先将中缀表达式利用栈转换为后缀表达式，然后再利用栈由后缀表达式计算算数表达式的值，具体代码如下：

#include<iostream>usingnamespacestd;#include<string>#include<vector>#include<stack>enumType{OP_NUM,OP_SYMBOL,};enumOperat{ADD,SUB,MUL,DIV,};structCell{Type_type;int_num;};//input=1+((2+3)*4)-5;//中缀到后缀stringtopolishNotation(constchar*input){stack<char>s1;//运算符stack<char>s2;//数字size_tiCount=0;while(input[iCount]!='\0'){//是数字将其压入s2if(input[iCount]>='0'&&input[iCount]<='9'){while(input[iCount]!='\0'&&input[iCount]>='0'&&input[iCount]<='9'){s2.push(input[iCount++]);}s2.push('');--iCount;//最后会统一加1，所以先减一}//是运算符比较其与S1栈顶运算符的优先级while(input[iCount]=='+'||input[iCount]=='-'||input[iCount]=='*'||input[iCount]=='/'){//s1为空，或栈顶运算符为左括号“(”，则直接将此运算符入栈if(s1.empty()||s1.top()=='('){s1.push(input[iCount]);break;}//否则，若优先级比栈顶运算符的高，也将运算符压入s1elseif((input[iCount]=='*'||input[iCount]=='/')&&(s1.top()=='+'||s1.top()=='-')){s1.push(input[iCount]);break;}//否则，将S1栈顶的运算符弹出并压入到S2中，再次与S1中新的栈顶运算符相比较else{s2.push(s1.top());s1.pop();}}//如果是左括号“(”，则直接压入S1；if(input[iCount]=='('){s1.push(input[iCount]);}/*如果是右括号“)”，则依次弹出S1栈顶的运算符，并压入S2，*直到遇到左括号为止，此时将这一对括号丢弃；*/if(input[iCount]==')'){while(s1.top()!='('){s2.push(s1.top());s1.pop();}s1.pop();//将'('也出栈}++iCount;//统一加一次}//将S1中剩余的运算符依次弹出并压入S2；while(!s1.empty()){s2.push(s1.top());s1.pop();}stringret;while(!s2.empty()){ret.push_back(s2.top());s2.pop();}reverse(ret.begin(),ret.end());returnret;}//后缀到数组vector<Cell>StrBehindToVect(conststring&strBehind){vector<Cell>call;size_tiCount=0;while(strBehind[iCount]!='\0'){if(strBehind[iCount]>='0'&&strBehind[iCount]<='9'){intret=0;while(strBehind[iCount]!='\0'&&strBehind[iCount]>='0'&&strBehind[iCount]<='9'){ret=ret*10+strBehind[iCount]-'0';++iCount;}call.push_back({OP_NUM,ret});--iCount;}elseif(strBehind[iCount]=='+'){call.push_back({OP_SYMBOL,ADD});}elseif(strBehind[iCount]=='-'){call.push_back({OP_SYMBOL,SUB});}elseif(strBehind[iCount]=='*'){call.push_back({OP_SYMBOL,MUL});}elseif(strBehind[iCount]=='/'){call.push_back({OP_SYMBOL,DIV});}++iCount;}returncall;}//计算值intRPNCount(constvector<Cell>&array,size_tsize){stack<int>val;for(size_ti=0;i<size;++i){if(array[i]._type==OP_NUM){val.push(array[i]._num);}else{intright=val.top();val.pop();switch(array[i]._num){caseADD:val.top()+=right;break;caseSUB:val.top()-=right;break;caseMUL:val.top()*=right;break;caseDIV:if(right==0){throw(array[i]);}val.top()/=right;break;default:cout<<"请输入合法字符"<<endl;exit(0);}/*switch*/}}returnval.top();}intmain(){stringstrMid="12*(3+4)-6+8/2";stringstrBehind=topolishNotation(strMid.c_str());vector<Cell>call=StrBehindToVect(strBehind);try{intret=RPNCount(call,call.size());cout<<ret<<endl;}catch(Cell){cout<<"除数为0!"<<endl;}system("pause");return0;}