英雄会第四届在线编程大赛·线上初赛：带通配符的数

英雄会第四届在线编程大赛·线上初赛：带通配符的数

个人信息：就读于燕大本科软件工程专业 目前大三;
本人博客：百度搜索“cqs_2012”即可;
个人爱好：酷爱数据结构和算法，希望将来搞科研为人民作出自己的贡献;
博客内容：带通配符的数;
知识选自：编程题;
博客时间：2014-3-25;
 

[align=left]引言[/align]

我一天的时间做了这个题目，后来去提交，真心不想说了，我提交的代码一直在编译和测试，我就无语了，是不是测试系统有问题？头疼了。。。

[align=left]题目[/align]

带通配符的数：
给定一个带通配符问号的数W，问号可以代表任意一个一位数字。

再给定一个整数X，和W具有同样的长度。

问有多少个整数符合W的形式并且比X大？

输入格式

多组数据，每组数据两行，第一行是W，第二行是X，它们长度相同。在[1..10]之间.

输出格式

每行一个整数表示结果。

[align=left]思路[/align]

看到这个题目，我首先用笔在纸上做了半个小时，渐渐发现了思路，后来在纸上写伪代码，写算法。
个人思路用几个例子说明：



我们从左向右依次比较W[i] 和 X[i] 的值
有以下四种情况



好吧，我们模拟算法，看看怎么样吧。



相等，这时候我们比较下一组，ok;



还是相等，接着比较下一组，ok



出现？，这时候把X[2] 加入栈中;接着比较下一组



这时候已经找到不平等元素，发现 W[3] >  X[3] 比较结束。
这时候我们就可以知道在W中，5后面的？可以取10中可能（0~9）;而栈中的？可以取 （9 - 9 + 1）= 1 中情况；
前后两情况之和想乘即可 为 1*10 = 10 ；
退回上一步，如果是另一中情况怎么办？如下



这时候 W[3] < X[3] , 我们也停止比较。
这时候
这时候我们就可以知道在W中，5后面的？可以取10中可能（0~9）;而栈中的？可以取 （9 - 9 ）中情况；
前后两情况之和想乘即可 为 0 * 10 = 0 ；
ok，算法演示结束，各种情况都已处理到。

[align=left]实验[/align]



[align=left]代码[/align]

test.cpp

// include: head file
#include<iostream>
#include<stack>
#include<string>
#include<utility>
using namespace std;

// extra the class of string
class String:public string
{
public:

// mode the add of int
static string ADD_Int(string a,string b)
{
// exception of input
if( a.empty() )
return b;
else if( b.empty() )
return "0";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input ADD_Int";
}
Standardization(a);
Standardization(b);

if(a[0] != '-' && b[0] != '-')
return AddInt(a,b);
else if(a[0] != '-'&& b[0] == '-')
return MinusInt( a,b.substr( 1,b.size() ) );
else if(a[0] == '-'&& b[0] != '-')
return MinusInt(b,a.substr(1,a.size()));
else return '-'+AddInt(a.substr(1,a.size()),b.substr( 1,b.size() ));
}

// make a-b mode int a - b;
static string MINUS_Int(string a,string b)
{
// exception of input
if( a.empty() )
return b;
else if( b.empty() )
return "0";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input Multiplies_Int";
}
Standardization(a);
Standardization(b);
if(a[0] != '-' && b[0] != '-')
return MinusInt(a,b);
else if(a[0] != '-' && b[0] == '-')
return AddInt(a,b.substr(1,b.size()));
else if(a[0] == '-' && b[0] != '-')
return "-"+AddInt(a.substr(1,a.size()),b);
else return MinusInt( b.substr(1,b.size()) , a.substr(1,a.size()) );
}

// make a*b mode int a * b;
static string MULT_Int(string a,string b)
{
// exception of input
if( a.empty() )
return b;
else if( b.empty() )
return "0";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input Multiplies_Int";
}
Standardization(a);
Standardization(b);
string::size_type i = a.size(),j = b.size();
string c = "0",d = "";
bool fushu = (a[0] == '-' && b[0] != '-')||(a[0] != '-' && b[0] == '-');
if(a[0] == '-')
a = a.substr(1,a.size());
if(b[0] == '-')
b = b.substr(1,b.size());

int jinwei = 0;
for( j = b.size()-1 ; j < b.size() ;j--)
{
// each number of b to * a
jinwei = 0;
for( i = a.size()-1 ; i < a.size() ;i-- )
{
d = IntToChar(   ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) % 10 )+ d ;
jinwei = ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) / 10 ;
}
if(jinwei)
d = IntToChar(jinwei) +d;
// add all number result
c = ADD_Int(c,d);
d = "";
unsigned int zero = 0 ;
while( zero < b.size() - j )
{
d = d + '0';
zero ++;
}

