How can I create a loop that iterates thru +/- values of an array to find a solution?

Question

Nick 2017-4-18

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评论： Nick 2017-4-21

Basically, the code I'm trying to write will take an array of data, sum it, and find the solution. The sum is known before hand, but whether the data values are positive or negative are not. I'm thinking I could do this using some sort of double for loop marking coefficients as either 1 or -1 but I'm stuck. Any advice? (I'll show an example)

clear,clc
summ = 2
data = [8, 12, 2]
%loops
%...
%SOLUTION
ans = [8 -12 6]
>>

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Answer 1

Roger Stafford 2017-4-18

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If ‘data’ is a row vector and ‘summ’ is the desired sum, do this:

n = length(data);
d = dec2bin(0:2^n-1,n)-‘0’;
d = repmat(data,2^n,1).*(2*d-1);
f = find(sum(d,2)==summ);
s = d(f,:);

Each row of s should be a “solution” for you with appropriate sign changes, if any are found. It is assumed here that all elements of ‘data’ are integers - otherwise the exact equality requirement in the ‘find’ operation would be too demanding.

Warning: Beware of data vectors that are too long - they can result in an enormous ‘d’ array.