põrandalgoritmi

Põrandalgoritmi, also known as the floor function, is a mathematical function that takes a real number as input and returns the greatest integer less than or equal to that number. It is often denoted by the symbol $\lfloor x \rfloor$ or sometimes just [x]. For example, the floor of 3.14 is 3, and the floor of -2.7 is -3. The floor function always rounds down to the nearest integer.

The floor function has several important properties. It is an idempotent function, meaning that applying the floor function twice has the same effect as applying it once: $\lfloor \lfloor x \rfloor \rfloor = \lfloor x \rfloor$. It is also monotonic, meaning that if $x \le y$, then $\lfloor x \rfloor \le \lfloor y \rfloor$. The floor function can be used to define other related functions, such as the ceiling function, which returns the smallest integer greater than or equal to a given number.

In computer science, the floor function is frequently used in algorithms related to integer division, array indexing, and the analysis of time complexity. For instance, when dividing two integers $a$ by $b$ and taking the integer part, the result is equivalent to $\lfloor a/b \rfloor$ for positive integers. This operation is fundamental in many computational tasks and programming languages often provide a built-in function for its implementation.