I need to take input values, and in the most efficient manner possible find a sum closest to a value X, between value X and Y.(adsbygoogle = window.adsbygoogle || []).push({});

The number of input values is variable, and all input is negative. X doesn't have to be lower than Y, and vice versa. That is, X can be -8388608 or -(2^23) and Y can be 0, or X can be -8388609 and Y can be -16777216 or -(2^24).

I am usingVBAfor quick testing which will be put into aVB.Netapplication.

Remember,efficiency... the number of tests that would have to be performed via loops would range from around 32768 to well over 16777216 (32^3 and 256^3, respectively)...

The values inputted will be applied to an array. The input may occur as "45" and "63" and mean 45 through 63 as input values, but the array that is calculated, Array(45) maybe -8388600 or some other negative number.

Because of the huge number of calculations that may unnecessarily performed, I need either an efficient way to loop through common values (ergo, the sum value of 0, 0, 1 shouldn't be recalculated later as as 0, 1, 0 or 1, 0, 0) or a simple mathematical approach to finding a sum of appropriate value.

This help would be greatly appreciated. Thank you.

The arithmatic is usually modular, and related to level (game is Diablo 2, although this is the hacking side of it involving 1.09d and extraordinarily large numbers.)

For example, the BoCL value 8 for level X is Level * 8 / x

The math is modular, and signed, for -8,388,608 to positive 8,388,607. So having two BoCL(8) is the same as BoCL(16), but I am using a derivative arithmatic in the game that only applies to the negative values. The sum of these values must be negative, and is not modular. Moreover, let's say I have the values:

10, 10, 0

Well, that isn't BoCL(20) but rather the sum of the modular values for BoCL(10) and BoCL(10). If BoCL(10) = -8388608, then (10, 10, 0) is -16,777,216.

This presents a unique problem, as I cannot simply perform a loop check on the values 1 to X, X being the highest possible value times three. Let's say it's 63 normally.

(63, 0, 0) is not necessarily equal to (32, 31, 0) and thus any operation that derives the answer must take that into account, it cannot simply do BoCL(1) through BoCL(189).

Edit: An efficient implementation could also occur so that the values BoCL(1) to BoCL(Limit * 3)... such that you could take the modular sum you want, say, -8388609, and specify the closest value to 8388607 (that value taken modular). So you could specify that if 8388607 is BoCL(100) then any number of negative values that sum to 100, such as BoCL(25) + BoCL(25) + BoCL(50) would sum to -8388609. Does this make sense?

So, for the sake of simplicity using 63 as the new limit just for ease... you can say that any two negative values that sum to the value 63, will have a value equal to the negative 63 which is -8,781,824. And this can be tested, using the values 31 and 32, which are -4,587,520, and -4,194,304 respectively.Code (Text):BoCL Value

22 -8126464

23 -7733248

24 -7340032

25 -6946816

26 -6553600

27 -6160384

28 -5767168

29 -5373952

30 -4980736

31 -4587520

32 -4194304

33 -3801088

34 -3407872

35 -3014656

36 -2621440

37 -2228224

38 -1835008

39 -1441792

40 -1048576

41 -655360

42 -262144

43 131072

44 524288

45 917504

46 1310720

47 1703936

48 2097152

49 2490368

50 2883584

51 3276800

52 3670016

53 4063232

54 4456448

55 4849664

56 5242880

57 5636096

58 6029312

59 6422528

60 6815744

61 7208960

62 7602176

63 7995392

However, there will be impossible values, such as the values of BoCL(1) to BoCL(21), as that range is positive there are no negative sums for 1 to 21.

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# Looking for efficient solution to problem

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