The recurrence is T(1) = 0 If n > 1, then write m = floor of n/2 T(n) = T(m) + T(n-m) + n-1 Example: T(37) = T(18) + T(19) + 36 Col A: n Col B: T(n) = number of comparisons needed to mergesort n items Col C: ceiling of lg(n) Col D: formula given in problem 12.7, where lg(n) is replaced by ceiling lg(n) Col E: lg(n!) A simple closed form formula for T(n) is n*(ceiling(lg(n))) - 2^(ceiling(lg(n)) + 1 For example, if n = 37, then ceiling(lg(n)) = 6, while 2^(ceiling(lg(n)) = 64. Thus the formula gives 37*6 - 64 + 1 = 159