I am having an array with positive integers, and i want to know all the possibility that the sum of elements of the array is close to or equal to a number say (N))

I am having an array with positive integers, and i want to know all the possibility that the sum of elements of the array is close to or equal to a number say (N)) and no index (element in the array) will be repeated

A = [ 0 7 30 16 23 11 19 15 28 8 8 7 14 6 19 11 12 26 17 6 15 5 10 ]

N = 40 (or close to 40 like 36,37,38,39)

the possible sum of the numbers are like

8+6+26 = 40

23+15 = 38

16+17+6=39

15+5+19=39

and so on

[Dyuman Joshi]

Please specify what does close mean? 41, 42 43, and 44 are close to 40 as well.

What tolerance of numbers counts as close?

[Ashish Verma]

Close means in between (40-min no. in the array) to 40. Not more than 40.

[Matt J]

Why is 23+15 = 38 an acceptable selection when it is still possible to add further A(i) to the sequence without exceeding N=40? In particular: 23+15+0 = 38

[Torsten]

23+15+0 = 39

?

Answer 1

[Matt J]

N=40;
A = [1 7 13 20 38 39 40];

A=unique(A);
n=find(cumsum(A)<=N,1,'last');

result=cell(n,1);
for i=1:n

    tmp=subCollection(N,A,i);

    tmp(:,end+1:n)=nan;

    result{i}=tmp;

end

result=cell2mat(result) %final result

result = 7×3

40 NaN NaN 1 38 NaN 1 39 NaN 1 7 13 1 7 20 1 13 20 7 13 20

function T=subCollection(N,A,m)

  
  J=nchoosek(1:numel(A),m);

  I=repmat( (1:height(J))'  ,1,m);

  %S=sparse(I,J,1);
  S=accumarray([I(:),J(:)],1);

  delta=N-S*A(:);

  C=(1./(1-S));

  mincomp=min( C.*A(:).' ,[],2);

  idx=delta<mincomp & delta>=0;

  T=(1./S).*A(:).';
  T=sort(T(idx,:),2);
  T(isinf(T))=nan;
  T=T(:,1:m);


end

[Ashish Verma]

According to me results will be some matrices, where the sum will be close to 40 and the matrix contains distinct elements or no index of array will be repeated (because of duplicacy). For eg, possibility of 3 elements sum will be

[8+6+26 = 40

23+15 = 38

16+17+6=39

15+5+19=39

...]

[Matt J]

That is what I have given you.