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使用C#代碼計(jì)算數(shù)學(xué)表達(dá)式實(shí)例

更新時(shí)間：2025年01月20日 15:38:51 作者：坐井觀老天

這段文字主要講述了如何使用C#語(yǔ)言來(lái)計(jì)算數(shù)學(xué)表達(dá)式,該程序通過(guò)使用Dictionary保存變量,定義了運(yùn)算符優(yōu)先級(jí),并實(shí)現(xiàn)了EvaluateExpression方法來(lái)執(zhí)行表達(dá)式計(jì)算,該方法通過(guò)查找優(yōu)先級(jí)最低的運(yùn)算符來(lái)拆分表達(dá)式,并遞歸調(diào)用自身來(lái)評(píng)估子表達(dá)式

C#代碼計(jì)算數(shù)學(xué)表達(dá)式

此程序展示了如何使用 C# 代碼來(lái)計(jì)算數(shù)學(xué)表達(dá)式。

該程序以以下代碼開(kāi)始。

此代碼聲明了一個(gè)Dictionary，稍后將使用它來(lái)保存變量。（例如，如果用戶想要 A = 10、B = 3 和 Pi = 3.14159265。）

然后它定義了一個(gè)Precedence枚舉來(lái)表示運(yùn)算符的優(yōu)先級(jí)。例如，乘法的優(yōu)先級(jí)高于加法。

單擊“Evaluate”按鈕時(shí)，程序會(huì)復(fù)制您輸入到“ Primatives Dictionary”中的任何基元，然后調(diào)用EvaluateExpression方法，該方法會(huì)執(zhí)行所有有趣的工作。

該方法很長(zhǎng)，因此我將分段描述

// Stores user-entered primitives like X = 10.
private Dictionary<string, string> Primatives;

private enum Precedence
{
    None = 11,
    Unary = 10,     // Not actually used.
    Power = 9,      // We use ^ to mean exponentiation.
    Times = 8,
    Div = 7,
    Modulus = 6,
    Plus = 5,
}

// Evaluate the expression.
private double EvaluateExpression(string expression)
{
    int best_pos = 0;
    int parens = 0;

    // Remove all spaces.
    string expr = expression.Replace(" ", "");
    int expr_len = expr.Length;
    if (expr_len == 0) return 0;

    // If we find + or - now, then it's a unary operator.
    bool is_unary = true;

    // So far we have nothing.
    Precedence best_prec = Precedence.None;

    // Find the operator with the lowest precedence.
    // Look for places where there are no open
    // parentheses.
    for (int pos = 0; pos < expr_len; pos++)
    {
        // Examine the next character.
        string ch = expr.Substring(pos, 1);

        // Assume we will not find an operator. In
        // that case, the next operator will not
        // be unary.
        bool next_unary = false;

        if (ch == " ")
        {
            // Just skip spaces. We keep them here
            // to make the error messages easier to
        }
        else if (ch == "(")
        {
            // Increase the open parentheses count.
            parens += 1;

            // A + or - after "(" is unary.
            next_unary = true;
        }
        else if (ch == ")")
        {
            // Decrease the open parentheses count.
            parens -= 1;

            // An operator after ")" is not unary.
            next_unary = false;

            // if parens < 0, too many )'s.
            if (parens < 0)
                throw new FormatException(
                    "Too many close parentheses in '" +
                    expression + "'");
            }
        else if (parens == 0)
        {
            // See if this is an operator.
            if ((ch == "^") || (ch == "*") ||
                (ch == "/") || (ch == "\\") ||
                (ch == "%") || (ch == "+") ||
                (ch == "-"))
            {
                // An operator after an operator
                // is unary.
                next_unary = true;

                // See if this operator has higher
                // precedence than the current one.
                switch (ch)
                {
                    case "^":
                        if (best_prec >= Precedence.Power)
                        {
                            best_prec = Precedence.Power;
                            best_pos = pos;
                        }
                        break;

                    case "*":
                    case "/":
                        if (best_prec >= Precedence.Times)
                        {
                            best_prec = Precedence.Times;
                            best_pos = pos;
                        }
                        break;

                    case "%":
                        if (best_prec >= Precedence.Modulus)
                        {
                            best_prec = Precedence.Modulus;
                            best_pos = pos;
                        }
                        break;

                    case "+":
                    case "-":
                        // Ignore unary operators
                        // for now.
                        if ((!is_unary) &&
                            best_prec >= Precedence.Plus)
                        {
                            best_prec = Precedence.Plus;
                            best_pos = pos;
                        }
                        break;
                } // End switch (ch)
            } // End if this is an operator.
        } // else if (parens == 0)

        is_unary = next_unary;
    } // for (int pos = 0; pos < expr_len; pos++)

該方法的這一部分用于查找表達(dá)式中優(yōu)先級(jí)最低的運(yùn)算符。為此，它只需循環(huán)遍歷表達(dá)式，檢查其運(yùn)算符字符，并確定它們的優(yōu)先級(jí)是否低于先前找到的運(yùn)算符。

下面的代碼片段顯示了下一步

    // If the parentheses count is not zero,
    // there's a ) missing.
    if (parens != 0)
    {
        throw new FormatException(
            "Missing close parenthesis in '" +
            expression + "'");
    }

