How to create a tree diagram with indexes which are related to each other in a matrix?

Hello, it will be a long question, sorry for it and thanks in advance. If you suggest me any other way to solve the problem, I will appreciate.

Shortly it is kind of a creating tree diagram problem.

I have the matrix as below

connectionDots = [
    1     2     3   NaN   NaN
    2     1     3   NaN   NaN
    3     1     2     4     5
    4     3     5     6   NaN
    5     3     4     6   NaN
    6     4     5     7     8
    7     6     8     9    10
    8     6     7     9   NaN
    9     7     8    10   NaN
    10     7     9   NaN   NaN ]

First column is the ID of dots. For example, Dot 1 is connected with 2 and 3. Dot 6 is connected with 4,5,7,8 as I show below.

The program is asking for "from" and "to" dot inputs as below

from = input('Where is the start point?\n-> ');
to = input('Where is the end point?\n-> ');

Lets assume that to is 10, from is 1. I want this programme to discover the way of 10 to 7, 7 to 6, 6 to 4, 4 to 3, 3 to 1. That is not the only way, it can be also another way, it is ok.

Lets assume that to is 9, from is 5. I want this programme to discover the way of 9 to 7, 7 to 6, 6 to 4, 4 to 3, 3 to 1 => Couldnt find number 5. So it will delete last number which is 1. Then continue to question next as 3 to 2, again not 5, 3 to 4, again not 5, 3 to 5.

(first red is tried, then green, then blue, then black)

So I thought I can firstly question the next column member of the to ID. Then go to that row and question next column and again and again. I added the path IDs to theConRoad(the connection of road) variable. So I wrote the code below. It deosn't work properly.

theConRoad = (to); % The Matix of path from 'from' to 'to'.
i = 1;
while i <= size(connectionDots,2)
    qPoint = connectionDots(to,i+1); % it is 'i + 1' because when i = 1 it will check the first column which is already 'to' value 
    fprintf("i = %d, qPoint = %d, to = %d, from = %d\n",i,qPoint,to,from); %Just to see what is going on.
    i = i + 1;
    if qPoint == from % The path is found
        theConRoad = [theConRoad, from];
        break
    else % The 'from' is not found
        if i == size(connectionDots,2)
            i = 1; %i has reached the max number of column, i is set to 1
        end
        if ~ismember(theConRoad,qPoint)
            to = qPoint;
            if isnan(to) % Checking 'to' because it shouldnt be NaN anytime.
                i = i + 1;
                fprintf("%d point doesnt solve, so it is deleted from theConRoad\n",theConRoad(end));
                theConRoad(end) = [];
                to = theConRoad(end);
                fprintf("to is changed because of being NaN, new to is %d\n",to);
                continue
            end
            qPoint = to;
            theConRoad = [theConRoad, qPoint] %Creating the path Matrix
            fprintf("%d is added to theConRoad\n",qPoint)
            i = i + 1;
        end
        to = theConRoad(end);
        fprintf("to is %d (qPoint) now\n",qPoint);
        continue
    end
end

Thanks in advance for any suggestions.

Answer 1

[Steven Lord]

Turn your connection matrix into a graph object then use shortestpath or allpaths on that graph.

[Fatih]

Thanks a lot, that exactly works for me :)