資料結構之應用 “棧(Stack)” 實現: 解析算術運算式及計算求值 (C#/Java)

中綴運算式到尾碼運算式的轉換要把運算式從中綴運算式的形式轉換成用尾碼標記法
表示的等價運算式

C# Code:

//using System;
class Class1
{
 public static void Main()
 {
  System.Console.WriteLine("Hello World!");
  //中綴 => 尾碼運算式
  string s = "(  1.9   +  (20 +  41)    / (25 * 11) -     3          )              * 2"; //中綴; //中綴
  string S = ""; //尾碼
  char[] Operators = new char[s.Length];
  int Top = -1;
  for (int i = 0; i < s.Length; i++)
  {
   char C = s[i];
   switch (C)
   {
    case ' ' : //忽略空格
     break;
    case '+' : //操作符
    case '-' :
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       Operators[++Top] = c; //push Operator
       break;
      }
      else
      {
       S = S + c;
      }
     }
     Operators[++Top] = C; //push Operator
     S += " ";
     break;
    case '*' : //忽略空格
    case '/' :
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       Operators[++Top] = c; //push Operator
       break;
      }
      else
      {
       if (c == '+' || c == '-')
       {
        Operators[++Top] = c; //push Operator
        break;
       }
       else
       {
        S = S + c;
       }
      }
     }
     Operators[++Top] = C; //push Operator
     S += " ";
     break;
    case '(' :
     Operators[++Top] = C;
     S += " ";
     break;
    case ')' :
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       break;
      }
      else
      {
       S = S + c;
      }
     }
     S += " ";
     break;
    default :
     S = S + C;
     break;
    
   }
  }
  while (Top >= 0)
  {
   S = S + Operators[Top--]; //pop Operator
  }

  System.Console.WriteLine(S); //尾碼

  //尾碼運算式計算
  double[] Operands = new double[S.Length];
  double x, y, v;
  Top = - 1;
  string Operand = "";
  for (int i = 0; i < S.Length; i++)
  {
   char c = S[i];
   if ((c >= '0' && c <= '9') || c == '.')
   {
    Operand += c;
   }

   if ((c == ' ' || i == S.Length - 1) && Operand != "") //Update
   {
    Operands[++Top] = System.Convert.ToDouble(Operand) ; //push Operands
    Operand = "";
   }

   if (c == '+' || c == '-' || c == '*' || c == '/')
   {
    if ((Operand != ""))
    {
     Operands[++Top] = System.Convert.ToDouble(Operand) ; //push Operands
     Operand = "";
    }
    y = Operands[Top--]; //pop 雙目運算子的第二運算元 (後進先出)注意運算元順序對除法的影響
    x = Operands[Top--]; //pop 雙目運算子的第一運算元
    switch (c)
    {
     case '+' :
      v = x + y;
      break;
     case '-' :
      v = x - y;
      break;
     case '*' :
      v = x * y;
      break;
     case '/' :
      v = x / y; // 第一運算元 / 第二運算元 注意運算元順序對除法的影響
      break;
     default :
      v = 0;
      break;
    }
    Operands[++Top] = v; //push 中間結果再次入棧
   }
  }
  v = Operands[Top--]; //pop 最終結果
  System.Console.WriteLine(v);
  System.Console.ReadLine();
 }
}

 

Java Code:

class Class1
{
 public static void main(String[] args)
 {
  System.out.println("Hello World!");
  //中綴 => 尾碼運算式
  String s = "(  1.9   +  (20 +  41)    / (25 * 11) -     3          )              * 2"; //中綴
  String S = ""; //尾碼
  char[] Operators = new char[s.length()];
  int Top = -1;
  for (int i = 0; i < s.length(); i++)
  {
   char C = s.charAt(i);
   switch(C)
   {
    case ' ' :
     break;
    case '+' : //操作符
    case '-' :
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       Operators[++Top] = c; //push Operator
       break;
      }
      else
      {
       S = S + c;
      }
     }
     Operators[++Top] = C; //push Operator
     S += " ";
     break;
    case '*' : //操作符
    case '/' :
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       Operators[++Top] = c; //push Operator
       break;
      }
      else
      {
       if (c == '+' || c == '-')
       {
        Operators[++Top] = c; //push Operator
        break;
       }
       else
       {
        S = S + c;
       }
      }
     }
     Operators[++Top] = C; //push Operator
     S += " ";
     break;
    case '(' : //操作符
     Operators[++Top] = C;
     S += " ";
     break;
    case ')' : //操作符
     while (Top >= 0) //棧不為空白時
     {
      char c = Operators[Top--]; //pop Operator
      if (c == '(')
      {
       break;
      }
      else
      {
       S = S + c;
      }
     }
     S += " ";
     break;
    default : //運算元
     S = S + C;
     break;
   }
  }
  while (Top >= 0)
  {
   S = S + Operators[Top--]; //pop Operator
  }

  System.out.println(S); //尾碼

  //尾碼運算式計算
  double[] Operands = new double[S.length()];
  double x, y, v;
  Top = - 1;
  String Operand = "";
  for (int i = 0; i < S.length(); i++)
  {
   char c = S.charAt(i);
   if ((c >= '0' && c <= '9') || c == '.')
   {
    Operand += c;
   }

   if ((c == ' ' || i == S.length() - 1) && Operand != "") //Update
   {
    Operands[++Top] = java.lang.Double.parseDouble(Operand) ; //push Operands
    Operand = "";
   }

   if (c == '+' || c == '-' || c == '*' || c == '/')
   {
    if ((Operand != ""))
    {
     Operands[++Top] = java.lang.Double.parseDouble(Operand) ; //push Operands
     Operand = "";
    }
    y = Operands[Top--]; //pop 雙目運算子的第二運算元 (後進先出)注意運算元順序對除法的影響
    x = Operands[Top--]; //pop 雙目運算子的第一運算元
    switch (c)
    {
     case '+' :
      v = x + y;
      break;
     case '-' :
      v = x - y;
      break;
     case '*' :
      v = x * y;
      break;
     case '/' :
      v = x / y; // 第一運算元 / 第二運算元 注意運算元順序對除法的影響
      break;
     default :
      v = 0;
      break;
    }
    Operands[++Top] = v; //push 中間結果再次入棧
   }
  }
  v = Operands[Top--]; //pop 最終結果
  System.out.println(v);
 }
}