the analysis of the worst-case running time of searching in binary search tree is simple algorithm treesearch is recursive and executes constant number of primitive operations for each recursive call each recursive call of treesearch is made on child of the previous node that istreesearch is called on the nodes of path of that starts at the root and goes down one level at time thusthe number of such nodes is bounded by where is the height of in other wordssince we spend ( time per node encountered in the searchmethod find on dictionary runs in (htimewhere is the height of the binary search tree used to implement (see figure figure illustrating the running time of searching in binary search tree the figure uses standard visualization shortcuts of viewing binary search tree as big triangle and path from the root as zig-zag line