}

Standardization(c);
if( fushu )
return '-'+c;
else return c;
}

// mode the division a/b
static string DIV_Int(string a,string b)
{
// exception of input
if( a.empty() )
return "0";
else if( b.empty() )
return "e";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input DIV_Int";
}
Standardization(a);
Standardization(b);
if(b == "0")
return "e";
bool fushu =  (a[0] == '-' && b[0] != '-')||(a[0] != '-' && b[0] == '-');
if( a[0] == '-' )
a = a.substr(1,a.size());
if( b[0] == '-' )
b = b.substr(1,b.size());
if( Compare(a,b) == '<' )
return "0";

string yushu = "";

string beichushu = a.substr(0,b.size());
string shang = Division( beichushu , b);
yushu =  MinusInt( beichushu ,MULT_Int( shang, b) );
string c = shang;

for(string::size_type i = b.size(); i<a.size(); i++)
{
// beichushu = (yushu * 10 + a.substr(i,b.size()))
// shang = beichushu/ b;
// c = c + shang;
// yushu = beichushu  - b* shang;
beichushu =   yushu+ a[i]     ;
shang = Division( beichushu , b);
c = c + shang;
yushu =  MinusInt( beichushu ,MULT_Int( shang, b) );
}
Standardization(c);
return fushu?('-'+c):c;
}

// function: pow number x,y
static string Pow_Int(string a,string b)
{
// exception of input
if( a.empty() )
return "0";
else if( b.empty() )
return "e";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input DIV_Int";
}
Standardization(a);
Standardization(b);
string result = "1" ;
if(Compare(b,"0") != '<')
for(string i ="0" ;Compare(i,b) == '<' ;i = AddInt(i,"1"))
{
result = MULT_Int(result,a);
}
else
for(string i ="0" ;Compare(i,b) == '>' ;i = MINUS_Int(i,"1"))
{
result = DIV_Int(result,a);
}
return result ;
}

// function : int To string
static string Int_To_String(int x)
{
bool fushu = false;
string result="";
if(x < 0 )
{
fushu = true ;
x = -x;
}
else if( x == 0 )
return "0";
while(x)
{
result = IntToChar(x % 10) + result;
x = x/10;
}
return result;
}

// static char division a/b
static string Division(string a,string b)
{
// exception of input
if( a.empty() )
return "0";
else if( b.empty() )
return "e";
if(!check_all_number(a) || !check_all_number(b))
{
cout<<"exception of input Division"<<endl;
return "e";
}
Standardization(a);
Standardization(b);
int i = 0;
while( i<=9 )
{
// if a - b*i < b
if(  Compare(   MINUS_Int(   a  ,   MULT_Int(IntToChar(i),b)    ) , b ) == '<'    )
break;
i++;
}
if( i>9 )
return "e";
return ""+IntToChar(i);
}

// make a-b mode int a - b;
static string MinusInt(string a,string b)
{
// exception of input
if(!check_all_number(a) || !check_all_number(b))
return "exception of input MinusInt";
Standardization(a);
Standardization(b);
// particular string of input
if(a.empty())
{
if(b.empty())
return "0";
else
return "-"+b;
}
else if(b.empty())
{
return a;
}

// normal number a < b
string c = "";
bool check = true ;
if(Compare(a,b) == '=')
return "0";
else if(Compare(a,b) == '<')
{
c = a ;
a = b ;
b = c ;
c = "";
check = false ;
}
// normal number a >= b
string::size_type i = a.size()-1, j = b.size()-1;
int jiewei = 0,now;

while(i < a.size() && j < b.size())
{
now = CharToNumber(a[i]) - CharToNumber(b[j]) - jiewei ;

if( now < 0 )
{
jiewei = 1;
now = 10 + now ;
}
else jiewei = 0;
c = IntToChar(now)  + c ;
i--;j--;
}
while(i < a.size())
{
now = CharToNumber(a[i]) - jiewei ;
if( now < 0 )
{
jiewei = 1;
now = 10 + now ;
}
else jiewei = 0;
c = IntToChar( now )  + c ;
i--;
}
Standardization(c);
if(!check)
c = '-' + c;
return c;
}

// mode the add of int
static string AddInt(string a,string b)
{
// exception of input
if( a.empty() )
return b;
else if( b.empty() )
return "0";
if(!check_all_number(a) || !check_all_number(b))
{
return "exception of input AddInt";
}
Standardization(a);
Standardization(b);
string::size_type i = a.size()-1 ,j = b.size()-1 , k = 0 ;
string c = "";
int jinwei = 0;
while( i < a.size() && j < b.size() )
{
c = IntToChar( ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) % 10 ) + c;
jinwei = ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) / 10;
j--;i--;
}
while( j < b.size()  )
{
c =  IntToChar( ( CharToNumber(b[j]) + jinwei ) % 10 ) + c;
jinwei = ( jinwei + CharToNumber(b[j]) ) / 10;
j--;
}
while( i < a.size() )
{
c =  IntToChar( ( CharToNumber(a[i]) + jinwei ) % 10 ) + c;
jinwei = ( jinwei + CharToNumber(a[i]) ) / 10;
i--;
}
if( jinwei )
c = IntToChar(  jinwei  ) + c;
Standardization(c);
return c;
}

