CATALAN_number.cpp

// catalan number by DP

#include <cstdio>
#include <iomanip>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <algorithm>
#include <string>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <sstream>
#include <stack>
#include <list>
#include <iostream>
#include <assert.h>

/**Define memory set function**/
#define mem(x,y) memset(x,y,sizeof(x))
#define CLEAR(x) memset(x,0,sizeof(x))

/**Define function and object**/
#define pb push_back
#define Sort(v) sort(v.begin(),v.end())
#define _sort(s, n) sort(s, s+n)
#define sqr(x) ((x)*(x))

/**Define constant value**/
#define le 5001
#define ERR 1e-9
#define pi (2*acos(0))
#define PI 3.141592653589793

/**Define input**/
#define scanint(a) scanf("%d",&a)
#define scanLLD(a) scanf("%lld",&a)

typedef unsigned long long ll;

using namespace std;

/**********************End*******************/

ll cnt = 0;

ll catalanDP(int n) {
    ll catalan[n+1];
    catalan[0] = catalan[1] = 1;
    for (int i = 2; i <= n; i++) {
        catalan[i] = 0;
        for (int j = 0; j < i; cnt++, j++)
            catalan[i] += catalan[j] * catalan[i-j-1];
    }
    return catalan[n];
}

int main() {
    for (int i = 0; i < 20; i++)
        cout << catalanDP(i) << " " << cnt << endl;
}