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Catalan_number.cpp
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Catalan_number.cpp
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#include<bits/stdc++.h>
#define ll long long
#define mxn 103
using namespace std;
vector<string> ctl;
char InToCha(int n){
return char(n + '0');
}
int ChaToIn(char c){
return c - '0';
}
void chuanHoa(string &a,string &b){
int l1 = a.size(),l2 = b.size();
if(l1<l2){
a.insert(0,l2-l1,'0');
}
else
b.insert(0,l1-l2,'0');
}
string cong(string a,string b){
string res = "";
chuanHoa(a,b);
int temp = 0;
for(int i=a.size()-1;i>=0;i--){
int so = ChaToIn(a[i])+ChaToIn(b[i])+temp;
temp = so/10;
res.insert(0,1,InToCha(so%10));
}
if(temp>0)
res.insert(0,1,InToCha(temp));
return res;
}
string nhanNho(string a,char b){
string res = "";
int c = ChaToIn(b);
int temp = 0;
for(int i=a.size()-1;i>=0;i--){
int so = ChaToIn(a[i])*c + temp;
temp = so/10;
res.insert(0,1,InToCha(so%10));
}
if(temp>0)
res.insert(0,1,InToCha(temp));
return res;
}
string nhanLon(string a,string b){
string res = "";
int l = b.size();
string str[l];
for(int i=l-1;i>=0;i--){
str[i] = nhanNho(a,b[i]);
str[i].insert(str[i].size(),l-i-1,'0');
res = cong(res,str[i]);
}
return res;
}
void init(){
ctl.resize(mxn,"0");
ctl[0] = ctl[1] = "1";
for(int i=2;i<mxn;i++){
string rs = "0";
for(int j=0;j<i;j++) ctl[i] = cong(nhanLon(ctl[j],ctl[i-j]),ctl[i]);
}
}
int main(){
init();
int t;
cin>>t;
while(t--){
int n;
cin>>n;
cout<<ctl[n+1]<<endl;
}
}