[参考文献:严蔚敏.数据结构(C语言版)]
表达式求值是程序设计语言编译中的一个最基本问题,它的实现是栈应用的一个典型例子.
搞了一天,有相关的好的算法请大家传上来,一起分享.
表3.1: 定义了算符之间的优先关系:
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
namespace EvaluateExpression
{
class EvaluateExpression
{
private static string Precede(string t1, string t2) //根据表3.1，判断两符号的优先关系
{
string f = string.Empty;
switch (t2)
{
case "+":
case "-":
if (t1 == "(" || t1 == "#")
f = "<";
else
f = ">";
break;
case "*":
case "/":
if (t1 == "*" || t1 == "/" || t1 == ")")
f = ">";
else
f = "<";
break;
case "(":
if (t1 == ")")
throw new ArgumentOutOfRangeException("表达式错误");
else
f = "<";
break;
case ")":
switch (t1)
{
case "(": f = "="; break;
case "#": throw new ArgumentOutOfRangeException("表达式错误");
default: f = ">"; break;
}
break;
case "#":
switch (t1)
{
case "#": f = "="; break;
case "(": throw new ArgumentOutOfRangeException("表达式错误");
default: f = ">"; break;
}
break;
}
return f;
}
private static bool In(string c) //判断c是否为运算符
{
switch(c)
{
case"+":
case"-":
case"*":
case"/":
case"(":
case")":
case"#": return true ;
default: return false ;
}
}
private static int Operate(int a, string oper, int b)
{
int c=0;
switch (oper)
{
case "+": c = a + b; break;
case "-": c = a - b; break;
case "*": c = a * b; break;
case "/": c = a / b; break;
}
return c;
}
public static int Calculate(string exp) //算术表达式求值的算符优先算法。设OPTR和OPND分别为运算符栈和运算数栈
{
expr S = new expr(exp); //将传过来的表达式打包成一个类对象,便于计算
string C =string.Empty ;
int oper1, oper2;
string theta = string.Empty;
Stack OPTR = new Stack();
OPTR.Push("#");
Stack OPND = new Stack();
C = S.GetS (); //取表达式里的分量
while (C != "#" || OPTR.Peek().ToString() != "#")
{
if (!In(C)) //不是运算符则进栈
{
OPND.Push(C);
C = S.GetS();
}
else
switch (Precede(OPTR.Peek().ToString(), C))
{
case "<": //栈顶元素优先权低
OPTR.Push(C);
C = S.GetS();
break;
case "=": //脱括号并接收下一个字符
OPTR.Pop();
C = S.GetS();
break;
case ">": //退栈并将运算结果入栈
theta = OPTR.Pop().ToString();
oper2 = Convert.ToInt32(OPND.Pop());
oper1 = Convert.ToInt32(OPND.Pop());
OPND.Push(Operate(oper1, theta, oper2).ToString());
break;
}//switch
}//while
return Convert.ToInt32(OPND.Peek());
}
private class expr //表达式类, 用于取表达式里的各个分量
{
//成员
private string exp;
private int length; //为GetS()方法服务
//构造器
public expr(string exp)
{
this.exp = exp;
length = exp.Length;
if (!IsRight()) { Console.WriteLine("表达式有错"); return; }
}
//方法
public string GetS() //取表达式里的字符串
{
string ch, token, f;
ch = token = f = string.Empty;
if (length == 0)
throw new ArgumentOutOfRangeException("表达式取完");
while (length != 0)
{
ch = exp.Substring(exp.Length - length, 1);
if (IsNumeric(ch)) //是数字 : 说明第一次取的就是数字
{
token += ch;
length--;
}
else //不是数字
{
if (IsNumeric(token))
{
f = token;
break;
}
else //说明第一次取的就不是数字
{
if (ch == " ")
{
length--;
continue;
}
length--; //如取的是非数字
f = ch;
break;
}
}
}
return f;
}//GetS
private bool IsRight() //判断表达式是否合法: (1)两数字中间是否有空格
{
bool f = true;
string ch = string.Empty;
int i = 0;
int j = 0;
for (int p = 0; p < exp.Length; p++)
{
ch = exp.Substring(p, 1);
if (IsNumeric(ch))
{
if (j == 1) return false;
i = 1;
continue;
}
if (ch == " ")
{
if (i == 1) j = 1; continue;
}
i = j = 0;
}
return f;
}
private bool IsNumeric(string input) //判断字符串是否为数
{
bool flag = true;
string pattern = (@"^\d+$");
Regex validate = new Regex(pattern);
if (!validate.IsMatch(input))
{
flag = false;
}
return flag;
}
}//class:expr
}
}
附一个测试代码:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace EvaluateExpression
{
class Program
{
static void Main(string[] args)
{
Console.WriteLine ("算术表达式, 以#结束!");
string expression = " 3022 * ( 17 - 12) /2 #";
Console .WriteLine ( Convert .ToString ( EvaluateExpression.Calculate(expression)));
Console.ReadLine();
}
}
}
