100行以内C++代码实现逆波兰式

逆波兰式（Reverse Polish notation，RPN，或逆波兰记法），也叫后缀表达式（将运算符写在操作数之后）。

算术表达式转逆波兰式例子：

逆波兰式整体的算法流程图如下：

下面给出我基于C++ 语言对逆波兰式算法的实现代码，值得注意的是：

1、算法中对操作数，仅支持一个字符的字母或数字的操作数，如：x，y，j，k，3，7等；如果要支持多个字符的操作数，如：var1，3.14等。需要读者自己扩展对算术表达式操作数的分词部分的代码。

2、为了为了增加转换后的逆波兰表达式的可读性，我在每个操作数和操作符输出时后面追加了一个空格。

代码如下：

/// file: ReversePolishNotation.h
#include 
#include 

class ReversePolishNotation {
private:
 std::string _expr;
 unsigned _idx;
 std::stack _stk;
public:
 ReversePolishNotation(const std::string &expr);

 std::string nextWord();

 std::string operator()();

 static int getOpPriority(const std::string &word);

 bool isWord(const std::string &word);

 bool isOperator(const std::string &word);
};

/// file: ReversePolishNotation.cpp
#include 
#include 
#include "ReversePolishNotation.h"
#include 
#include 

using std::cout;
using std::endl;

ReversePolishNotation::ReversePolishNotation(
 const std::string &expr) : _idx(0), _expr(expr) {}

std::string ReversePolishNotation::nextWord() {
 if (_idx >= _expr.length()) {
 return "";
 }
 return _expr.substr(_idx++, 1);
}

std::string ReversePolishNotation::operator()() {
 std::stringstream outExpr;
 std::string word;
 std::string topElem;
 while (true) {
 word = nextWord();
 if (isWord(word)) {
 outExpr << word << " ";
 } else if (isOperator(word)) {
 if (_stk.empty() || _stk.top() == "(") {
 _stk.push(word);
 continue;
 }
 topElem = _stk.top();
 while (getOpPriority(topElem) > getOpPriority(word)) {
 outExpr << topElem << " ";
 _stk.pop();
 if (_stk.empty()) {
  break;
 }
 topElem = _stk.top();
 }
 _stk.push(word);

 } else if (word == "(") {
 _stk.push(word);
 } else if (word == ")") {
 while (true) {
 topElem = _stk.top();
 _stk.pop();
 if (topElem == "(") {
  break;
 }
 assert(!_stk.empty() && "[E]Expr error. Missing '('.");
 outExpr << topElem << " ";
 }
 } else if (word == "") {
 while (!_stk.empty()) {
 topElem = _stk.top();
 assert (topElem != "(" && "[E]Expr error. Redundant '('.");
 outExpr << topElem << " ";
 _stk.pop();
 }
 break;
 } else {
 assert(false && "[W]>>>Can not recognize this word");
 }
 }
 return outExpr.str();
}

int ReversePolishNotation::getOpPriority(const std::string &word) {
 if (word == "+") { return 1; }
 if (word == "-") { return 1; }
 if (word == "*") { return 2; }
 if (word == "/") { return 2; }
 return 0;
}

bool ReversePolishNotation::isWord(const std::string &word) {
 return isalpha(word.c_str()[0]) || isdigit(word.c_str()[0]);
}

bool ReversePolishNotation::isOperator(const std::string &word) {
 return word == "+" ||
  word == "-" ||
  word == "*" ||
  word == "/";
}

/// ---测试代码---
int main() {
 assert(ReversePolishNotation("a+b*c")() == "a b c * + ");
 assert(ReversePolishNotation("(a+b)*c-(a+b)/e")() == "a b + c * a b + e / - ");
 assert(ReversePolishNotation("3*(2-(5+1))")() == "3 2 5 1 + - * ");
// assert(ReversePolishNotation("3*((2-(5+1))")() == "3 2 5 1 + - * "); // Failed Case: Redundant '('
// assert(ReversePolishNotation("3*(?2-(5+1))")() == "3 2 5 1 + - * "); // Failed Case: Can not recognize '?'
 return 0;
}