Explanation
In reverse Polish notation the operators follow their operands; for instance, to add 3 and 4, one would write "3 4 +" rather than "3 + 4". If there are multiple operations, the operator is given immediately after its second operand; so the expression written "3 − 4 + 5" in conventional infix notation would be written "3 4 − 5 +" in RPN: first subtract 4 from 3, then add 5 to that. An advantage of RPN is that it obviates the need for parentheses that are required by infix. While "3 − 4 * 5" can also be written "3 − (4 * 5)", that means something quite different from "(3 − 4) * 5". In postfix, the former could be written "3 4 5 * −", which unambiguously means "3 (4 5 *) −" which reduces to "3 20 −"; the latter could be written "3 4 - 5 *" (or 5 3 4 - *, if you wish to keep similar formatting), which unambiguously means "(3 4 -) 5 *".
Despite the name, reverse Polish notation is not exactly the reverse of Polish notation, for the operands of non-commutative operations are still written in the conventional order (e.g. "/ 6 3" in Polish notation and "6 3 /" in reverse Polish both evaluating to 2, whereas "3 6 /" in reverse Polish notation would evaluate to ½).
Read more about this topic: Reverse Polish Notation
Famous quotes containing the word explanation:
“We live between two worlds; we soar in the atmosphere; we creep upon the soil; we have the aspirations of creators and the propensities of quadrupeds. There can be but one explanation of this fact. We are passing from the animal into a higher form, and the drama of this planet is in its second act.”
—W. Winwood Reade (1838–1875)
“My companion assumes to know my mood and habit of thought, and we go on from explanation to explanation, until all is said that words can, and we leave matters just as they were at first, because of that vicious assumption.”
—Ralph Waldo Emerson (1803–1882)
“How strange a scene is this in which we are such shifting figures, pictures, shadows. The mystery of our existence—I have no faith in any attempted explanation of it. It is all a dark, unfathomed profound.”
—Rutherford Birchard Hayes (1822–1893)