cascading-cut takes ( time exclusive of recursive calls thereforethe actual cost of decreaseval_fib-heap including all recursive calls is (cexample decrease the value of node to in the fibonacci heap given below solution min[ min[ min[ (step (step (step (step (step figure min[ min[ min[ fibonacci heap deleting node node from fibonacci heap can be very easily deleted in ( ( )amortized time the procedure to delete node is given in fig del_fib-heap (hxdel_fib-heap assigns minimum value to the node is then removed from the fibonacci heap by step decrease-val_fib-heap(hx-*step extract-min_fib-heap(hmaking call to the extract-min_fib-heap procedure step end the amortized time of the delete procedure is the sum of the ( amortized time of decrease-val_fib-heap and figure algorithm to delete node from fibonacci heap the ( ( )amortized time of extract-min_fib-heap comparison of binarybinomialand fibonacci heaps table makes comparison of the operations that are commonly performed on heaps table comparison of binarybinomialand fibonacci heaps operation description create heap find min delete min insert decrease value union creates an empty heap finds the node with minimum value deletes the node with minimum value inserts new node in the heap decreases the value of node unites two heaps into one time complexity in big notation binary (no( (log no(log no(log no(nbinomial (no(log no(log no(log no(log no(log nfibonacci (no(no(log no( ( ( applications of heaps heaps are preferred for applications that includeheap sort it is one of the best sorting methods that has no quadratic worst-case scenarios heap sort algorithm is discussed in