data structures using link ptr to nextmaking next the parent of the node pointed by ptr prev head [hptr next figure (elink next to ptrmaking ptr the parent of the node pointed by next prev ptr head [ (step next figure (fbinomial heap insert_binomial-heap(hxstep set hcreate_binomial-heap(step set parent[xnullchild[xnull and sibling[xnulldegree[xnull step set head[ ' step set head[hunion_binomial-heap(hh'step end figure algorithm to insert new element in binomial heap min-extract_binomial heap (hstep find the root having minimum value in the root list of step remove from the root list of step set hccreate_binomial-heap(step reverse the order of ' children thereby forming linked list step set head[hc/to point to the head of the resulting list step set union_binomial-heap(hhc/figure algorithm to extract the node with minimum key from binomial heap inserting new node the insert_binomial-heap(procedure is used to insert node into the binomial heap the pre-condition of this procedure is that has already been allocated space and val[xhas already been filled in the algorithm shown in fig simply makes binomial heap hcin ( time hccontains just one node which is finallythe algorithm unites hcwith the -node binomial heap in (log ntime note that the memory occupied by hcis freed in the union_binomialheap(hhc/procedure extracting the node with minimum key the algorithm to extract the node with minimum key from binomial heap is shown in fig the min-extract_binomial-heap procedure accepts heap as parameter and returns pointer to the extracted node in the first stepit finds root node with the minimum value and removes it from the