// make char to the int number
static int CharToNumber(char c)
{
if( c >= '0' && c <= '9' )
return int(c - '0');
else
{
cout<<c<<" exception of input CharToNumber "<<endl;
system("pause");
return 0;
}
}

// make int to the model char
static string IntToChar(int i)
{
if( i >= 0 && i <= 9 )
{
string c = "";
return c+char(i+48);
}
else
{
cout<<i<<" exception of input IntToChar"<<endl;
system("pause");
return "e";
}
}

// check whether the string is legal
static bool check_all_number(string a)
{
if(a.empty())
return true ;
string::size_type L = a.size(),i = 0;
if(a[0] == '-')
i++;
while( i < L )
{
if( a[i] < '0' || a[i] > '9')
return false;
i++;
}
return true ;
}

// compare string a and b
static char Compare(string a,string b)
{
if(a.empty() || b.empty())
{
cout<<"error of input compare";
return 'e';
}
else
{

if(!check_all_number(a) || !check_all_number(b))
{
return 'e';
}
Standardization(a);
Standardization(b);
if(a[0] == '-' && b[0] != '-')
return '<';
else if( a[0] != '-' && b[0] == '-')
return '>';
bool fushu = (a[0] == '-');

if(a.size() > b.size() )
return fushu?'<':'>';
else if(a.size() == b.size())
{
for(string::size_type i = 0;i < a.size(); i++)
{
if(a[i] > b[i])
return fushu?'<':'>';
if(a[i] < b[i])
return fushu?'>':'<';
}
return '=';
}
return fushu?'>':'<';
}
}

// make string into standard number
static void Standardization(string &a)
{
if(!check_all_number(a))
{
cout<<a<<" exception of input Standardization"<<endl;
}
string::size_type i = 0;
bool fushu = false ;
if( a[0] == '-' )
{
fushu = true;
i = 1;
}
while(i < a.size())
{
if(a[i] != '0')
break;
i++;
}
if(i == a.size())
i--;
a = a.substr(i,a.size());
if( fushu && a != "0")
a = '-' + a;
}

};

// function: test for string
std::pair<bool,int> test_for_string(string W,string X);
// function: X and W
string W_and_X(string W,string X);

// function: main
int main()
{
string a,b;
cout<<"please input w and x"<<endl;

while(cin>>a>>b)
{

cout<<"result= "<<W_and_X(a,b)+"\n";
}

system("pause");
return 0;
}

// function: X and W
string W_and_X(string W,string X)
{
std::pair<bool,int> r = test_for_string(W,X);
if( r.first )
{
stack<char> * S = new stack<char>;
char fuhao = '=';
string result;
for(size_t i = 0;i<W.length();i++)
{
if(W[i] < X[i])
{
fuhao = '<';
break ;
}
else if(W[i] > X[i] )
{
if(W[i] != 63)
{
fuhao = '>';
break ;
}
else
{
S -> push(X[i]) ;
}
}
}
size_t length = S->size();

if(fuhao == '<')
{
string N = String::Int_To_String(r.second - S->size());
string result_houmian = String::Pow_Int("10",N);
string result_qianmian ="";
char now ;
while(! S->empty() )
{
now = S->top();
S->pop();
result_qianmian = String::Int_To_String( 9 - String::CharToNumber(now) ) + result_qianmian;
}
if(!result_qianmian.empty())
result = String::MULT_Int(result_qianmian,result_houmian);
else return "0";
String::Standardization(result);
return result;
}
else if(fuhao == '>')
{
string N = String::Int_To_String(r.second - S->size());
string result_houmian = String::Pow_Int("10",N);

string result_qianmian ="";
char now ;
while(! S->empty() )
{
now = S->top();
S->pop();
result_qianmian = String::Int_To_String( 9 - String::CharToNumber(now)+1 ) + result_qianmian;
}
if(!result_qianmian.empty())
result = String::MULT_Int(result_qianmian,result_houmian);
else result = result_houmian;
String::Standardization(result);
return result;
}
else if(! S->empty())
{
string N = String::Int_To_String(r.second - S->size());
string result ="";
char now ;
while(! S->empty() )
{
now = S->top();
S->pop();
result = String::Int_To_String( 9 - String::CharToNumber(now) ) + result;
}
String::Standardization(result);
return result;
}
}
return string("0");
}

// function: test for string
std::pair<bool,int> test_for_string(string W,string X)
{
if(W.length() != X.length())
return std::make_pair(false,0);
int n = 0;
if(W.length() > 0)
{
for(size_t i =0;i<W.length();i++)
{
if(    !((W[i] <= 57 && W[i] >= 48) || W[i] == 63 ) )
{
return std::make_pair(false,0);
}
if( W[i] == 63 )
n++;
}
}
if(X.length() > 0)
{
for(size_t i=0;i<X.length();i++)
{
if( X[i] > 57 || X[i] < 48 )
{
return std::make_pair(false,0);
}
}
}
return std::make_pair(true,n);
}