这道题做不出来啊！

#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<cctype>
using namespace std;
double _log10(int n)
{
    return log(n+0.0)/log(10.0);
}
double fac[1000000];
string str;
int len;
int sol()
{
    double sum=0;
    for(int i=0;i<len;)
    {
        if(isdigit(str[i]))
        {
            int num=0;
            for(;i<len&&isdigit(str[i]);i++) num=num*10+str[i]-'0';
            if((i<len&&str[i]=='*')||i==len)
            {
                sum+=_log10(num);
                i++;
                continue;
            }
            else if(i<len&&str[i]=='^')
            {
                i++;
                int f=0;
                for(;i<len&&isdigit(str[i]);i++) f=f*10+str[i]-'0';
                sum+=f*_log10(num);
                i++;
                continue;
            }
            else if(i<len&&str[i]=='!')
            {
                i++;
                sum+=fac[num];
                i++;
                continue;
            }
        }
        else i++;
    }
    return (int) sum+1;
}
int main()
{
    for(int i=1;i<1000000;i++) fac[i]=fac[i-1]+_log10(i);
    char ch;
    while(cin>>ch) str+=ch;
        len=str.size();
        int cnt=sol();
        printf("%d/n",cnt);
    return 0;
}