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：

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。

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。

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

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;
}

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+/ = 0
9-5+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