Implementing a priority queue in matlab in order to solve optimization problems using BRANCH AND BOUND

I'm trying to code a priority queue in MATLAB, I know there is the SIMULINK toolbox for priority queue, but I'm trying to code it in MATLAB. I have a pseudo code that uses priority queue for a method called BEST First Search with Branch and Bound. The branch and bound algorithm design strategy is a state space tree and it is used to solve optimization problems. [simple explanation of what is branch and bound][1] [1]: http://optlab-server.sce.carleton.ca/POAnimations2007/BranchAndBound.html

I have read chapter 5: Branch and Bound from a book called 'FOUNDATIONS OF ALGORITHMS', it's the 4th edition by Richard Neapolitan and Kumarss Naimipour , and the text is about designing algorithms, complexity analysis of algorithms, and computational complexity (analysis of problems), very interesting book, and I came across this pseudocode:

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    Void BeFS( state_space_tree T, number& best)

    {

    priority _queue-of_node PQ; 

    node(u,v); 

    initialize (PQ)   % initialize PQ to be empty

    u=root of T;

    best=value(v);

    insert(PQ,v)      insert(PQ,v) is a procedure that adds v to the priority queue PQ 

      while(!empty(PQ){   % remove node with best bound

         remove(PQ,v);

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    remove(PQ,v) is a procedure that removes the node with the best bound and it assigns    its value to v

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       if(bound(v) is better than best) % check if node is still promising

         for (each child of u of v){

if (value (u) is better than best)

(best=value(u);

if (bound(u) is better than best)

insert(PQ,u) } } }

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I don't know how to code it in matlab, and branch and bound is an interesting general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization, instead of using heuristics to find an optimal solution, since branch and bound reduces calculation time and finds the optimal solution faster.