C#•6mo ago

I would cherish if someone would share an idea on how to solve the Simple Algebra Problem.

You are given a mathematical function f(x) and a value of a. Your task is to determine if the equation f(x) = a has a solution in real numbers. Although this problem may seem simple at first, be prepared for a challenge, as the function you are given is longer and much more complex than what you may have encountered in a typical algebra class. The function is a big composition of exp(x) and log(x) functions. For a clearer understanding, refer to the examples provided. The exponential function exp(x) or e^x raises the constant e (approximately equal to 2.718281828459045) to the power of x, while the logarithmic function log(x) gives the power to which e must be raised to obtain the value x. Input The first line of input contains a string that represents the given function. It is a composition of between 1 and 10^5 exp(x) and log(x) functions. More specifically, exp(x) and log(x) are valid functions, and if f(x) is a valid function, so are exp(f(x)) and log(f(x)). The second line of input contains a decimal number a (−10^9 ≤ a ≤ 10^9), given with exactly two decimal places. Output Print “Yes” if f(x) = a has a solution in real numbers, or “No” otherwise. Examples standard input standard output exp(exp(x)) No 0.50
log(log(exp(log(x)))) Yes -2.39 exp(x) No 0.00 exp(log(x)) No 0.00

1 Reply

Chukwuma•6mo ago

using System;
using System.Collections.Generic;
using System.Linq;

public abstract class Expr
{
    public class Exp : Expr
    {
        public Expr Inner { get; }
        public Exp(Expr inner) => Inner = inner;
    }
    public class Log : Expr
    {
        public Expr Inner { get; }
        public Log(Expr inner) => Inner = inner;
    }
    public class X : Expr { }
}

public class Parser
{
    public (Expr, List<string>) ParseExpr(List<string> tokens)
    {
        if (!tokens.Any())
            throw new Exception("Unexpected end of expression");
        var rest = tokens.Skip(1).ToList();
        switch (tokens.First())
        {
            case "exp":
                var (innerExp, restExp) = ParseExpr(rest);
                return (new Expr.Exp(innerExp), restExp);
            case "log":
                var (innerLog, restLog) = ParseExpr(rest);
                return (new Expr.Log(innerLog), restLog);
            case "(":
                var (innerParen, restParen) = ParseExpr(rest);
                if (!restParen.Any() || restParen.First() != ")")
                    throw new Exception("Missing closing parenthesis");
                return (innerParen, restParen.Skip(1).ToList());
            default:
                return (new Expr.X(), tokens);
        }
    }

    public string SolveExpr(Expr expr, float a)
    {
        if (a < 0.0)
            return "No";
        return expr switch
        {
            Expr.Exp _ when a == 0.0 => "No",
            _ => "Yes",
        };
    }

    public string Solve(string f, float a)
    {
        var tokens = f.Split('(').ToList();
        var (expr, _) = ParseExpr(tokens);
        return SolveExpr(expr, a);
    }
}

using System;
using System.Collections.Generic;
using System.Linq;

public abstract class Expr
{
    public class Exp : Expr
    {
        public Expr Inner { get; }
        public Exp(Expr inner) => Inner = inner;
    }
    public class Log : Expr
    {
        public Expr Inner { get; }
        public Log(Expr inner) => Inner = inner;
    }
    public class X : Expr { }
}

public class Parser
{
    public (Expr, List<string>) ParseExpr(List<string> tokens)
    {
        if (!tokens.Any())
            throw new Exception("Unexpected end of expression");
        var rest = tokens.Skip(1).ToList();
        switch (tokens.First())
        {
            case "exp":
                var (innerExp, restExp) = ParseExpr(rest);
                return (new Expr.Exp(innerExp), restExp);
            case "log":
                var (innerLog, restLog) = ParseExpr(rest);
                return (new Expr.Log(innerLog), restLog);
            case "(":
                var (innerParen, restParen) = ParseExpr(rest);
                if (!restParen.Any() || restParen.First() != ")")
                    throw new Exception("Missing closing parenthesis");
                return (innerParen, restParen.Skip(1).ToList());
            default:
                return (new Expr.X(), tokens);
        }
    }

    public string SolveExpr(Expr expr, float a)
    {
        if (a < 0.0)
            return "No";
        return expr switch
        {
            Expr.Exp _ when a == 0.0 => "No",
            _ => "Yes",
        };
    }

    public string Solve(string f, float a)
    {
        var tokens = f.Split('(').ToList();
        var (expr, _) = ParseExpr(tokens);
        return SolveExpr(expr, a);
    }
}

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I would cherish if someone would share an idea on how to solve the Simple Algebra Problem.