, , , this situation is very much like the ordered array discussed in in that casethe number of comparisons for binary search was approximately equal to the base- logarithm of the number of cells in the array hereif we call the number of nodes in the first column nand the number of levels in the second column lthen we can say that is less than raised to the power lor adding to both sides of the equationwe have + this is equivalent to log ( + thus the time needed to carry out the common tree operations is proportional to the base- log of in big- notation we say such operations take (logntime if the tree isn' fullanalysis is difficult we can say that for tree with given number of levelsaverage search times will be shorter for the non-full tree than the full tree because fewer searches will proceed to lower levels compare the tree to the other data-storage structures we've discussed so far in an unordered array or linked list containing , , itemsit would take you on the average , comparisons to find the one you wanted but in tree of , , itemsit takes (or fewercomparisons in an ordered array you can find an item equally quicklybut inserting an item requireson the averagemoving , items inserting an item in tree with , , items requires or fewer comparisonsplus small amount of time to connect the item similarlydeleting an item from , , -item array requires moving an average of , itemswhile deleting an item from , , -node tree requires or fewer comparisons to find the itemplus (possiblya few more comparisons to find its successorplus short time to disconnect the item and connect its successor thus tree provides high efficiency for all the common data-storage operations traversing is not as fast as the other operations howevertraversals are probably not very commonly carried out in typical large database they're more appropriate when tree is used as an aid to parsing algebraic or similar expressionswhich are probably not too long anyway trees represented as arrays our code examples are based on the idea that tree' edges are represented by leftchild and rightchild references in each node howeverthere' completely different way to represent treewith an array in the array approachthe nodes are stored in an array and are not linked by references