min_binomial-heap(hstep [initializationset nullx head[hand min step repeat steps and while null step if val[xmin set min val[xset [end of ifstep set sibling[ [end of loopstep return figure algorithm to find the node with minimum value we have already discussed that binomial heap is heap-orderedthereforethe node with the minimum value in particular binomial tree will appear as root node in the binomial heap thusthe min_ binomial-heap(procedure checks all roots since there are at most log ( roots to checkthe running time of this procedure is (log nexample this case head [hconsider the binomial heap given below and see how the procedure works in head [hx step (min (initiallywe have min * head [hx head [hy step step (min (min figure binomial heap uniting two binomial heaps the procedure of uniting two binomial heaps is used as subroutine by other operations the union_binomial-heap(procedure links together binomial link_binomial-tree(yztrees whose roots have the same degree the algorithm to link bi- tree rooted at node to the bi- tree rooted at node step set parent[yz step set sibling[ychild[zzmaking the parent of yis shown in fig step set child[zy the link_binomial-tree(procedure makes the new step set degree[zdegree[ ] head of the linked list of node ' children in ( time step end the algorithm to unite two binomial heaps and is figure algorithm to link two binomial trees given in fig