后缀符号来EX pression树 [英] Postfix notation to expression tree

问题描述

有足够的资源如何转换前pression树为后缀符号，它并不难。

There are enough resources on how to convert an expression tree into postfix notation, and it's not that hard.

不过，我要解析后缀EX pression到前pression树。

But I have to parse a postfix expression into an expression tree.

这位前pression是：

The expression is:

一个2 ^ 2 A * B * - B 2 ^ + A B - /

A 2 ^ 2 A * B * - B 2 ^ + A B - /

我真的没有一个线索如何跨preT前pression。是否有人对如何PROCES这个线索？

I don't really have a clue on how to interpret the expression. Does someone has a clue on how to proces this?

推荐答案

创建一个包含节点，可能是树的一部分一叠

Create a stack containing nodes that could be part of a tree

1. 在堆栈（A，2，B等是操作数）为叶节点推送操作数，没有绑定到任何树在任何方向
2. 对于运营商，流行的必要的操作数从堆栈中，创建与操作在顶部的节点，并挂在它下面的操作数，推新节点到堆栈

有关数据：

1. 在推一个压入堆栈
2. 2推入堆栈
3. 在弹出2和A，创建^ -node（A和2所示），将其推堆栈上
4. 在堆栈
推2
5. 按A对堆栈
6. 在弹出一个和2相结合，形成了* -node
7. 等
8. 等

1. Push A onto the stack
2. Push 2 onto the stack
3. Pop 2 and A, create ^-node (with A and 2 below), push it on the stack
4. Push 2 on stack
5. Push A on stack
6. Pop A and 2 and combine to form the *-node
7. etc.
8. etc.

下面是一个 LINQPad 程序，可以与尝试：

Here is a LINQPad program that can be experimented with:

// Add the following two using-directives to LINQPad:
// System.Drawing
// System.Drawing.Imaging

static Bitmap _Dummy = new Bitmap(16, 16, PixelFormat.Format24bppRgb);
static Font _Font = new Font("Arial", 12);

void Main()
{
    var elementsAsString = "A 2 ^ 2 A * B * - B 2 ^ + A B - / 2 ^";
    var elements = elementsAsString.Split(' ');

    var stack = new Stack<Node>();
    foreach (var element in elements)
        if (IsOperator(element))
        {
            Node rightOperand = stack.Pop();
            Node leftOperand = stack.Pop();
            stack.Push(new Node(element, leftOperand, rightOperand));
        }
        else
            stack.Push(new Node(element));

    Visualize(stack.Pop());
}

void Visualize(Node node)
{
    node.ToBitmap().Dump();
}

class Node
{
    public Node(string value)
        : this(value, null, null)
    {
    }

    public Node(string value, Node left, Node right)
    {
        Value = value;
        Left = left;
        Right = right;
    }

    public string Value;
    public Node Left;
    public Node Right;

    public Bitmap ToBitmap()
    {
        Size valueSize;
        using (Graphics g = Graphics.FromImage(_Dummy))
        {
            var tempSize = g.MeasureString(Value, _Font);
            valueSize = new Size((int)tempSize.Width + 4, (int)tempSize.Height + 4);
        }

        Bitmap bitmap;
        Color valueColor = Color.LightPink;
        if (Left == null && Right == null)
        {
            bitmap = new Bitmap(valueSize.Width, valueSize.Height);
            valueColor = Color.LightGreen;
        }
        else
        {
            using (var leftBitmap = Left.ToBitmap())
            using (var rightBitmap = Right.ToBitmap())
            {
                int subNodeHeight = Math.Max(leftBitmap.Height, rightBitmap.Height);
                bitmap = new Bitmap(
                    leftBitmap.Width + rightBitmap.Width + valueSize.Width,
                    valueSize.Height + 32 + subNodeHeight);

                using (var g = Graphics.FromImage(bitmap))
                {
                    int baseY  = valueSize.Height + 32;

                    int leftTop = baseY; // + (subNodeHeight - leftBitmap.Height) / 2;
                    g.DrawImage(leftBitmap, 0, leftTop);

                    int rightTop = baseY; // + (subNodeHeight - rightBitmap.Height) / 2;
                    g.DrawImage(rightBitmap, bitmap.Width - rightBitmap.Width, rightTop);

                    g.DrawLine(Pens.Black, bitmap.Width / 2 - 4, valueSize.Height, leftBitmap.Width / 2, leftTop);
                    g.DrawLine(Pens.Black, bitmap.Width / 2 + 4, valueSize.Height, bitmap.Width - rightBitmap.Width / 2, rightTop);
                }
            }
        }

        using (var g = Graphics.FromImage(bitmap))
        {
            float x = (bitmap.Width - valueSize.Width) / 2;
            using (var b = new SolidBrush(valueColor))
                g.FillRectangle(b, x, 0, valueSize.Width - 1, valueSize.Height - 1);
            g.DrawRectangle(Pens.Black, x, 0, valueSize.Width - 1, valueSize.Height - 1);
            g.DrawString(Value, _Font, Brushes.Black, x + 1, 2);
        }

        return bitmap;
    }
}

bool IsOperator(string s)
{
    switch (s)
    {
        case "*":
        case "/":
        case "^":
        case "+":
        case "-":
            return true;

        default:
            return false;
    }
}

输出：

这篇关于后缀符号来EX pression树的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！