with obtaining new tree of height we then merge this tree with obtaining tree of height which is the new priority queue we count this as three steps (two tree merges plus the stopping casethe next insertion after is inserted is another bad case and would require three tree merges deletemin can be performed by first finding the binomial tree with the smallest root let this tree be bk and let the original priority queue be we remove the binomial tree bk from the forest of trees in hforming the new binomial queue hwe also remove the root of bk creating binomial trees bk- which collectively form priority queue we finish the operation by merging hand as an examplesuppose we perform deletemin on which is shown again in figure the minimum root is so we obtain the two priority queues hand in figure and figure the binomial queue that results from merging hand is the final answer and is shown in figure for the analysisnote first that the deletemin operation breaks the original binomial queue into two it takes (log ntime to find the tree containing the minimum element and to create the queues hand merging these two queues takes (log ntimeso the entire deletemin operation takes (log ntime figure binomial queue figure binomial queue hcontaining all the binomial trees in except ' figure binomial queue  with removed