we can visualize an execution of the merge-sort algorithm by means of binary tree called the merge-sort tree each node of represents recursive invocation (or callof the merge-sort algorithm we associate with each node of the sequence that is processed by the invocation associated with the children of node are associated with the recursive calls that process the subsequences and of the external nodes of are associated with individual elements of scorresponding to instances of the algorithm that make no recursive calls figure summarizes an execution of the merge-sort algorithm by showing the input and output sequences processed at each node of the merge-sort tree the step-by-step evolution of the merge-sort tree is shown in figures through this algorithm visualization in terms of the merge-sort tree helps us analyze the running time of the merge-sort algorithm in particularsince the size of the input sequence roughly halves at each recursive call of merge-sortthe height of the merge-sort tree is about logn (recall that the base of log is if omitted ( (bfigure merge-sort tree for an execution of the merge-sort algorithm on sequence with elements(ainput sequences processed at each node of (boutput sequences generated at each node of