Meaning of floor in equations

Question

By reading the title it may sound like a silly question, but I have a data structures exam tomorrow and some formulas I need to know for algorithm analysis are read as (n – floor(log (n + 1)). What is the meaning of floor?

Thanks

Answer 1

floor(x) is the largest integer not greater than x. You can easily find this information on the web, here for example.

e.g.

floor(1.12) = 1  
floor(0.53) = 0
floor(-3.4) = -4

One thing that can confuse people is the floor of a negative value. Some might initially think that floor(-3.4) is -3 when in reality it is -4 by the definition of floor(x).

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As a note, floor(x) is often written as .

Answer 2

To round down to the nearest integer value.

Answer 3

For positive numbers: Remove the decimal portion. eg. floor(3.4): 3

For negative numbers: Remove the decimal portion and subtract one. eg. floor(-3.4): -3 - 1 = -4

Hope this helps.!