前言：
1.遇到操作数，直接输出；
2.栈为空时，遇到运算符，入栈；
3.遇到左括号，将其入栈；
4.遇到右括号，执行出栈操作，并将出栈的元素输出，直到弹出栈的是左括号，左括号不输出； (左括号丢弃 不输出)
5.遇到其他运算符 + - * / 时，弹出所有优先级大于或等于该运算符的栈顶元素，然后将该运算符入栈；
6.最终将栈中的元素依次出栈，输出。
全文地址请点击：/qq_34992845/article/details/70313588?utm_source=copy
后缀表达式的计算：从左到右遍历表达式的每个数字和符号，遇到是数字就进栈，遇到是符号，就将处于栈顶两个数字出栈，进行运算，运算结果进栈，一直到最终获得结果。
如何区分负号与减号
如果“-”是第一个字符时｛
在前面加上“0-”
｝
否则｛
如果“-”前一个字符是数字 “-”是减号
如果“-”前一个字符是“^”幂运算符 “-”是负号
否则在前面加上“0-”
｝
如-1-(-4^2)
会转换成0-1-(0-4^2)来处理
三角函数的运算思路（这里用的是角度制）
输入式子->转换成小写->转换成运算符->计算
如输入Sin(30)
转换成小写sin(30)
转换成运算符s(30)
运算0.5
代码：
若有不正之处，请多多谅解并欢迎指正。
using System;using System.Collections.Generic;using System.Linq;using System.Text;namespace 计算表达式{class Program{static void Errorchecking(string s,double d) {double a= Calculation(s);Console.WriteLine(string.Format("{0} 计算结果{1} 正确结果{2} ",s,a,d));}static void Main(string[] args){/*容易出错的式子：-2*(5-2)=-6-2*(-2)=41-(-4^2)=171+(-4^-2)=0.93751+(-4)^-2=1.0625*/Errorchecking("-2 * (5 - 2)" ,-6);Errorchecking("-2*(-2)" , 4);Errorchecking("-64*(-4)^(-2)" , -4);Errorchecking("1-(-4^2)" , 17);Errorchecking("-1+(-4^-2)" , -1.0625);Errorchecking("1+(-4)^-2" , 1.0625);Errorchecking("Sin(90)", 1);Errorchecking("1-4*Sin(-1*(-2^5+2))", -1);Errorchecking("8*sin(-1*(-2^5+2))^2", 2);Errorchecking("cos60*4", 2);Errorchecking("tan(44+1)", 1);Console.WriteLine(string.Format("{0} 计算结果{1} 正确结果{2} ", "tan(90)", Calculation("tan(90)"), "不存在的"));//Console.WriteLine(Calculation("S(-30)"));}public static double Calculation(string str)//函数已封装好 用到的时候直接调用该方法ok{//Console.WriteLine("中缀表达式:"+str);str=str.ToLower();//把字符串转换成小写RemoveSpaces(ref str);StrPreprocessing(ref str);//Console.WriteLine("中缀表达式:" + str + " 预处理");List<object> list = ToPostfix(str); //转换成中缀表达式return CalculationPostfix(list);}static double CalculationPostfix(List<object>list)//计算后缀表达式{List<double> stacks = new List<double>();//计算后缀表达式for (int i = 0; i < list.Count; i++){if (list[i] is double){stacks.Add((double)list[i]);}else{string c = (string)list[i];double aa, bb;switch (c){case "s":aa = stacks.Last();stacks.RemoveAt(stacks.Count - 1);stacks.Add(Math.Sin(aa*Math.PI/180));//这里用的是角度制 弧度制的话改成Math.Sin(aa)就行了break;case "c":aa = stacks.Last();stacks.RemoveAt(stacks.Count - 1);stacks.Add(Math.Cos(aa * Math.PI / 180));break;case "t":aa = stacks.Last();stacks.RemoveAt(stacks.Count - 1);stacks.Add(Math.Tan(aa * Math.PI / 180));break;default:bb = stacks.Last();stacks.RemoveAt(stacks.Count - 1);aa = stacks.Last();stacks.RemoveAt(stacks.Count - 1);stacks.Add(Operation(aa, bb, c));break;}}}return stacks[0];//返回计算结果}static List<object> ToPostfix(string infix)//转换成后缀表达式{List<object> list = new List<object>();//一个集合List<string> stacks = new List<string>();//用来存符号的栈int len = infix.Length;int a = 0, b = 0;for (int i = 0; i < len; i++){//该for循环作用是 把字符串的数字括号运算符区分开来并添加到集合liststring c = infix.Substring(i, 1);if (IsNum(c)){b++;if (i == len - 1) list.Add(ParseNum(infix.Substring(a, b)));}else{string sum = infix.Substring(a, b);if (sum.Length != 0) list.Add(ParseNum(sum));a = i + 1;b = 0;}switch (c) //符号栈操作{case "(": stacks.Add(c); break;case ")":while (stacks.Count > 0){if (stacks.Last() != "("){list.Add(stacks.Last());stacks.RemoveAt(stacks.Count - 1);}else{stacks.RemoveAt(stacks.Count - 1);break;}}break;case "+":case "-":case "*":case "/":case "%":case "^":case "s":case "c":case "t":while (stacks.Count > 0){if (Priority(c, stacks.Last())){list.Add(stacks.Last());stacks.RemoveAt(stacks.Count - 1);}else break;}stacks.Add(c);break;}}while (stacks.Count > 0) //最后的出栈{list.Add(stacks.Last());stacks.RemoveAt(stacks.Count - 1);}//Console.Write("后缀表达式:");//for (int i = 0; i < list.Count; i++) Console.Write(list[i]);return list;}static void StrPreprocessing(ref string infix)//字符串预处理{int len = infix.Length; StringBuilder str = new StringBuilder();//把sin cos tan分别改为s c t方便后面的运算while (infix.IndexOf("sin") >=0 || infix.IndexOf("cos") >=0 || infix.IndexOf("tan") >=0){int a = infix.IndexOf("sin");if(a!=-1) infix=infix.Remove(a+1,2);a = infix.IndexOf("cos");if (a != -1) infix=infix.Remove(a + 1, 2);a = infix.IndexOf("tan");if (a != -1) infix=infix.Remove(a + 1, 2);}len = infix.Length;str = new StringBuilder();for (int i = 0; i < len; i++){string c = infix.Substring(i, 1);if (c == "-"){if (i == 0){str.Append("0-");}else{string cc = infix.Substring(i - 1, 1);if (IsNum(cc)){str.Append(c);}else if (cc == "^"){//避免2^-2=0.25转换成2^0-2=-1str.Append("_");}else{// str+="_";str.Append("0-");}}}else str.Append(c);}infix = str.ToString();}static void RemoveSpaces(ref string infix)//删除空格{int len = infix.Length;StringBuilder str = new StringBuilder();///qq_28187979/article/details/76607253//删除空格for (int i = 0; i < len; i++){string c = infix.Substring(i, 1);if (c == " ") continue;str.Append(c);}infix = str.ToString();}static double Operation(double a,double b,string c)//运算{switch (c){case "+": return a + b;case "-": return a - b;case "*": return a * b;case "/": return a / b;case "%": return a % b;case "^": return Math.Pow(a, b);}throw new Exception();} static bool Priority(string a,string b)//优先级判断{//true为a优低于bif (Grade(a) <= Grade(b)) return true;return false;}static int Grade(string s)//返回该运算符的等级{switch (s){case "(": return 0;case "-": case "+": return 1;case "/":case "*":case "%": return 2;case "^": return 3;case "s":case "c":case "t": return 4;case ")": return 5;}return -1;}static bool IsNum(string s)//传入一个字符 判断该字符是不是数字。负号和点也属于数字 -3.14{switch (s){case "_"://预处理之后负号(-)转换成_ 减号-不变case "0":case "1":case "2":case "3":case "4":case "5":case "6":case "7":case "8":case "9":case ".": return true;}return false;}static bool IsSymbol(object s)//传入一个字符 判断该字符是不是符号{switch (s){case "+":case "-":case "*":case "/":case "%":case "^":case "s":case "c":case "t":return true;}return false;}static double ParseNum(string num)//string转换double 在double.Parse(str);的基础上处理{if (num.Length > 0){if (num.Substring(0, 1) == "_") return -double.Parse(num.Substring(1, num.Length - 1));else return double.Parse(num.Substring(0, num.Length));}throw new Exception();}}}
