binary trees table number of levels for specified number of nodes number of nodes number of levels , , , , , , , , , 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 lwe can say that is less than raised to the power lor adding to both sides of the equationwe have this is equivalent to log ( thusthe 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 , , itemsfinding the item you want takeson the average , comparisons but in tree of , , itemsonly (or fewercomparisons are required