Analyzing the Merge Sort Algorithm

• Let T(n) denote the number of visits to sort an array of n elements then
  • T(n) = T(n/2) + T(n/2) + 5n or
  • T(n) = 2T(n/2) + 5n
• The visits for an array of size n/2 is:    T(n/2) = 2T(n/4) + 5n/2
  • So T(n) = 2 × 2T(n/4) +5n + 5n
• The visits for an array of size n/4 is:     T(n/4) = 2T(n/8) + 5n/4
  • So T(n) = 2 × 2 × 2T(n/8) + 5n + 5n + 5n