matlab coding - finding shortest path problem

Question

Lately I've been trying to learn MATLAB and there's this project that have been assigned to me which I'm trying to do. the description of the project is as follows: we have a set of 100 points: $${(0,0),(0,1)....(0,10),...(1,0),(1,1)....,(1,0),...,(10,10)}$$ 1-choose 10 random points and color them red , those are points we can not go to.(others shall be green). 2-take point (0,0) as the start and color it blue 3-randomly choose the end point and color it black then the assignment asks us to find the shortest path from the start point to the end one (and to graph it). so I plotted the dots in the following code:

clc;clear;close all
all_dots=zeros(10,10);
red_dots_x=zeros(1,10);
red_dots_y=zeros(1,10);
for counter=1:10
    all_dots(randperm(10,10),randperm(10,10))=1;
    red_dots_x=randi(10,1,10);
    red_dots_y=randi(10,1,10);
end 
for counter2=1:10
        all_dots(red_dots_x(counter2),red_dots_y(counter2))=2;           
end
all_dots(1,1)=3; 
x1=randi([2,10]);
y1=randi([2,10]);
all_dots(randi(10),randi(10))=4;
for i=1:10
    for j=1:10
        if all_dots(i,j)==1
            figure(1);plot(i,j,'og','MarkerFaceColor','g');hold on;
        else if all_dots(i,j)==2
            figure(1);plot(i,j,'or','MarkerFaceColor','r');hold on;
        else if all_dots(i,j)==3
            figure(1);plot(i,j,'ob','MarkerFaceColor','b');hold on;
        else if all_dots(i,j)==4
            figure(1);plot(i,j,'ok','MarkerFaceColor','k');hold on;
            end
            end
            end
        end
    end
     xlim([0,11]);ylim([0,11]);
end

now I have to get on finding the shortest path. after a lot of search I found two algorithms that can be useful for my intention:

1-BFS

2-Dijkstra (setting all the weights as 1)

and again after reading on the MATHWORKS website I found out there are built-in functions for those algorithms. but the problem is I PREFER not to use those built-ins because the course coach haven't taught them (so I may not get the full point) and also I neither have an source-destination set nor the adjacency matrix required for using those functions. literally ANY kind of help even for the code I have already written is very much appreciated.

p.s: I am allowed to move diagonaly, vertically and horizontally and all distances (even the diagonal distance) between points are the same.

Answer 1

So after a lot of search a CS student helped me solve the problem. this is the algorithm:

1-from any point (initially the start point) find all the adjacent points and list them.

2-from the list delete the unavailable points (red ones).

3-for all available points find the euclidean distance from the end point.

4-choose the available adjacent point in which you will have the least distance from the end point.

5-while you haven't reached the end point repeat the loop.

it was really fascinating for me that non of the BFS,DFS or Dijkstra algorithms were needed for this problem. for further use I will put the code for this project.

clc;clear;close all
all_dots=zeros(10,10);
red_dots_x=zeros(1,10);
red_dots_y=zeros(1,10);
for counter=1:10
    all_dots(randperm(10,10),randperm(10,10))=1;
    red_dots_x=randi(10,1,10);
    red_dots_y=randi(10,1,10);
end 
for counter2=1:10
        all_dots(red_dots_x(counter2),red_dots_y(counter2))=2;           
end
all_dots(1,1)=3; 
x1=randi([2,10]);
y1=randi([2,10]);
rand1=randi(10);
rand2=randi(10);
all_dots(rand1,rand2)=4;
for i=1:10
    for j=1:10
        if all_dots(i,j)==1
            figure(1);plot(i,j,'og','MarkerFaceColor','g','MarkerSize',15,'MarkerEdgeColor','b');hold on;
        else if all_dots(i,j)==2
            figure(1);plot(i,j,'or','MarkerFaceColor','r','MarkerSize',15,'MarkerEdgeColor',[107 76 154]./255);hold on;
        else if all_dots(i,j)==3
            figure(1);plot(i,j,'ob','MarkerFaceColor','b','MarkerSize',15);hold on;
        else if all_dots(i,j)==4
            figure(1);plot(i,j,'ok','MarkerFaceColor','k','MarkerSize',15);hold on;
            end
            end
            end
        end
    end
     xlim([0,11]);ylim([0,11]);
end
dot=[1,1];
counter100=1;
while dot(1)~=rand1 || dot(2)~=rand2
    steper(counter100,:)=dot;
    dots=[dot(1)+1,dot(2);dot(1),dot(2)+1;dot(1)-1,dot(2);dot(1),dot(2)-1;dot(1)+1,dot(2)+1;dot(1)+1,dot(2)-1;dot(1)-1,dot(2)+1];
    for i=1:7
            if dots(i,1)>=1 && dots(i,2)>=1 && all_dots(dots(i,1),dots(i,2))~=2
                availdots(i,:)=dots(i,:);
            end
    end
    sizea=size(availdots);
        for i=1:sizea(1,1)
                distances(i)=hypot(availdots(i,1)-rand1,availdots(i,2)-rand2);
        end
        [m,next]=min(distances);
        dot=availdots(next,:);
        counter100=counter100+1; 
end
sth=size(steper);
steper(sth(1,1)+1,:)=[rand1,rand2];
plot(steper(:,1),steper(:,2),'k','LineWidth',8);

P.S:I will still very much appreciate any explanation about the way this method is working.