How to get every possible combinations of elements to approach a value and plot them together?

I have, x = [144.2,31,138.8,56,54,27,25,24,18,17,12,4,266,240.5,215,132,75,30.3,20,19,18,18] and I would like a function to find all possible combinations to get the closest possible to a given value y.

For example if I give the value 325, I want to have in return the elements, " 144.2 138.8 24 18 (since 144.2+138.8+24+18=325) ; error=0 ; ", " 144.2 138.8 25 17 (since 144.2+138.8+25+17=325) ; error=0; ", and so on.

Or if I give the value 208, I want to have in return the elements, "56 132 20 (since 56+132+20=208) ; error=0; ", " 31 56 54 25 4 20 18 (since 31+56+54+25+4+20+18=208) ; error=0; ", and so on.

The process needs to comply with following conditions:

• The combination to get the closest possible to a given value y but never more than y, always less or equal.
• If more than one combination contains error=0; or and equal error, all the possible combinations will be provided.
• Find the same for 0 to 325 and plot the closest value/s and it's error wrt y (0 to 325).

[Stephen23]

@Khalid Hassan: this sounds like homework. What have you tried so far?

http://web.archive.org/web/20210105072921/https://www.mathworks.com/matlabcentral/answers/709063-how-to-get-every-possible-combinations-of-elements-to-approach-a-value-and-plot-them-together

[Khalid Hassan]

I have tried this,

x = [144.2,31,138.8,56,54,27,25,24,18,17,12,4,266,240.5,215,132,75,30.3,20,19,18,18];

y = 325

X = [ x, -1;

-x, -1];

Y = [y; -y];

n = length(x);

f = [zeros(n,1); 1];

lo = [zeros(n,1); 0];

hi = [ones(n,1); Inf];

a = intlinprog(f, 1:n, X, Y, [], [], lo, hi);

keep = round(a(1:n))==1;

subx = x(keep)

sumsubx = sum(subx)

y

error = y - sumsubx

but the problem is, "error" is becoming negative in some cases, for example y=15, error=-1.which don't comply with 1st condition.

Answer 1

[KSSV]

x = [144.2,31,138.8,56,54,27,25,24,18,17,12,4,266,240.5,215,132,75,30.3,20,19,18,18] ;
n = 3 ;
val = 325 ;

y = nchoosek(x,n) ;
thesum = sum(y,2) ; 

idx = abs(thesum-val)<10^-2 ;
iwant = y(idx,:)

[Khalid Hassan]

n will not be fixed.

[KSSV]

Run a loop...for n.

[Khalid Hassan]

Hi, probably it's finding only the error=0 combinations. if, error is not zero, it isn't showing anything. but, I want to show the closest possible error values too.

[KSSV]

Change the tolerance value to your desired error.

tol = 1 ;
idx = abs(thesum-val)<tol ;
iwant = y(idx,:)

[Stephen23]

Given the requirement "...get the closest possible to a given value y but never more than y, always less or equal" using abs(..) does not help (hint: only positive or negative difference is useful for this task, you just need to think about which one).