C#后缀表达式解析计算字符串公式
当我们拿到一个字符串比如:20+31*(100+1)
的时候用口算就能算出结果为3151
,因为这是中缀表达式
对于人类的思维很简单,但是对于计算机就比较复杂了。相对的后缀表达式
适合计算机进行计算。
我们就从简单到复杂,逐步实现对公式的解析(下述的代码没有经过严格验证,可能会存在极端情况的BUG,作为一种思路仅供参考,商用环境还需细细修改)。
实现简单的数字的加减乘除
我们从实现简单的数字的加减乘除开始主要是提供一个思路有需要可以自己修改扩展比如增加函数、字符串、数组等(推荐一个项目写的感觉就不错https://github.com/KovtunV/NoStringEvaluating),那么我们只需要关注加减乘除等操作符、左右括号和操作数(整数、小数和负数),所以我们先建立三个枚举类BracketEnum
、NodeTypeEnum
和OperatorEnum
如下:
BracketEnum
是括号枚举,也就是左右括号"()"
public enum BracketEnum { /// <summary> /// Undefined /// </summary> Undefined = 0, /// <summary> /// 左括号 /// </summary> Open, /// <summary> /// 右括号 /// </summary> Close }
NodeTypeEnum
是节点类型枚举,就简单分为操作符、操作数和括号
public enum NodeTypeEnum { /// <summary> /// Null /// </summary> Null = 0, /// <summary> /// 操作数 /// </summary> Number, /// <summary> /// 操作符 /// </summary> Operator, /// <summary> /// 括号 /// </summary> Bracket, }
OperatorEnum
是操作符枚举,主要就是加减乘除这些简单的
public enum OperatorEnum { /// <summary> /// Undefined /// </summary> Undefined = 0, /// <summary> /// + /// </summary> Plus, /// <summary> /// - /// </summary> Minus, /// <summary> /// * /// </summary> Multiply, /// <summary> /// / /// </summary> Divide, /// <summary> /// ^ /// </summary> Power, }
然后我们需要做以下三步:
- 解析公式将字符转化为便于操作的节点信息
- 进行解析为后缀表达式
- 进行计算
1、解析公式转为节点信息
根据我们的NodeTypeEnum
节点类型枚举我们需要三个不同的节点信息类方便我们的操作,我们先创建基类BaseNode
以后的节点类都继承它
public class BaseNode { public BaseNode(NodeTypeEnum nodeType) { NodeType = nodeType; } /// <summary> /// 节点类型 /// </summary> public NodeTypeEnum NodeType { get; set; } }
然后我们分别创建BracketNode
、NumberNode
和OperatorNode
类,分别是括号节点信息、操作数节点新和操作符节点信息,它们各有自己的具体实现,如下:
public class BracketNode : BaseNode { /// <summary> /// 括号值 /// </summary> public BracketEnum Bracket { get; } /// <summary> /// 公式括号节点 /// </summary> public BracketNode(BracketEnum bracket) : base(NodeTypeEnum.Bracket) { Bracket = bracket; } }
public class NumberNode : BaseNode { /// <summary> /// 数字值 /// </summary> public double Number { get; } public NumberNode(double number) : base(NodeTypeEnum.Number) { Number = number; } }
public class OperatorNode : BaseNode { /// <summary> /// 操作字符串枚举 /// </summary> public OperatorEnum OperatorKey { get; } /// <summary> /// 优先级 /// </summary> public int Priority { get; } public OperatorNode(OperatorEnum operatorKey) : base(NodeTypeEnum.Operator) { OperatorKey = operatorKey; Priority = GetPriority(); } private int GetPriority() { var priority = OperatorKey switch { OperatorEnum.Power => 6, OperatorEnum.Multiply => 5, OperatorEnum.Divide => 5, OperatorEnum.Plus => 4, OperatorEnum.Minus => 4, _ => 0 }; return priority; } }
有了节点信息类,那我们肯定还要有对应的解析类分别是BracketReader(括号解析)
、NumberReader(操作数解析)
和OperatorReader(操作符解析)
,解析类就是为了将公式字符串解析为对应的节点信息具体如下:
public static class BracketReader { /// <summary> /// 左右括号字符 /// </summary> private const char OPEN_BRACKET_CHAR = '('; private const char CLOSE_BRACKET_CHAR = ')'; /// <summary> /// 尝试获取左括号 /// </summary> /// <param name="nodes">公式节点信息</param> /// <param name="formula">公式字符</param> /// <param name="index">公式读取的下标</param> /// <returns></returns> public static bool TryProceedOpenBracket(List<BaseNode> nodes, ReadOnlySpan<char> formula, ref int index) { if (formula[index].Equals(OPEN_BRACKET_CHAR)) { nodes.Add(new BracketNode(BracketEnum.Open)); return true; } return false; } /// <summary> /// 尝试获取右括号 /// </summary> /// <param name="nodes">公式节点信息</param> /// <param name="formula">公式字符</param> /// <param name="index">公式读取的下标</param> /// <returns></returns> public static bool TryProceedCloseBracket(List<BaseNode> nodes, ReadOnlySpan<char> formula, ref int index) { if (formula[index].Equals(CLOSE_BRACKET_CHAR)) { nodes.Add(new BracketNode(BracketEnum.Close)); return true; } return false; } }
