在C#中解析骰子表达式(例如3d6 + 5):从哪里开始？

Question

所以我希望能够在C#中解析和评估"骰子表达式".骰子表达式定义如下:

<expr> :=   <expr> + <expr>
            | <expr> - <expr>
            | [<number>]d(<number>|%)
            | <number>
<number> := positive integer

所以例如d6+20-2d3是允许的,并且应该评估为

rand.Next(1, 7) + 20 - (rand.Next(1, 4) + rand.Next(1, 4))

也d%应该相当于d100.

我知道我可以解决一些解决方案,但我也知道这似乎是一个非常典型的计算机科学类型的问题,所以必须有一些我应该研究的超优雅解决方案.

我希望我的解析结果具有以下功能:

• 我应该能够输出表达式的规范化形式; 我首先考虑骰子,按骰子大小排序,并始终使用前缀.所以例如上面的样本会变成1d6-2d3+20.任何实例d%也会变成d100标准化形式.
• 我应该能够随意评估表达式,每次滚动不同的随机数.
• 我应该能够用最大化的所有骰子卷来评估表达式,因此例如上面的样本将给出(确定性地)1*6+20+2*3 = 32.

我知道这正是Haskell的类型,可能还有其他功能类型的语言,但是如果可能的话,我想留在C#中.

我最初的想法倾向于递归,列表,也许还有一些LINQ,但是,如果我尝试没有知道事物的人的一些指示,我肯定它最终会成为一个不优雅的混乱.

另一种可能有效的策略是一些基于正则表达式的初始字符串替换,将骰子表达式转换为rand.Next调用,然后进行即时评估或编译......这实际上有用吗？我怎么能避免rand每次都创建一个新对象？

Answer 1

这是我最终提出的:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

public enum DiceExpressionOptions
{
    None,
    SimplifyStringValue
}
public class DiceExpression
{
    /* <expr> :=   <expr> + <expr>
     *           | <expr> - <expr>
     *           | [<number>]d(<number>|%)
     *           | <number>
     * <number> := positive integer
     * */
    private static readonly Regex numberToken = new Regex("^[0-9]+$");
    private static readonly Regex diceRollToken = new Regex("^([0-9]*)d([0-9]+|%)$");

    public static readonly DiceExpression Zero = new DiceExpression("0");

    private List<KeyValuePair<int, IDiceExpressionNode>> nodes = new List<KeyValuePair<int, IDiceExpressionNode>>();

    public DiceExpression(string expression)
        : this(expression, DiceExpressionOptions.None)
    { }
    public DiceExpression(string expression, DiceExpressionOptions options)
    {
        // A well-formed dice expression's tokens will be either +, -, an integer, or XdY.
        var tokens = expression.Replace("+", " + ").Replace("-", " - ").Split(' ', StringSplitOptions.RemoveEmptyEntries);

        // Blank dice expressions end up being DiceExpression.Zero.
        if (!tokens.Any())
        {
            tokens = new[] { "0" };
        }

        // Since we parse tokens in operator-then-operand pairs, make sure the first token is an operand.
        if (tokens[0] != "+" && tokens[0] != "-")
        {
            tokens = (new[] { "+" }).Concat(tokens).ToArray();
        }

        // This is a precondition for the below parsing loop to make any sense.
        if (tokens.Length % 2 != 0)
        {
            throw new ArgumentException("The given dice expression was not in an expected format: even after normalization, it contained an odd number of tokens.");
        }

        // Parse operator-then-operand pairs into this.nodes.
        for (int tokenIndex = 0; tokenIndex < tokens.Length; tokenIndex += 2)
        {
            var token = tokens[tokenIndex];
            var nextToken = tokens[tokenIndex + 1];

            if (token != "+" && token != "-")
            {
                throw new ArgumentException("The given dice expression was not in an expected format.");
            }
            int multiplier = token == "+" ? +1 : -1;

            if (DiceExpression.numberToken.IsMatch(nextToken))
            {
                this.nodes.Add(new KeyValuePair<int, IDiceExpressionNode>(multiplier, new NumberNode(int.Parse(nextToken))));
            }
            else if (DiceExpression.diceRollToken.IsMatch(nextToken))
            {
                var match = DiceExpression.diceRollToken.Match(nextToken);
                int numberOfDice = match.Groups[1].Value == string.Empty ? 1 : int.Parse(match.Groups[1].Value);
                int diceType = match.Groups[2].Value == "%" ? 100 : int.Parse(match.Groups[2].Value);
                this.nodes.Add(new KeyValuePair<int, IDiceExpressionNode>(multiplier, new DiceRollNode(numberOfDice, diceType)));
            }
            else
            {
                throw new ArgumentException("The given dice expression was not in an expected format: the non-operand token was neither a number nor a dice-roll expression.");
            }
        }