    // Hopefully we have the operator.
    if (best_prec < Precedence.None)
    {
        string lexpr = expr.Substring(0, best_pos);
        string rexpr = expr.Substring(best_pos + 1);
        switch (expr.Substring(best_pos, 1))
        {
            case "^":
                return Math.Pow(
                    EvaluateExpression(lexpr),
                    EvaluateExpression(rexpr));
            case "*":
                return
                    EvaluateExpression(lexpr) *
                    EvaluateExpression(rexpr);
            case "/":
                return
                    EvaluateExpression(lexpr) /
                    EvaluateExpression(rexpr);
            case "%":
                return
                    EvaluateExpression(lexpr) %
                    EvaluateExpression(rexpr);
            case "+":
                return
                    EvaluateExpression(lexpr) +
                    EvaluateExpression(rexpr);
            case "-":
                return
                    EvaluateExpression(lexpr) -
                    EvaluateExpression(rexpr);
        }
    }

如果括號(hào)未閉合，該方法將引發(fā)異常。否則，它會(huì)使用優(yōu)先級(jí)最低的運(yùn)算符作為分界點(diǎn)，將表達(dá)式拆分成多個(gè)部分。然后，它會(huì)遞歸調(diào)用自身來(lái)評(píng)估子表達(dá)式，并使用適當(dāng)?shù)牟僮鱽?lái)合并結(jié)果。

例如，假設(shè)表達(dá)式為 2 * 3 + 4 * 5。那么優(yōu)先級(jí)最低的運(yùn)算符是 +。該函數(shù)將表達(dá)式分解為 2 * 3 和 4 * 5，并遞歸調(diào)用自身來(lái)計(jì)算這些子表達(dá)式的值（得到 6 和 20），然后使用加法將結(jié)果合并（得到 26）。

以下代碼顯示該方法如何處理函數(shù)調(diào)用

    // if we do not yet have an operator, there
    // are several possibilities:
    //
    // 1. expr is (expr2) for some expr2.
    // 2. expr is -expr2 or +expr2 for some expr2.
    // 3. expr is Fun(expr2) for a function Fun.
    // 4. expr is a primitive.
    // 5. It's a literal like "3.14159".

    // Look for (expr2).
    if (expr.StartsWith("(") & expr.EndsWith(")"))
    {
        // Remove the parentheses.
        return EvaluateExpression(expr.Substring(1, expr_len - 2));
    }

    // Look for -expr2.
    if (expr.StartsWith("-"))
    {
        return -EvaluateExpression(expr.Substring(1));
    }

    // Look for +expr2.
    if (expr.StartsWith("+"))
    {
        return EvaluateExpression(expr.Substring(1));
    }

    // Look for Fun(expr2).
    if (expr_len > 5 & expr.EndsWith(")"))
    {
        // Find the first (.
        int paren_pos = expr.IndexOf("(");
        if (paren_pos > 0)
        {
            // See what the function is.
            string lexpr = expr.Substring(0, paren_pos);
            string rexpr = expr.Substring(paren_pos + 1,
                expr_len - paren_pos - 2);
            switch (lexpr.ToLower())
            {
                case "sin":
                    return Math.Sin(EvaluateExpression(rexpr));
                case "cos":
                    return Math.Cos(EvaluateExpression(rexpr));
                case "tan":
                    return Math.Tan(EvaluateExpression(rexpr));
                case "sqrt":
                    return Math.Sqrt(EvaluateExpression(rexpr));
                case "factorial":
                    return Factorial(EvaluateExpression(rexpr));
                // Add other functions (including
                // program-defined functions) here.
            }
        }
    }

此代碼檢查表達(dá)式是否以 ( 開(kāi)頭并以結(jié)尾。如果是，則刪除這些括號(hào)并計(jì)算表達(dá)式的其余部分。

接下來(lái)，代碼確定表達(dá)式是否以一元 + 或 - 運(yùn)算符開(kāi)頭。如果是，程序?qū)⒂?jì)算不帶運(yùn)算符的表達(dá)式，如果運(yùn)算符為 -，則對(duì)結(jié)果取反。

然后，代碼會(huì)查找Sin、Cos和Factorial等函數(shù)。如果找到，它會(huì)調(diào)用該函數(shù)并返回結(jié)果。（下載示例以查看Factorial函數(shù)。）您可以類似地添加其他函數(shù)。

以下代碼顯示了該方法的其余部分

    // See if it's a primitive.
    if (Primatives.ContainsKey(expr))
    {
        // Return the corresponding value,
        // converted into a Double.
        try
        {
            // Try to convert the expression into a value.
            return double.Parse(Primatives[expr]);
        }
        catch (Exception)
        {
            throw new FormatException(
                "Primative '" + expr +
                "' has value '" +
                Primatives[expr] +
                "' which is not a Double.");
        }
    }

    // It must be a literal like "2.71828".
    try
    {
        // Try to convert the expression into a Double.
        return double.Parse(expr);
    }
    catch (Exception)
    {
        throw new FormatException(
            "Error evaluating '" + expression +
            "' as a constant.");
    }
}

如果表達(dá)式仍未求值，則它必須是您在文本框中輸入的原始值或數(shù)值。

代碼將檢查原始字典以查看表達(dá)式是否存在。

如果值在字典中，則代碼獲取其值，將其轉(zhuǎn)換為雙精度值，然后返回結(jié)果。