The Program in C++Program to Display First 10 Catalan Numbers is given below:
#include <iostream>
#include <cmath>
using namespace std;
unsigned long long binomialCoeff(unsigned int n, unsigned int k)
{
unsigned long long res = 1;
// Since C(n, k) = C(n, n-k)
if (k > n - k)
k = n - k;
// Calculate value of [n*(n-1)*---
// *(n-k+1)] / [k*(k-1)*---*1]
for (int i = 0; i < k; ++i)
{
res *= (n - i);
res /= (i + 1);
}
return res;
}
unsigned long long catalan(unsigned int n)
{
// Calculate value of 2nCn
unsigned long long c = binomialCoeff(2*n, n);
// return 2nCn/(n+1)
return c/(n+1);
}
int main()
{
for (int i = 0; i < 10; i++)
cout << catalan(i) << " ";
return 0;
}
Output:
1 1 2 5 14 42 132 429 1430 4862
Pro-Tips💡
The binomialCoeff function calculates the binomial coefficient, which is used in the calculation of Catalan numbers.
The function uses a loop to perform the calculation and returns the result.
The catalan function uses the binomialCoeff function to calculate the Catalan number and returns the result.
The calculation is performed by dividing the binomial coefficient by n + 1.
The main function loops through the first 10 numbers and prints the result of calling the catalan function for each number.
The output is the first 10 Catalan numbers.
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