中缀表达式转后缀表达式

使用c++11， 实现一个简单的计算器，计算数学上常用的中缀表达式的值。

最重要的演示中缀表达式转换为后缀表达式算法。

目前支持+-* / 任意四则运算，除法为计算机的整除法，要改为浮点除法也是很容易的事。

输入为常用的数学中缀表达式，
输入为表达式的值。

计算分为以下几步：

1. 预处理，将字符串转化为独立的操作数和操作符，同时去掉空格，存放在字符串vector里。
2. 中缀表达式转后缀表达式。中缀表达式虽然最合适人类阅读，但后缀（或者前缀）表达式更方便计算机计算，同时后缀表达式不需要中缀表达式里改变计算优先级的括号（）。这是最重要的一步。
3. 最后通过扫描后缀表达式计算表达式的值。

github https://github.com/gjwang/Calculator.git

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代码如下

////  main.cpp//  Calculator////  Created by gjwang on 11/22/15.//  Copyright (c) 2015 gjwang. All rights reserved.//#include <iostream>#include <cstdlib>#include <vector>#include <map>#include <string>#include <cassert>using namespace std;string expr = "(3+2*5 + (80-79)*2*2)*2";string expr0 = "(3+2)*(4-2)/(8+7)";string expr1 = "9-5+2";string expr2 = "(9-5)+2";string expr3 = "(9-(5+2))";string expr4 = "(((9-  ((((5+2))))  )))";string expr5 = " (9-   ( 20 + 10 ) ) * 2 ";vector<string> infixExprVec={    expr,    expr0,    expr1,    expr2,    expr3,    expr4,    expr5,};typedef int (*BiOpdFuns)(int, int);typedef map<const string, BiOpdFuns> BiOpdFunsMap_t;BiOpdFunsMap_t BiOpdFunsMap;const string operatorAdd = "+";const string operatorMinus = "-";const string operatorMult = "*";const string operatorDiv = "/";inline int addOpd(int a, int b){    return a + b;}inline int minusOpd(int a, int b){    return a - b;}inline int multOpd(int a, int b){    return a * b;}inline int divOpd(int a, int b){    return a / b;}inline bool isBlank(const char c){    return c == ' ';}inline bool isDigit(const char c){    return c >= '0' && c <= '9';}inline int charToDigit(const char c){    return c - '0';}inline bool isOperand(const char c){    //For now    return isDigit(c);}inline bool isOperator(const char c){    return c == '+' || c == '-' || c == '*' || c == '/';}bool isOperator(const BiOpdFunsMap_t& map, const string& s){    return map.find(s) != map.end();}int GetPriority(const char c){    if (c == '+' || c == '-') {        return 10;    } else if ( c == '*' || c == '/') {        return 11;    } else {        assert(false);        return 0;    }}int GetPriority(const string& s){    if (s.compare("+") == 0 || s.compare("-") == 0) {        return 10;    } else if ( s.compare("*") == 0 || s.compare("/") == 0) {        return 11;    } else {        assert(false);        return 0;    }}vector<string> preProcessInfixExpr(const string& infixExpr){    vector<string> infixExprVec;    string tmp("");    for_each(infixExpr.begin(), infixExpr.end(), [&](char c){        if (isDigit(c)) {            tmp.push_back(c);        }else{            if (tmp.length() != 0) {                infixExprVec.push_back(tmp);                tmp.clear();            }            if ( !isBlank(c) ) {                //skip any blank                infixExprVec.push_back(string(1, c));            }        }    });    //push the last operand into stack    if (tmp.length() != 0) {        infixExprVec.push_back(tmp);    }    return infixExprVec;}vector<string> convertInfixToPostfixExprStack(const vector<string>& infixExpr){    vector<string> postFixExpr(128);    vector<string> opStack(32);    vector<string>::const_iterator it = infixExpr.begin();    for (; it != infixExpr.end(); it++) {        if (it->compare("(") == 0) {            opStack.push_back(*it);        }else if (it->compare(")") == 0) {            //pop all operator within ()            for (auto it=opStack.rbegin(); it->compare("(") != 0; it++) {                postFixExpr.push_back(opStack.back());                opStack.pop_back();//pop operator            }            opStack.pop_back();//pop "("        }else if (isOperator(BiOpdFunsMap, *it)) {            if (!opStack.empty()           &&                isOperator(BiOpdFunsMap, opStack.back()) &&                GetPriority(opStack.back()) >= GetPriority(*it)                ) {                //meet an operator, it's priority is great_or_equal to the last one's                postFixExpr.push_back(opStack.back());                opStack.pop_back();                opStack.push_back(*it);            }else {                opStack.push_back(*it);            }        }else{            //if (isOperand(*it)) {            postFixExpr.push_back(*it);        }    }    postFixExpr.insert(postFixExpr.end(), opStack.rbegin(), opStack.rend());    return postFixExpr;}int calcutorPostfixExpr(const vector<string>& postfixExpr){    int ret = 0;    vector<string> opdStack(32); //operand stack    vector<string> opStack(32);  //operator stack    for_each(postfixExpr.begin(), postfixExpr.end(), [&](const string s){        if (isOperator(BiOpdFunsMap, s)){            auto opd2 = opdStack.back();            opdStack.pop_back();            auto opd1 = opdStack.back();            opdStack.pop_back();            auto it = BiOpdFunsMap.find(s);            if (it != BiOpdFunsMap.end()) {                auto operand = it->second(stoi(opd1), stoi(opd2));                //cout << "operand=" << operand << " ";                opdStack.push_back(to_string(operand));                ret = operand;            } else {                //should not happen                assert(false);            }        }else{            //s is operand            opdStack.push_back(s);        }    });    return ret;}int main(int argc, const char * argv[]) {    BiOpdFunsMap.insert(make_pair(operatorAdd, addOpd));    BiOpdFunsMap.insert(make_pair(operatorMinus, minusOpd));    BiOpdFunsMap.insert(make_pair(operatorMult, multOpd));    BiOpdFunsMap.insert(make_pair(operatorDiv, divOpd));    for_each(infixExprVec.begin(), infixExprVec.end(), [](const string& inFixExp){        for_each(inFixExp.begin(), inFixExp.end(), [](char c){            cout << c;        });        cout << " = ";        auto infixExprString = preProcessInfixExpr(inFixExp);        auto postfixExpr =convertInfixToPostfixExprStack(infixExprString);        for_each(postfixExpr.begin(), postfixExpr.end(), [](const string& expr){            cout << expr;        });        //cout << endl;        int ret = calcutorPostfixExpr(postfixExpr);        cout << " = " << ret << endl;    });    return 0;}

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测试输出：

(3+2*5 + (80-79)*2*2)*2 = 325*8079-2*2*++2* = 34(3+2)*(4-2)/(8+7) = 32+42-*87+/ = 09-5+2 = 95-2+ = 6(9-5)+2 = 95-2+ = 6(9-(5+2)) = 952+- = 2(((9-  ((((5+2))))  ))) = 952+- = 2 (9-   ( 20 + 10 ) ) * 2  = 92010+-2* = -42