        // Sort the nodes in an aesthetically-pleasing fashion.
        var diceRollNodes = this.nodes.Where(pair => pair.Value.GetType() == typeof(DiceRollNode))
                                      .OrderByDescending(node => node.Key)
                                      .ThenByDescending(node => ((DiceRollNode)node.Value).DiceType)
                                      .ThenByDescending(node => ((DiceRollNode)node.Value).NumberOfDice);
        var numberNodes = this.nodes.Where(pair => pair.Value.GetType() == typeof(NumberNode))
                                    .OrderByDescending(node => node.Key)
                                    .ThenByDescending(node => node.Value.Evaluate());

        // If desired, merge all number nodes together, and merge dice nodes of the same type together.
        if (options == DiceExpressionOptions.SimplifyStringValue)
        {
            int number = numberNodes.Sum(pair => pair.Key * pair.Value.Evaluate());
            var diceTypes = diceRollNodes.Select(node => ((DiceRollNode)node.Value).DiceType).Distinct();
            var normalizedDiceRollNodes = from type in diceTypes
                                          let numDiceOfThisType = diceRollNodes.Where(node => ((DiceRollNode)node.Value).DiceType == type).Sum(node => node.Key * ((DiceRollNode)node.Value).NumberOfDice)
                                          where numDiceOfThisType != 0
                                          let multiplicand = numDiceOfThisType > 0 ? +1 : -1
                                          let absNumDice = Math.Abs(numDiceOfThisType)
                                          orderby multiplicand descending
                                          orderby type descending
                                          select new KeyValuePair<int, IDiceExpressionNode>(multiplicand, new DiceRollNode(absNumDice, type));

            this.nodes = (number == 0 ? normalizedDiceRollNodes
                                      : normalizedDiceRollNodes.Concat(new[] { new KeyValuePair<int, IDiceExpressionNode>(number > 0 ? +1 : -1, new NumberNode(number)) })).ToList();
        }
        // Otherwise, just put the dice-roll nodes first, then the number nodes.
        else
        {
            this.nodes = diceRollNodes.Concat(numberNodes).ToList();
        }
    }

    public override string ToString()
    {
        string result = (this.nodes[0].Key == -1 ? "-" : string.Empty) + this.nodes[0].Value.ToString();
        foreach (var pair in this.nodes.Skip(1))
        {
            result += pair.Key == +1 ? " + " : " ? "; // NOTE: unicode minus sign, not hyphen-minus '-'.
            result += pair.Value.ToString();
        }
        return result;
    }
    public int Evaluate()
    {
        int result = 0;
        foreach (var pair in this.nodes)
        {
            result += pair.Key * pair.Value.Evaluate();
        }
        return result;
    }
    public decimal GetCalculatedAverage()
    {
        decimal result = 0;
        foreach (var pair in this.nodes)
        {
            result += pair.Key * pair.Value.GetCalculatedAverage();
        }
        return result;
    }

    private interface IDiceExpressionNode
    {
        int Evaluate();
        decimal GetCalculatedAverage();
    }
    private class NumberNode : IDiceExpressionNode
    {
        private int theNumber;
        public NumberNode(int theNumber)
        {
            this.theNumber = theNumber;
        }
        public int Evaluate()
        {
            return this.theNumber;
        }

        public decimal GetCalculatedAverage()
        {
            return this.theNumber;
        }
        public override string ToString()
        {
            return this.theNumber.ToString();
        }
    }
    private class DiceRollNode : IDiceExpressionNode
    {
        private static readonly Random roller = new Random();

        private int numberOfDice;
        private int diceType;
        public DiceRollNode(int numberOfDice, int diceType)
        {
            this.numberOfDice = numberOfDice;
            this.diceType = diceType;
        }

        public int Evaluate()
        {
            int total = 0;
            for (int i = 0; i < this.numberOfDice; ++i)
            {
                total += DiceRollNode.roller.Next(1, this.diceType + 1);
            }
            return total;
        }

        public decimal GetCalculatedAverage()
        {
            return this.numberOfDice * ((this.diceType + 1.0m) / 2.0m);
        }

        public override string ToString()
        {
            return string.Format("{0}d{1}", this.numberOfDice, this.diceType);
        }

        public int NumberOfDice
        {
            get { return this.numberOfDice; }
        }
        public int DiceType
        {
            get { return this.diceType; }
        }
    }
}

Answer 2

你可以在C#的编译器编译器(比如Yacc)中使用你的语法(比如antlr),或者只是开始写你的递归下降解析器.

然后,您构建一个可访问的内存数据结构(如果您想要除+之外的任意数学运算的树),那么您需要编写几个访问者:

• RollVisitor:初始化rand种子,然后访问每个节点,累积结果
• GetMaxVisitor:求和每个骰子的上限
• 其他访客？(如PrettyPrintVisitor,RollTwiceVisitor等等)

我认为可访问树在这里是一个值得解决的问题.

Answer 3

一些尝试:

评估骰子滚动符号字符串