWAP Array(j), Array(j + 1)
Changes = Changes + 1
END IF
NEXT
LOOP WHILE Changes > 0
END SUB
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