java - Converting tree representing math expression to a string without redundant parentheses

Question

I want to convert a tree that represents a math expression into the actual math expression (a string like "a+b/c")

The tree representation is the simplest you could imagine:

A+B/C would be this tree:

OperationNode(+, A, OperationNode(/, B, C))

And (A+B)/C would be this tree:

OperationNode(/, OperationNode(+, A, B), C)

In order to convert the tree into the string, I'm using the Visitor pattern. The problem comes with parentheses.

My current Visitor implementation ALWAYS adds parentheses to the nodes, so every tree I generate turns into a string like this:

(((A+B)+C)+D)

Notice the redundant parentheses.

So the question is: how could I make my Visitor generate the string with no redundant parentheses?

标签： javac#.netalgorithmvisitor-pattern

Answer 1

正如 NelFeal 在遍历树时所写的那样，您只需要检查子操作的优先级是否小于当前操作的优先级。

我为您实现了访问者模式，希望对您有所帮助。

enum Operation
{
    Add,
    Multiply,
    Power,
    UnaryMinus,
    None,
}

static class OperationExtensions
{
    public static string ToFriendlyString(this Operation me)
    {
        switch (me)
        {
            case Operation.None:
                return "";
            case Operation.Add:
                return "+";
            case Operation.Multiply:
                return "*";
            case Operation.Power:
                return "^";
            case Operation.UnaryMinus:
                return "-";
            default:
                throw new ArgumentException();
        }
    }
}

class OperationNode
{
    public Operation Op;
    public OperationNode(Operation op)
    {
        Op = op;
    }
}

interface IVisitor
{
    void Visit(OperationNodeLeaf node);
    void Visit(OperationNode1 node);
    void Visit(OperationNode2 node);
}

sealed class Visitor : IVisitor
{
    public string Text { get; set; }

    private void Enclose(OperationNode subNode, Operation op)
    {
        if (subNode.Op < op)
        {
            Text = Text + "(";
            Visit((dynamic)subNode);
            Text = Text + ")";
        }
        else
        {
            Visit((dynamic)subNode);
        }
    }

    public void Visit(OperationNodeLeaf node)
    {
        Text = Text + node.Op.ToFriendlyString();
        Text = Text + node.Value.ToString();
    }

    public void Visit(OperationNode1 node)
    {
        Text = Text + node.Op.ToFriendlyString();
        Enclose(node.SubNode, node.Op);
    }

    public void Visit(OperationNode2 node)
    {
        Enclose(node.LeftSubNode, node.Op);
        Text = Text + node.Op.ToFriendlyString();
        Enclose(node.RightSubNode, node.Op);
    }
}

class OperationNodeLeaf : OperationNode
{
    public int Value;
    public OperationNodeLeaf(int v, Operation op = Operation.None) : base(op)
    {
        Value = v;
    }
    void Accept(IVisitor v)
    {
        v.Visit(this);
    }
}

class OperationNode1 : OperationNode
{
    public OperationNode SubNode;
    public OperationNode1(OperationNode sn, Operation op) : base(op)
    {
        SubNode = sn;
    }
    void Accept(IVisitor v)
    {
        v.Visit(this);
    }
}

class OperationNode2 : OperationNode
{
    public OperationNode LeftSubNode;
    public OperationNode RightSubNode;
    public OperationNode2(OperationNode lsn, OperationNode rsn, Operation op) : base(op)
    {
        LeftSubNode = lsn;
        RightSubNode = rsn;
    }
    void Accept(IVisitor v)
    {
        v.Visit(this);
    }
}

class Program
{
    static void Main(string[] args)
    {
        var tree = 
            new OperationNode2(
                new OperationNode2(
                    new OperationNode2(new OperationNodeLeaf(5), new OperationNodeLeaf(6), Operation.Add),
                    new OperationNode2(new OperationNodeLeaf(5), new OperationNodeLeaf(6), Operation.Multiply),
                    Operation.Power
                    ),
                new OperationNode2(
                    new OperationNode2(new OperationNodeLeaf(1), new OperationNodeLeaf(2), Operation.Multiply),
                    new OperationNode1(new OperationNodeLeaf(7, Operation.None), Operation.UnaryMinus),
                    Operation.Add
                    ),
                Operation.Multiply
                );
        var visitor = new Visitor();
        visitor.Visit(tree);
        System.Diagnostics.Debug.WriteLine(visitor.Text);
    }
}

(5+6)^(5*6)*(1*2+-7)