Are there any example of Mutual recursion?

Question

Are there any examples for a recursive function that calls an other function which calls the first one too ?

Example :

function1()
{    
    //do something         


        

Answer 1

Here is my coded solution. For a calculator app that performs *,/,- operations using mutual recursion. It also checks for brackets (()) to decide the order of precedence.

Flow:: expression -> term -> factor -> expression 

    Calculator.h
    #ifndef CALCULATOR_H_
    #define CALCULATOR_H_

    #include 
    using namespace std;

    /****** A Calculator Class holding expression, term, factor ********/
    class Calculator
    {
    public:
        /**Default Constructor*/
        Calculator();

        /** Parameterized Constructor common for all exception
         * @aparam e exception value
         * */
        Calculator(char e);

        /**
         * Function to start computation
         * @param input - input expression*/
        void start(string input);

        /**
         * Evaluates Term*
         * @param input string for term*/
        double term(string& input);

         /* Evaluates factor*
         * @param input string for factor*/
        double factor(string& input);

         /* Evaluates Expression*
          * @param input string for expression*/
        double expression(string& input);


         /* Evaluates number*
          * @param input string for number*/
        string number(string n);

        /**
         * Prints calculates value of the expression
         * */
        void print();

        /**
         * Converts char to double
         * @param c input char
         * */
        double charTONum(const char* c);

        /**
         * Get error
         */
        char get_value() const;
        /** Reset all values*/
        void reset();
    private:
        int lock;//set lock to check extra parenthesis
        double result;// result
        char error_msg;// error message
    };

    /**Error for unexpected string operation*/
    class Unexpected_error:public Calculator
    {
    public:
        Unexpected_error(char e):Calculator(e){};
    };

    /**Error for missing parenthesis*/
    class Missing_parenthesis:public Calculator
    {
    public:
        Missing_parenthesis(char e):Calculator(e){};
    };

    /**Error if divide by zeros*/
    class DivideByZero:public Calculator{
    public:
        DivideByZero():Calculator(){};
    };
    #endif
    ===============================================================================

    Calculator.cpp

    //============================================================================
    // Name        : Calculator.cpp
    // Author      : Anurag
    // Version     :
    // Copyright   : Your copyright notice
    // Description : Calculator using mutual recursion in C++, Ansi-style
    //============================================================================

    #include "Calculator.h"
    #include 
    #include 
    #include 
    #include 
    using namespace std;


    Calculator::Calculator():lock(0),result(0),error_msg(' '){

    }

    Calculator::Calculator(char e):result(0), error_msg(e) {

    }

    char Calculator::get_value() const {
        return this->error_msg;
    }

    void Calculator::start(string input) {
        try{
        result = expression(input);
        print();
        }catch (Unexpected_error e) {
            cout<='0' && input[0]<='9'){
            string nums = input.substr(0,1) + number(input.substr(1));
            input = input.substr(nums.size());
            return stod(nums);
        }
        else {
            result = factor;
            throw Unexpected_error(input[0]);
        }
        return factor;
    }

    string Calculator::number(string input) {
        if(input.substr(0,2)=="E+" || input.substr(0,2)=="E-" || input.substr(0,2)=="e-" || input.substr(0,2)=="e-")
            return input.substr(0,2) + number(input.substr(2));
        else if((input[0]>='0' && input[0]<='9') || (input[0]=='.'))
            return input.substr(0,1) + number(input.substr(1));
        else
            return "";
    }

    void Calculator::print() {
        cout << result << endl;
    }

    void Calculator::reset(){
        this->lock=0;
        this->result=0;
    }
    int main() {

        Calculator* cal = new Calculator;
        string input;
        cout<<"Expression? ";
        getline(cin,input);
        while(input!="."){
            cal->start(input.substr(0,input.size()-2));
            cout<<"Expression? ";
            cal->reset();
            getline(cin,input);
        }
        cout << "Done!" << endl;
        return 0;
    }
    ==============================================================
    Sample input-> Expression? (42+8)*10 =
    Output-> 500