node doesn' change the structure of the tree of courseit also means that memory can fill up with "deletednodes this approach is bit of cop-outbut it may be appropriate where there won' be many deletions in tree (if ex-employees remain in the personnel file foreverfor example the efficiency of binary trees as you've seenmost operations with trees involve descending the tree from level to level to find particular node how long does it take to do thisin full treeabout half the nodes are on the bottom level (actually there' one more node on the bottom row than in the rest of the tree thus about half of all searches or insertions or deletions require finding node on the lowest level (an additional quarter of these operations require finding the node on the next-to-lowest leveland so on during search we need to visit one node on each level so we can get good idea how long it takes to carry out these operations by knowing how many levels there are assuming full treetable shows how many levels are necessary to hold given number of nodes table number of levels for specified number of nodes number of nodes number of levels , , , , , ,