C++ :

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#include<stack>
#define Int stack<int>
#define Char stack<char>
using namespace std;
int n,m;
Int s1;//操作数栈
Char s2;//运算符栈

int lev(char x)//运算符优先级
{
    if(x=='+'||x=='-')
        return 1;
    if(x=='*'||x=='/')
        return 2;
    if(x=='^')
        return 3;
    return 0;
}

void calculate(Int &s1,Char &s2)//弹出栈顶元素并计算
{
    /*取出后弹出栈*/
    int y=s1.top();
        s1.pop();
    int x=s1.top();
        s1.pop();
    char z=s2.top();
        s2.pop();

    /*根据运算符计算,并压入栈*/
    if(z=='+')
        s1.push(x+y);
    if(z=='-')
        s1.push(x-y);
    if(z=='*')
        s1.push(x*y);
    if(z=='/')
        s1.push(x/y);
    if(z=='^')
        s1.push(pow(x,y));
}

int c(int x)
{
    return x!=0;
}
char str[1000000];
int sum[1000000];
int main()
{
    int i;

    scanf("%s",str+1);
    n=strlen(str+1)-1;//忽略掉@的字符串长度

    for(i=1;i<=n;i++)//检查匹配
    {
        sum[i]+=sum[i-1];
        if(str[i]=='(')
            sum[i]++;
        if(str[i]==')')
            sum[i]--;
    }

    bool out=false;
    for(i=2;i<=n;i++)
        if( c(lev(str[i])) && c(lev(str[i-1])) )
        {
            out=1;
            break;
        }

    if( ( n==1 && c(lev(str[1])) )||sum[n]||out )//表达式不合法
    {
        cout<<"NO"<<endl;
        return 0;
    }

    Int s1;
    Char s2;
    int temp=0;
    bool flag=false;
    for(i=1;i<=n;i++)
    {
        if('0'<=str[i]&&str[i]<='9')//判断当前字符是否为数字
        {
            temp=(temp<<3)+(temp<<1)+str[i]-'0';
            flag=true;
        }
        else
        {
            if(flag)
            {
                s1.push(temp);
                temp=0;
                flag=false;
            }
            if(str[i]=='(')
            {
                s2.push(str[i]);
                continue;
            }
            if(str[i]==')')
            {
                while(s2.top()!='(')
                    calculate(s1,s2);
                s2.pop();
                continue;
            }
            while(!s2.empty()&&lev(s2.top())>=lev(str[i]))//优先级判断
                calculate(s1,s2);
            s2.push(str[i]);//运算符入栈
        }
    }
    if(flag)
    {
        s1.push(temp);
        temp=0;
        flag=false;
    }
    while(!s2.empty())
        calculate(s1,s2);
    cout<<s1.top()<<endl;
    return 0;
}