hyperf/docs/en/rpn.md

RPN - Reverse Polish Notation

RPN is a mathematical expression method introduced by Polish mathematician Jan Vukasevich in 1920. In reverse Polish notation, all operators are placed after the operand, so it is also called postfix notation. . Reverse Polish notation does not require parentheses to identify operator precedence.

composer require hyperf/rpn

RPN logic

basic logic

• while with input
  • read in the next symbol X
  • IF X is an operand
    • push the stack
  • ELSE IF X is an operator
    • there is a table of a priori that the operator takes n arguments
    • IF less than n operands on stack
      • (Error) User did not enter enough operands
  • Else, pop n operands from stack
  • Computational operators.
  • push the calculated value onto the stack
• There is only one value in the IF stack
  • This value is the result of the entire calculation
• ELSE more than one value
  • (Error) User entered redundant operands

Example

The infix expression 5 + ((1 + 2) * 4) - 3 is written

5 1 2 + 4 * + 3 -

The following table shows how this Reverse Polish expression is evaluated from left to right, with the intermediate values ​​given in the stack bar, which is used to keep track of the algorithm.

input	action	stack	comment
5	Push	5
1	Push	5, 1
2	Push	5, 1, 2
+	Addition	5, 3	Pop 1, 2, push result 3
4	Push	5, 3, 4
*	Multiplication	5, 12	3, 4 pop, push result 12
+	Add operation	17	5, 12 pop, push result 17
3	push	17, 3
-	Subtraction	14	17, 3 pop, push result 14

When the calculation is complete, there is only one operand on the stack, which is the result of the expression: 14

use

Evaluate RPN expressions directly

<?php
use Hyperf\Rpn\Calculator;

$calculator = new Calculator();
$calculator->calculate('5 1 2 + 4 * + 3 -', []); // '14'

Set calculation precision

<?php
use Hyperf\Rpn\Calculator;

$calculator = new Calculator();
$calculator->calculate('5 1 2 + 4 * + 3 -', [], 2); // '14.00'

set variable

<?php
use Hyperf\Rpn\Calculator;

$calculator = new Calculator();
$calculator->calculate('[0] 1 2 + 4 * + [1] -', [5, 10]); // '7'

Convert infix expressions to postfix expressions

The use of variables is temporarily not supported

<?php
use Hyperf\Rpn\Calculator;

$calculator = new Calculator();
$calculator->toRPNExpression('4 - 2 * ( 5 + 5 ) - 10'); // 4 2 5 5 + * - 10 -