[笔试题]比较两个阶乘的大小

此题目的意思是：形如下面的两个字符串阶乘，判断哪个更大。

12!!!! 和 3!!!!!。前者有4个阶乘号，后者有5个。

利用的原理就是：越大的数的同阶阶乘越大。也就是阶乘的单调性。所以可以直接去掉相同个数的阶乘号后再作比较。

没有写大整数类，所以请不要用剩余两个！！以上的数测试，会溢出。

下面是主要函数的代码：

#include <iostream>
#include <string>
#include <algorithm>

using namespace std;

long long factorial( string& str )
{
    int excl = count( str.begin(), str.end(), '!' );
    string temp = str.substr( 0, str.size() - excl );
    long long number = atoi( temp.c_str() );
    
    for ( int i = 0 ; i < excl ; i++ )
     {
        long long t = 1;
        for( long long k = 1 ; k <= number ; k++ )
         {
             t *= k;
         }
         number = t;
     }
     cout<<"The value of longer number cut off is : "<<number<<endl;
     cout<<"----------------"<<endl;
    return number;
}

//return 1 if a > b. else return -1
int compare(string& a, string& b)
{
    int excl_a = count( a.begin(), a.end(), '!');
    int excl_b = count( b.begin(), b.end(), '!');

    int excl = min( excl_a, excl_b );

    //cut off exclamation
    string aa = a.substr( 0, a.size() - excl );
     cout<<"The first number cut off is : "<<aa<<endl;
    string bb = b.substr( 0, b.size() - excl );
     cout<<"The second number cut off is : "<<bb<<endl;
     cout<<"-------------"<<endl;

    //without exclamation
    if ( aa.find( '!', 0 ) != string::npos ) //exclamation in aa
     {
        long long first = factorial( aa );
        long long second = atoi( bb.c_str() );
        if ( first > second )
            return 1;
        else
            return -1;
     }
    else //no exclamation in aa
     {
        long long first = factorial( bb );
        long long second = atoi( aa.c_str() );
        if ( first > second )
            return -1;
        else
            return 1;
     }
}

下面是测试的主函数：

int main()
{
    string a( "12!!!!" );
     cout<<"The first number is : "<<a<<endl;
    string b( "3!!!!!" );
     cout<<"The second number is : "<<b<<endl;
     cout<<"------------"<<endl;

     cout<<a<<" "<<( ( compare( a, b ) > 0 ) ? ">" : "<" )<<" "<<b<<endl;

     cout<<endl<<endl;

    string c( "6!!!" );
     cout<<"The first number is : "<<c<<endl;
    string d( "500!!" );
     cout<<"The second number is : "<<d<<endl;
     cout<<"------------"<<endl;

     cout<<c<<" "<<( ( compare( c, d ) > 0 ) ? ">" : "<" )<<" "<<d<<endl;
}

---

通过 Wiz 发布