When do floors and ceilings matter while solving recurrences?

Question

every time while finding recurence solution (in CLRS book , page 88)  a statement "Floors and ceilings usually do not matter when solving recurrences" but my doubt is when they matter ?

Answer 1

Whenever we need to find exact recurrence expression then floor and celing matters.. otherwise it is useless because one or two, in general constant people doesn't affect time Complexity..

Let , (n/2) and n is odd then we can take value as Floor (n/2) or Ceil (n/2).. difference between floor and ceil value is one .. here n is no of input.. one less or one more input doesn't affect asymptotic complexity..

 

But whenever we need to find something like exact no of comparison then we need floor ceil  precisely..

Answer 2

floor and ceiling values matters when the no. of element is odd.

in sorting algo ... lets say merge sort ,for finding the middle element of the entire array

better check the algo .. of merge sort  u will get cleared