we can analyze recursive algorithm by using visual tool known as recursion trace we used recursion tracesfor exampleto analyze and visualize the recursive fibonacci function of section and we will similarly use recursion traces for the recursive sorting algorithms of sections and to draw recursion tracewe create box for each instance of the method and label it with the parameters of the method alsowe visualize recursive call by drawing an arrow from the box of the calling method to the box of the called method for examplewe illustrate the recursion trace of the linearsum algorithm of code fragment in figure we label each box in this trace with the parameters used to make this call each time we make recursive callwe draw line to the box representing the recursive call we can also use this diagram to visualize stepping through the algorithmsince it proceeds by going from the call for to the call for to the call for and so onall the way down to the call for when the final call finishesit returns its value back to the call for which adds in its valueand returns this partial sum to the call for and so onuntil the call for returns its partial sum to the call for figure recursion trace for an execution of linearsum( ,nwith input parameters { , , , , and from figure it should be clear that for an input array of size nalgorithm linearsum makes calls henceit will take an amount of time that is roughly proportional to nsince it spends constant amount of time performing the