note that unlike the insert operation in the case of binomial heapwhen we insert node in fibonacci heapno attempt is made to consolidate the trees within the fibonacci heap soeven if consecutive insert operations are performedthen single-node trees are added to the root list insert_fib-heap(hxstep [initializationset degree[xparent[xnullchild[xnullmark[xfalse step set left[xx and right[xx step concatenate the root list containing with the root list of step if min[hnull or val[xval[min[ ]]then set min[hx [end of ifstep set [hn[ ] step end figure algorithm to insert new node in fibonacci heap example insert node in the fibonacci heap given below min[ solution min[ figure fibonacci heap finding the node with minimum key fibonacci heaps maintain pointer min[hthat points to the root having the minimum value thereforefinding the minimum node is straightforward task that can be performed union_fib-heap( in just ( time step create_fib-heap(step set min[hmin[ step concatenate root list of with that of step if (min[ nullor (min[ !null and min[ min[ ])then set min[hmin[ [end of ifstep set [hn[ [ step free and step return figure algorithm to unite two fibonacci heaps uniting two fibonacci heaps the algorithm given in fig unites two fibonacci heaps and in the algorithmwe first concatenate the root lists of and into new root list thenthe minimum node of is set and the total number of nodes in is updated finallythe memory occupied by and is freed and the resultant heap is returned