priority queues (heaps figure merging two binomial trees in order to merge two binomial queueswe need routine to merge two binomial trees of the same size figure shows how the links change when two binomial trees are merged the code to do this is simple and is shown in figure we provide simple implementation of the merge routine is represented by the current object and is represented by rhs the routine combines and placing the result in and making empty at any point we are dealing with trees of rank and are the trees in and respectivelyand carry is the tree carried from previous step (it might be nullptrdepending on each of the eight possible casesthe tree that results for rank and the carry tree of rank is formed this process proceeds from rank to the last rank in the resulting binomial queue the code is shown in figure improvements to the code are suggested in exercise the deletemin routine for binomial queues is given in figure (on pages - we can extend binomial queues to support some of the nonstandard operations that binary heaps allowsuch as decreasekey and removewhen the position of the affected element is known decreasekey is percolateupwhich can be performed in (log ntime if we add data member to each node that stores parent link an arbitrary remove can be performed by combination of decreasekey and deletemin in (log ntime /*return the result of merging equal-sized and *binomialnode combinetreesbinomialnode * binomialnode * ift ->element element return combinetreest ) ->nextsibling ->leftchildt ->leftchild return figure routine to merge two equal-sized binomial trees