栈的应用--后缀表达式和中缀表达式的实现

数据结构中对栈的应用，典型的例子是后缀表达式和中缀表达式的实现。代码如下：

class CCalculator{public:CCalculator(int sz);~CCalculator();int Run();void clean();private:void AddOperand(int value);bool Get2Operand(int &left, int &right);void DoOperator(char op);void postfix(char* mid,char *post);int isp(char id);int icp(char id);CStack* m_pStack;}; 

操作符的优先级表：

nt prioTable[7][3] = {{'#',0,0},{'(',1,8},{'*',5,4},{'/',5,4},{'+',3,2},{'-',3,2},{')',8,1}}; 

优先级表的查询，栈内优先级和栈外优先级：

int CCalculator::isp(char id){int i=0; for(i=0; i<7; i++){if(prioTable[i][0] == id){return prioTable[i][1];}}return -1;}int CCalculator::icp(char id){int i=0; for(i=0; i<7; i++){if(prioTable[i][0] == id){return prioTable[i][2];}}return -1;} 

其它实现：

void CCalculator::postfix(char *mid, char* post){CStack *pStack = new CStack(20);pStack->makeEmpty();char* pCh = mid;//char* pTemp;int iTemp;pStack->push('#');while(*pCh != '#'){if(isdigit(*pCh)){*post++ = *pCh;}else if(*pCh == ')'){//for(*pTemp = pStack->pop(); *pTemp != '('; *pTemp = pStack->pop()){//*post++ = *pTemp;//}for(iTemp = pStack->pop(); iTemp != '('; iTemp = pStack->pop()){*post++ = iTemp;}}else{//for(*pTemp = pStack->pop(); isp(*pTemp) > icp(*pCh); *pTemp = pStack->pop()){//*post++ = *pTemp;//}for(iTemp = pStack->pop(); isp(iTemp) > icp(*pCh); iTemp = pStack->pop()){*post++ = iTemp;}pStack->push(iTemp);pStack->push(*pCh);}pCh++;}while(!pStack->isEmpty()){iTemp = pStack->pop();if(iTemp != '#'){*post++ = iTemp;}}*post = '=';}int CCalculator::Run(){//char chIn[] = "1243-*+55/-=";char chIn[] = "1+2*(4-3)-5/5#";char chOut[20];postfix(chIn,chOut);int newOperand;char* pCh = chOut;while(*pCh != '='){switch(*pCh){case '+':case '-':case '*':case '/':DoOperator(*pCh);break;default:AddOperand(*pCh);break;}pCh++;}return m_pStack->pop();}void CCalculator::clean(){}void CCalculator::AddOperand(int value){m_pStack->push(value);}bool CCalculator::Get2Operand(int &left, int &right){ASSERT(!m_pStack->isEmpty());right = m_pStack->pop();ASSERT(!m_pStack->isEmpty());left = m_pStack->pop();return true;}void CCalculator::DoOperator(char op){int iLeft,iRight;bool result;result = Get2Operand(iLeft,iRight);if(result){switch(op){case '+':m_pStack->push(iLeft+iRight);break;case '-':m_pStack->push(iLeft-iRight);break;case '*':m_pStack->push(iLeft*iRight);break;case '/':if(iRight != 0){m_pStack->push(iLeft/iRight);}break;default:RETAILMSG(TRUE,(L"illegal operator"));break;}}} 

 

在这个过程中，遇到的一些问题：

1. prioTable的定义；用prioTable[][]编译无法通过，必须指明prioTable[][3];

2. isp和icp；为什么要有栈内优先级和栈外优先级？栈内优先级和栈外优先级主要是用在中缀表达式到后缀表达式的转换中。中缀表达式，人类容易识别；后缀表达式，计算机容易处理；例如A+B*(C-D)-E/F是中缀表达式，而ABCD-*+EF/-是后缀表达式。栈内优先级和栈外优先级不同有几个目的；一个目的是处理括号；一个目的是为了处理相同优先级的情况下，先右后左的运算顺序。

3. 中缀表达式到后缀表达式转换的基本思想是：遇到操作数直接输出，遇到操作符，比较该操作符和栈顶操作符的优先级，如果该操作符优先级更高，则入栈；如果栈内操作符优先级更高，则就要先将栈内的操作符处理掉。

4. 指针必须要先赋值后使用，我之前定义了char* pTemp，就出现了问题。

5. bool instead of Boolean

6. L必须加括号