头文件

// expressions.h: interface for the expression class.
//
//////////////////////////////////////////////////////////////////////
#if !defined(AFX_EXPRESSION_H__5CBE655C_7DC8_432D_9777_4F8B16458183__INCLUDED_)
#define AFX_EXPRESSION_H__5CBE655C_7DC8_432D_9777_4F8B16458183__INCLUDED_
#if _MSC_VER > 1000
#pragma once
#endif // _MSC_VER > 1000
#include <string>
#include <map>
class expressions
{
public:
    expressions();
    virtual ~expressions();
    std::string postorder(std::string );//后缀表达式
private:
    int priority(char op1,char op2);//优先级 op1 > op2 1 op1==op2 0 op1 < op2 -1
    std::map<char,int> mOp;
};
#endif // !defined(AFX_EXPRESSION_H__5CBE655C_7DC8_432D_9777_4F8B16458183__INCLUDED_)

源文件

// expressions.cpp: implementation of the expressions class.
//
//////////////////////////////////////////////////////////////////////
#include "stdafx.h"
#include "expressions.h"
#include <utility>
#include <stack>
#include <iostream>
//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////
using namespace std;
typedef struct _op{
public:
    char opstr;
    int  level;
}op;
static op oparr[] = {
    {‘ ‘,0},
    {‘+‘,1},
    {‘-‘,1},
    {‘*‘,2},
    {‘/‘,2}
};
expressions::expressions()
{
    char ckey;
    int nvalue;
    for(int i=0;i<sizeof(oparr)/sizeof(op);++i)
    {
        ckey = oparr[i].opstr;
        nvalue = oparr[i].level;
        mOp.insert(std::make_pair<char,int>(ckey,nvalue));
    }
}
expressions::~expressions()
{
}
std::string expressions::postorder(std::string expstr)
{
    stack<char> ops;
    string sret;
    string svalue;
    string ssep = "     \n()\r+-*/";
    string ssp = "  \n\r";
    string sop = "+-*/";
    for(int i=0;i<expstr.size();++i)
    {
        char& ch = expstr[i];
        if(ssep.find(ch) == -1)
        {
            //元素
            svalue += ch;
        }
        else
        {
            //分隔符
            sret += svalue;
            svalue = "";
            if(ssp.find(ch) != -1)
            {
                //空白符
                continue;
            }
            sret += ‘ ‘;
        }
        if(ch == ‘(‘)
        {
            ops.push(ch);
        }
        else if(ch == ‘)‘)
        {
            while(ops.size() > 0)
            {
                char ctop = ops.empty() ? ‘ ‘ : ops.top();
                if(ctop == ‘(‘)
                {
                    ops.pop();
                    break;
                }
                else
                {
                    sret += ctop;
                    sret += ‘ ‘;
                    ops.pop();
                }
            }
        }
        else if(sop.find(ch) != -1)
        {
            //操作符
            //比较当前操作符和栈顶操作符优先级
            char ctop = ops.empty() ? ‘ ‘ : ops.top();
            int ret = priority(ch, ctop);
            if(ret > 0 || ch == ‘(‘)
            {
                ops.push(ch);
            }
            else
            {
                while(ops.size() > 0)
                {
                    char ctop = ops.empty() ? ‘ ‘ : ops.top();
                    int ret = priority(ch, ctop);
                    if(ret > 0 || ctop == ‘(‘)
                    {
                        ops.push(ch);
                        break;
                    }
                    else
                    {
                        sret += ctop;
                        sret += ‘ ‘;
                        ops.pop();
                    }
                }
                if(ops.size() == 0)
                {
                    ops.push(ch);
                }
            }
        }
    }
    sret += svalue;
    sret += ‘ ‘;
    //所有操作符出栈
    while(ops.size() > 0)
    {
        sret += ops.top();
        sret += ‘ ‘;
        ops.pop();
    }
    return sret;
}

int expressions::priority(char op1,char op2)
{
    int level1 = 0,level2 = 0;
    level1 = mOp[op1];
    level2 = mOp[op2];
    if(level1 > level2)
    {
        return 1;
    }
    else if(level1 < level2)
    {
        return -1;
    }
    return 0;
              
}

测试

// expessiontest.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include "expressions.h"
#include <iostream>
using namespace std;
int main(int argc, char* argv[])
{
    expressions exp;
    cout<<exp.postorder("  a + b - c* 10 / 2+34");
    return 0;
}

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后缀表达式c++实现