MATLAB: How to change a sequence of integers

sequence

I am new to Matlab and coming up already with a tricky question. Suppose a sequence of integers
[2 1 3 4 1 1 3 1 2 1 2 2 5 3 2];
that I want to change according to the following rules:
  • When there is a one not followed or preceeded by another one, I want to replace the one, the preceeding and following number by the sum of the two numbers around the one.
  • If for two given ones, the preceeding and following numbers overlap, I want to add them allogether.
So in my example, I should obtain:
[5 5 5 4 1 1 7 7 7 7 7 2 5 3 2]
The first three numbers turn to be 5 because I add 2 + 3, according to rule 1. The next three numbers 4 1 1 remain unchanged, also according to rule 1. The then coming 5 numbers [3 1 2 1 2] should all be added together, because of rule 2. Lastly, 2 5 3 2 remain unchanged.
I cannot figure out how to do this. Perhaps there is a way of writing a recursive function that picks a one, checks if and how much numbers have to be added from the left and then looks at the right and finally sums the numbers up. Does anyone have a clue? Many thanks in advance

Best Answer

Rule 1 is easy:
x = [2 1 3 4 1 1 3 1 2 1 2 2 5 3 2];
m      = strfind(x == 1, [false, true, false]);
y      = x;
xm     = x(m) + x(m+2);
y(m)   = xm;
y(m+1) = xm;
y(m+2) = xm;
To find a similar approach for rule 2 we need a unique definition at first. See my comment above. Are the elements, which are not 1 always greater than 1 or does the input contain negative values and zeros also?
If there are not sequences with more than 2 ones surrounded by non-ones, the above approach can be expanded and run at first:
m      = strfind(x == 1, [false, true, false, true, false]);
xm     = x(m) + x(m+2) + x(m+4);
... etc.
[EDITED] Including rule 2:
x = [2 1 3 4 1 1 3 1 2 1 2 2 5 3 2 2,1,3,1,4,1,5];
m = strfind(x == 1, [false, true, false]);  % Search for [a,1,b]
p      = false(1, numel(x) + 2);  % Mask [a,b,1,c,d] as 
p(m+1) = true;                    % [false, true, true, true, false]
p(m+2) = true;
p(m+3) = true;
% x:   2 1 3 4 1 1 3 1 2 1 2 2 5 3 2 2 1 3 1 4 1 5
% p: 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0
%    ^   to detect initial [0 1] and final [1 0]   ^
ini = strfind(p, [false, true]);  % Search for starts and ends of blocks
fin = strfind(p, [true, false]) - 1;
for k = 1:numel(ini)              % Loop over sequences
   rep              = sum(x(ini(k):2:fin(k)));  % Sum values surrounding the 1s
   x(ini(k):fin(k)) = rep;        % Replace elements
end
% Check:
isequal(x, ...
   [5 5 5 4 1 1 7 7 7 7 7 2 5 3 2 14 14 14 14 14 14 14])
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