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96 lines
2.6 KiB
Markdown
96 lines
2.6 KiB
Markdown
# RPN - Reverse Polish Notation
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`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.
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```
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composer require hyperf/rpn
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```
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## RPN logic
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basic logic
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- while with input
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- read in the next symbol X
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- IF X is an operand
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- push the stack
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- ELSE IF X is an operator
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- there is a table of a priori that the operator takes n arguments
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- IF less than n operands on stack
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- (Error) User did not enter enough operands
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- Else, pop n operands from stack
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- Computational operators.
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- push the calculated value onto the stack
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- There is only one value in the IF stack
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- This value is the result of the entire calculation
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- ELSE more than one value
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- (Error) User entered redundant operands
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Example
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The infix expression `5 + ((1 + 2) * 4) - 3` is written
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`5 1 2 + 4 * + 3 -`
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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.
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| input | action | stack | comment |
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| ---- | -------- | ------- | ---------------------------- |
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| 5 | Push | 5 | |
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| 1 | Push | 5, 1 | |
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| 2 | Push | 5, 1, 2 | |
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| + | Addition | 5, 3 | Pop 1, 2, push result 3 |
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| 4 | Push | 5, 3, 4 | |
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| * | Multiplication | 5, 12 | 3, 4 pop, push result 12 |
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| + | Add operation | 17 | 5, 12 pop, push result 17 |
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| 3 | push | 17, 3 | |
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| - | Subtraction | 14 | 17, 3 pop, push result 14 |
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When the calculation is complete, there is only one operand on the stack, which is the result of the expression: 14
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## use
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Evaluate RPN expressions directly
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```php
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<?php
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use Hyperf\Rpn\Calculator;
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$calculator = new Calculator();
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$calculator->calculate('5 1 2 + 4 * + 3 -', []); // '14'
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```
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Set calculation precision
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```php
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<?php
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use Hyperf\Rpn\Calculator;
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$calculator = new Calculator();
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$calculator->calculate('5 1 2 + 4 * + 3 -', [], 2); // '14.00'
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```
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set variable
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```php
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<?php
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use Hyperf\Rpn\Calculator;
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$calculator = new Calculator();
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$calculator->calculate('[0] 1 2 + 4 * + [1] -', [5, 10]); // '7'
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```
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### Convert infix expressions to postfix expressions
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> The use of variables is temporarily not supported
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```php
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<?php
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use Hyperf\Rpn\Calculator;
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$calculator = new Calculator();
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$calculator->toRPNExpression('4 - 2 * ( 5 + 5 ) - 10'); // 4 2 5 5 + * - 10 -
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```
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