Step by Step solution about How to resolve the algorithm Parsing/RPN to infix conversion step by step in the Go programming language

The provided Go program is designed to convert a postfix (also known as Reverse Polish Notation) expression into its equivalent infix (standard mathematical notation) expression. Here's a step-by-step explanation of what the code does:

1. Main Function: The main function defines a slice of postfix expressions (tests) as input for the program.

2. Operand-Operator Lookup Map: The program defines a map called opa (Operand-Operator Lookup), which maps operator strings ("^", "*", "/", "+", "-") to a struct with two fields:

   • prec: Precedence of the operator (highest precedence has the lowest integer value)
   • rAssoc: Boolean value indicating whether the operator is right-associative (e.g., ^)

3. Parsing the Postfix Expression: For each postfix expression in the tests slice, the program calls the parseRPN function to convert it to infix notation.

4. parseRPN Function:

   • This function prints the original postfix expression and initializes an empty stack of sf structs.

5. Stack of sf Structs (sf = Stack Frame):

   • Each stack frame represents a subexpression in the process of being converted to infix notation.
   • An sf struct has two fields:
     • prec: Precedence of the subexpression
     • expr: String representing the subexpression

6. Tokenization and Operator Processing:

   • The function splits the postfix expression into tokens (individual characters or words) using strings.Fields.
   • For each token, it checks if it's an operator (opa[tok]) in the opa map:
     • If it's an operator, it pops the top two stack frames (rhs and lhs) to combine them into a new subexpression.
     • Based on operator precedence and associativity, it decides whether to add parentheses around the operands (lhs and rhs).
     • It pushes the new subexpression back onto the stack, updating the precedence and expression accordingly.
   • If it's not an operator, it pushes a new stack frame with precedence nPrec (highest precedence) and the token as the expression.

7. Displaying Partial Results:

   • After processing each token, the program prints the current stack, showing the precedence and expression of each subexpression.

8. Final Result:

   • After processing all tokens, the program prints the infix expression, which is the final result of converting the postfix expression to infix notation.

package main

import (
    "fmt"
    "strings"
)

var tests = []string{
    "3 4 2 * 1 5 - 2 3 ^ ^ / +",
    "1 2 + 3 4 + ^ 5 6 + ^",
}

var opa = map[string]struct {
    prec   int
    rAssoc bool
}{
    "^": {4, true},
    "*": {3, false},
    "/": {3, false},
    "+": {2, false},
    "-": {2, false},
}

const nPrec = 9

func main() {
    for _, t := range tests {
        parseRPN(t)
    }
}

func parseRPN(e string) {
    fmt.Println("\npostfix:", e)
    type sf struct {
        prec int
        expr string
    }
    var stack []sf
    for _, tok := range strings.Fields(e) {
        fmt.Println("token:", tok)
        if op, isOp := opa[tok]; isOp {
            rhs := &stack[len(stack)-1]
            stack = stack[:len(stack)-1]
            lhs := &stack[len(stack)-1]
            if lhs.prec < op.prec || (lhs.prec == op.prec && op.rAssoc) {
                lhs.expr = "(" + lhs.expr + ")"
            }
            lhs.expr += " " + tok + " "
            if rhs.prec < op.prec || (rhs.prec == op.prec && !op.rAssoc) {
                lhs.expr += "(" + rhs.expr + ")"
            } else {
                lhs.expr += rhs.expr
            }
            lhs.prec = op.prec
        } else {
            stack = append(stack, sf{nPrec, tok})
        }
        for _, f := range stack {
            fmt.Printf("    %d %q\n", f.prec, f.expr)
        }
    }
    fmt.Println("infix:", stack[0].expr)
}