Step by Step solution about How to resolve the algorithm Parsing/Shunting-yard algorithm step by step in the Julia programming language

The provided Julia code is an implementation of an infix to Reverse Polish Notation (RPN) parser. RPN, also known as postfix notation, is a mathematical notation where operators follow their operands.

Here's a detailed explanation of the code:

1. Function Signature: The code defines a function parseinfix2rpn(s) that takes a string s containing an infix expression as input and returns an array of tokens in RPN.

2. Data Structures:

   • outputq (output queue): An array to store the RPN tokens.
   • opstack (operator stack): A stack to store operators.

3. Initialization:

   • infix is obtained by splitting the input string into tokens.

4. Loop Over Tokens:

   • The code iterates over each token in the infix array.

5. Processing Tokens:

   • If the token is a number, it is pushed onto the outputq.
   • If the token is "(", it is pushed onto the opstack.
   • If the token is ")", operators are popped from the opstack and pushed onto the outputq until a "(" is encountered.
   • If the token is an operator, it is compared with the operators on the opstack. Operators with higher precedence are popped and pushed onto the outputq.

6. Remaining Operators: After processing all tokens, any remaining operators in the opstack are pushed onto the outputq.

7. Error Handling: If a mismatched parenthesis is encountered (e.g., missing closing parenthesis), an error is thrown.

8. Output: The RPN tokens are returned as an array.

9. Example Usage: The code provides an example by parsing the infix expression "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3" and printing the resulting RPN tokens.

This code essentially converts an infix expression into an equivalent RPN expression, which can be helpful for efficient evaluation using stacks or other data structures designed for postfix notation.

function parseinfix2rpn(s)
    outputq = []
    opstack = []
    infix = split(s)
    for tok in infix
        if all(isnumber, tok)
            push!(outputq, tok)
        elseif tok == "("
            push!(opstack, tok)
        elseif tok == ")"
            while !isempty(opstack) && (op = pop!(opstack)) != "("
               push!(outputq, op)
            end
        else # operator
            while !isempty(opstack)
                op = pop!(opstack)
                if Base.operator_precedence(Symbol(op)) > Base.operator_precedence(Symbol(tok)) ||
                   (Base.operator_precedence(Symbol(op)) ==
                     Base.operator_precedence(Symbol(tok)) && op != "^")
                    push!(outputq, op)
                else
                    push!(opstack, op)  # undo peek
                    break
                end
            end
            push!(opstack, tok)
        end
        println("The working output stack is $outputq")
    end
    while !isempty(opstack)
        if (op = pop!(opstack)) == "("
            throw("mismatched parentheses")
        else
            push!(outputq, op)
        end
    end
    outputq
end

teststring = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
println("\nResult: $teststring becomes $(join(parseinfix2rpn(teststring), ' '))")