priority queues (heapsfigure very large complete binary tree so there is no way to find any particular element without linear scan through the entire heap to see thisconsider the large heap structure (the elements are not shownin figure where we see that the only information known about the maximum element is that it is at one of the leaves half the elementsthoughare contained in leavesso this is practically useless information for this reasonif it is important to know where elements aresome other data structuresuch as hash tablemust be used in addition to the heap (recall that the model does not allow looking inside the heap if we assume that the position of every element is known by some other methodthen several other operations become cheap the first three operations below all run in logarithmic worst-case time decreasekey the decreasekey(poperation lowers the value of the item at position by positive amount since this might violate the heap orderit must be fixed by percolate up this operation could be useful to system administratorsthey can make their programs run with highest priority increasekey the increasekey(poperation increases the value of the item at position by positive amount this is done with percolate down many schedulers automatically drop the priority of process that is consuming excessive cpu time remove the remove(poperation removes the node at position from the heap this is done by first performing decreasekey( ,and then performing deletemin(when process