public static class NumberReader { /// <summary> /// 尝试读取数字 /// </summary> public static bool TryProceedNumber(List<BaseNode> nodes, ReadOnlySpan<char> formula, ref int index) { double value = 0; var isTry = false;//是否转换成功 var isNegative = formula[index] == '-';//是否是负数 var localIndex = isNegative ? index + 1 : index; //循环判断数字 for (int i = localIndex; i < formula.Length; i++) { var ch = formula[i]; var isLastChar = i + 1 == formula.Length; if (IsFloatingNumber(ch)) { //如果最后一个并且成功 if (isLastChar && double.TryParse(formula.Slice(index, formula.Length - index), out value)) { index = i; isTry = true; break; } } else if(double.TryParse(formula.Slice(index, i - index), out value)) { //如果不是数字比如是字母,则直接判断之前的数字 index = i - 1; isTry = true; break; } else { break; } } if (isTry) { nodes.Add(new NumberNode(value)); } return isTry; } /// <summary> /// 判断是不是数字或者. /// </summary> /// <param name="ch">字符</param> /// <returns></returns> private static bool IsFloatingNumber(char ch) { //是不是十进制数 var isDigit = char.IsDigit(ch); return isDigit || ch == '.'; } }
/// <summary> /// 操作符解读 /// </summary> public static class OperatorReader { private static readonly string[] _operators = new[] { "+", "-", "*", "/", "^" }; /// <summary> /// 尝试获取操作符 /// </summary> public static bool TryProceedOperator(List<BaseNode> nodes, ReadOnlySpan<char> formula, ref int index) { if (_operators.Contains(formula[index].ToString())) { nodes.Add(new OperatorNode(GetOperatorKey(formula[index].ToString()))); return true; } return false; } /// <summary> /// 获取对应枚举 /// </summary> /// <param name="name"></param> /// <returns></returns> private static OperatorEnum GetOperatorKey(string name) { return name switch { "+" => OperatorEnum.Plus, "-" => OperatorEnum.Minus, "*" => OperatorEnum.Multiply, "/" => OperatorEnum.Divide, "^" => OperatorEnum.Power, _ => OperatorEnum.Undefined }; } }
有了以上的准备,我们就可以将公式转为我们的节点信息了如下
/// <summary> /// 解析公式为节点 /// </summary> /// <param name="formula">公式字符串</param> /// <returns></returns> public static List<BaseNode> AnalysisFormulaToNodes(string formula) { var nodes = new List<BaseNode>(); for(var index = 0;index< formula.Length; index++) { if (NumberReader.TryProceedNumber(nodes, formula.AsSpan(), ref index)) continue; if (OperatorReader.TryProceedOperator(nodes, formula.AsSpan(), ref index)) continue; if (BracketReader.TryProceedOpenBracket(nodes, formula.AsSpan(), ref index)) continue; if (BracketReader.TryProceedCloseBracket(nodes, formula.AsSpan(), ref index)) continue; } return nodes; }
2、转为后缀表达式
转为后缀表达式需要执行以下条件:
/// <summary> /// 转为后缀表达式 /// </summary> /// <param name="nodes"></param> /// <returns></returns> public static List<BaseNode> GetRPN(List<BaseNode> nodes) { var rpnNodes = new List<BaseNode>(); var tempNodes = new Stack<BaseNode>(); foreach(var t in nodes) { //1、如果是操作数直接入栈 if(t.NodeType == NodeTypeEnum.Number) { rpnNodes.Add(t); continue; } //2、若取出的字符是运算符,则循环比较S1栈顶的运算符(包括左括号)优先级,如果栈顶的运算符优先级大于等于该运算符的优先级,则S1栈顶运算符弹出加入到S2中直至不满足条件为止,最后将该运算符送入S1中。 