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I need a layout algorithm and use it in the GUI, but I can't use existing GUI toolkits at the moment, so I would like to find a layout algorithm.

I only need to do a single row layout, and here is the description of the algorithm.

Input Data

First, there are three sequences. $$\begin{split} A &= x_1,x_2,\cdots,x_n \\ U &= u_1,u_2,\cdots,u_n \\ L &= l_1,l_2,\cdots,l_n \end{split}$$ Where:

  • $A$ is the recommended size of each interface element known from measurements (this is a row layout, so it may be $x$ or $y$ axis).
  • $U$ is the maximum size of each interface element.
  • $L$ is the minimum size of each interface element.

Obviously, the interface element will be restricted between the maximum and minimum values, and $A$ is also consistent with this restriction.

In addition, there is a value $$g\in \mathbb{R}$$

This is the "remaining space" as I know it. For example, all the measured elements add up to 1000 pixels, and the container has 2000 pixels of space, so $g=1000$. The layout algorithm will allocate this remaining space to all elements. $g$ may be negative number, which means that the container space is too small, and it is time to reduce the size of some elements.

The result of the layout

The return value of the layout algorithm is a sequence $A'=x_1',x_2',\cdots,x_n'$, which is the final displayed interface element size. The values of this sequence element $x_i'$ are described below

If $g > 0$: $$ \forall x_i' \in A' \rightarrow x_i' = \begin{cases} x_i & x_i > \overline{x}\\ u_i & u_i < \overline{x}\\ \overline{x} & \rm{other} \end{cases} $$ If $g < 0$: $$ \forall x_i' \in A' \rightarrow x_i' = \begin{cases} x_i & x_i < \overline{x}\\ l_i & l_i > \overline{x}\\ \overline{x} & \rm{other} \end{cases} $$ And I ignored $g=0$ (is too simple). $\overline{x}$ is also a real number, which means that if no restrictions are triggered the layout tends to adjust the interface elements to be equal. However, when there is space left on the layout axis, we cannot reduce the recommended size of an element larger than $\overline{x}$ and cannot let the element exceed the maximum size limit, similarly when there is not enough space on the layout axis.

Eventually I will use all the space in the container, so $$\sum{x_i'}=\sum{x_i}+g$$

For example, suppose $A=10, 20, 40, 100$, $g=50$, and ignore the maximum and minimum size limits, then the $A'=40,40,40,100$. Note that the elements with recommended sizes $40$ and $100$ are not actually resized. And the other elements are modified to $\overline{x}=40$.

However, the reality is that I need to solve $\overline{x}$ under all the previously mentioned constraints (after which it is easy to calculate the size of each element), and at the moment I don't know how to do that. So is there any good way to do this?

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    $\begingroup$ I don't understand the problem statement. I don't understand what $g$ is. What is $\overline{x}$? Please define all notation in the question. Are $\overline{x}$ and $g$ inputs to the algorithm? If so, they should be described in the "Inputs" part of the question. $\endgroup$
    – D.W.
    May 10 at 4:39
  • $\begingroup$ I have updated the question and added some examples, not sure if they are clear enough. Also I learned that maybe it is possible to use linear optimization to solve such problems. $\endgroup$
    – skiars
    May 10 at 6:01
  • $\begingroup$ What do you mean by "measured elements add up to 1000 pixels"? Is that the sum of $l_i$'s, the sum of $x_i$'s, something else? What do the "braces" mean? Do you mean, if $x_i>\overline{x}$, set $x'_i := x_i$, else if $u_i<\overline{x}$, set $x'_i := u_i$, else set $x'_i := \overline{x}$? $\endgroup$
    – D.W.
    May 10 at 6:23
  • $\begingroup$ Your revised question still doesn't tell us where $\overline{x}$ comes from or what the value of it is. Is it an input? Is the algorithm supposed to compute it? Can the algorithm set $\overline{x}$ to anything it wants or must it satisfy some conditions? If so, what are those conditions? Are you trying to solve an optimization problem, where the goal is to find the "best" solution? If so, how do you measure how good a candidate solution is? What is the objective function you are trying to minimize/maximize? $\endgroup$
    – D.W.
    May 10 at 6:24
  • $\begingroup$ You will probably have a better chance of getting a useful answer if you can figure out how to formulate the question in a clear and precise and self-contained way, so that readers can understand the requirements without having to ask multiple questions and requests for clarification or having to guess at what the intent might be. $\endgroup$
    – D.W.
    May 10 at 6:27

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