analyzing recursive algorithms in we introduced mathematical techniques for analyzing the efficiency of an algorithmbased upon an estimate of the number of primitive operations that are executed by the algorithm we use notations such as big-oh to summarize the relationship between the number of operations and the input size for problem in this sectionwe demonstrate how to perform this type of running-time analysis to recursive algorithms with recursive algorithmwe will account for each operation that is performed based upon the particular activation of the function that manages the flow of control at the time it is executed stated another wayfor each invocation of the functionwe only account for the number of operations that are performed within the body of that activation we can then account for the overall number of operations that are executed as part of the recursive algorithm by taking the sumover all activationsof the number of operations that take place during each individual activation (as an asidethis is also the way we analyze nonrecursive function that calls other functions from within its body to demonstrate this style of analysiswe revisit the four recursive algorithms presented in sections through factorial computationdrawing an english rulerbinary searchand computation of the cumulative size of file system in generalwe may rely on the intuition afforded by recursion trace in recognizing how many recursive activations occurand how the parameterization of each activation can be used to estimate the number of primitive operations that occur within the body of that activation howevereach of these recursive algorithms has unique structure and form computing factorials it is relatively easy to analyze the efficiency of our function for computing factorialsas described in section sample recursion trace for our factorial function was given in figure to compute factorial( )we see that there are total of activationsas the parameter decreases from in the first callto in the second calland so onuntil reaching the base case with parameter it is also cleargiven an examination of the function body in code fragment that each individual activation of factorial executes constant number of operations thereforewe conclude that the overall number of operations for computing factorial(nis ( )as there are activationseach of which accounts for ( operations