Sicily 1029 Rabbit(高精度运算+公式递推)

//高精度运算+公式递推
//当m = 1时，ans = 2^d;
//当m > 1时，f[1] = 1,f[2] = 2....f[m] = m,f[m+1] = f[m] + f[1]......f
= f[n-1] + f[n-m];
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
using namespace std;
struct Bigint
{
string num;
Bigint(int n)
{
while(n != 0)
{
num.push_back(n % 10 + '0');
n /= 10;
}
reverse(num.begin(),num.end());
}
};
int compare(string a,string b)
{
if(a.size() > b.size())	return 1;
else if(a.size() < b.size()) return -1;
else	return a.compare(b);
}
string add(string num1,string num2)
{
int len = max(num1.size(),num2.size()) + 1;
string ans;
ans.assign(len,0);
reverse(num1.begin(),num1.end());
reverse(num2.begin(),num2.end());
num1.append(len-num1.size(),'0');
num2.append(len-num2.size(),'0');

for(int i = 0;i < len;++i)
{
ans[i] += num1[i]-'0' + num2[i]-'0';
ans[i+1] += ans[i]/10;
ans[i] %= 10;
ans[i] += '0';
}
while(ans[len-1] == '0' && ans.size() != 1)//除去前导零，当两个数相等时，保留0
{
ans.erase(len-1,1);
len--;
}
reverse(ans.begin(),ans.end());
return ans;
}
string multiply(string num1,string num2)
{
int len = num1.size() + num2.size();
string ans;
ans.assign(len,0);
reverse(num1.begin(),num1.end());
reverse(num2.begin(),num2.end());
for(int i = 0;i < num2.size();++i)
{
for(int j = 0;j < num1.size();++j)
{
ans[i+j] += (num2[i]-'0') * (num1[j]-'0');
ans[i+j+1] += ans[i+j] / 10;
ans[i+j] %= 10;
}
}
for(int i = 0;i < len;++i)	ans[i] += '0';
while(ans[len-1] == '0' && ans.size() != 1)//除去前导零，当两个数相等时，保留0
{
ans.erase(len-1,1);
len--;
}
reverse(ans.begin(),ans.end());
return ans;
}
int main()
{
int m,d;
while(cin >> m >> d && m != 0)
{
if(m == 1)
{
Bigint ans(1);
Bigint factor(2);
for(int i = 1;i <= d;++i)
{
ans.num = multiply(ans.num,factor.num);
}
cout << ans.num<< endl;
}
else
{
vector<string> v;
for(int i = 1;i <= m;++i)
{
Bigint a(i);
v.push_back(a.num);
}
for(int i = 0;i <= 100;++i)
{
if(v.size() > d)	break;
v.push_back(add(v[i],v[i+m-1]));
}
cout << v[d] << endl;
}
}
return 0;
}