if (t.NodeType == NodeTypeEnum.Operator) { while (tempNodes.Count > 0) { var peekOperatorNode = tempNodes.Peek() as OperatorNode; if (peekOperatorNode != null && peekOperatorNode.Priority >= (t as OperatorNode).Priority) { rpnNodes.Add(tempNodes.Pop()); } else { break; } } tempNodes.Push(t); continue; } //3、若取出的字符是“(”,则直接送入S1栈顶 if(t.NodeType == NodeTypeEnum.Bracket) { if((t as BracketNode).Bracket == BracketEnum.Open) { tempNodes.Push(t); continue; } } //4、若取出的字符是“)”,则将距离S1栈栈顶最近的“(”之间的运算符,逐个出栈,依次送入S2栈,此时抛弃“(”。 if (t.NodeType == NodeTypeEnum.Bracket) { if ((t as BracketNode).Bracket == BracketEnum.Close) { while (tempNodes.Count > 0) { var peekBracketNode = tempNodes.Peek() as BracketNode; if (tempNodes.Peek().NodeType == NodeTypeEnum.Bracket && peekBracketNode != null && peekBracketNode.Bracket == BracketEnum.Open) { break; } else { rpnNodes.Add(tempNodes.Pop()); } } tempNodes.Pop(); continue; } } //5、重复上述步骤 } if(tempNodes.Count > 0) { rpnNodes.Add(tempNodes.Pop()); } return rpnNodes; }
3、计算后缀表达式
/// <summary> /// 计算后缀表达式 /// </summary> /// <param name="nodes"></param> /// <returns></returns> public static double CalculationRPN(List<BaseNode> nodes) { double result = 0; Stack<BaseNode> stack = new Stack<BaseNode>(); foreach(var t in nodes) { if(t.NodeType == NodeTypeEnum.Number) { //操作数直接入栈 stack.Push(t); } else if(t.NodeType == NodeTypeEnum.Operator) { //操作符弹出栈顶两个进行计算 var a = stack.Pop(); var b = stack.Pop(); var operate = t as OperatorNode; var value = operate.OperatorKey switch { // 数学操作符 OperatorEnum.Multiply => OperatorService.Multiply(a, b), OperatorEnum.Divide => OperatorService.Divide(a, b), OperatorEnum.Plus => OperatorService.Plus(a, b), OperatorEnum.Minus => OperatorService.Minus(a, b), OperatorEnum.Power => OperatorService.Power(a, b), }; stack.Push(new NumberNode(value)); } } result = (stack.Pop() as NumberNode).Number; return result; }
数学操作符执行代码如下主要为了进行加减乘除简单的计算:
/// <summary> /// 操作符服务 /// </summary> public static class OperatorService { #region Math public static double Multiply(in BaseNode a, in BaseNode b) { var (result, _a, _b) = IsNumber(a, b); if (result) { return _a * _b; } return default; } public static double Divide(in BaseNode a, in BaseNode b) { var (result, _a, _b) = IsNumber(a, b); if (result) { return _a / _b; } return default; } public static double Plus(in BaseNode a, in BaseNode b) { var (result, _a, _b) = IsNumber(a, b); if (result) { return _a + _b; } return default; } public static double Minus(in BaseNode a, in BaseNode b) { var (result, _a, _b) = IsNumber(a, b); if (result) { return _a - _b; } return default; } public static double Power(in BaseNode a, in BaseNode b) { var (result, _a, _b) = IsNumber(a, b); if (result) { return Math.Pow(_a, _b); } return default; } /// <summary> /// 判断是不是数字类型,并返回数字 /// </summary> /// <param name="a"></param> /// <returns></returns> private static (bool,double,double) IsNumber(BaseNode a, in BaseNode b) { if(a.NodeType == NodeTypeEnum.Number && b.NodeType == NodeTypeEnum.Number) { var _a = a as NumberNode; var _b = b as NumberNode; return (true, _a.Number, _b.Number); } return (false, default, default); } #endregion }
最后串在一起就能得到结果啦,就像下面这样
/// <summary> /// 计算 /// </summary> /// <param name="formula">公式字符串</param> /// <returns></returns> public static double Calculation(string formula) { //1、获取公式节点 var nodes = AnalysisFormulaToNodes(formula); //2、转后缀表达式 var rpnNodes = GetRPN(nodes); //3、计算对后缀表达式求值 var result = CalculationRPN(rpnNodes); return result; }