catalan_numbers.cpp File Reference

Provides utilities to compute Catalan numbers using dynamic programming. A Catalan numbers satisfy these recurrence relations: C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1 Read more about Catalan numbers here: https://en.wikipedia.org/wiki/Catalan_number https://oeis.org/A000108/. More...

#include <cassert>
#include <cstdint>
#include <cstdlib>
#include <numeric>
#include <vector>

Include dependency graph for catalan_numbers.cpp:

Classes
class	catalan_numbers
	computes and caches Catalan numbers More...

Functions
void	test_catalan_numbers_up_to_20 ()
void	test_catalan_numbers_25 ()
int	main ()

Detailed Description

Provides utilities to compute Catalan numbers using dynamic programming. A Catalan numbers satisfy these recurrence relations: C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1 Read more about Catalan numbers here: https://en.wikipedia.org/wiki/Catalan_number https://oeis.org/A000108/.

Function Documentation

main()

int main

(

void

)

           {
    test_catalan_numbers_up_to_20();
    test_catalan_numbers_25();
}

test_catalan_numbers_25()

void test_catalan_numbers_25

(

)

                               {
    // data verified with https://oeis.org/A000108/
    catalan_numbers cn;
    assert(cn.get(25) == 4861946401452ULL);
}

test_catalan_numbers_up_to_20()

void test_catalan_numbers_up_to_20

(

)

                                     {
    // data verified with https://oeis.org/A000108/
    catalan_numbers cn;
    assert(cn.get(0) == 1ULL);
    assert(cn.get(1) == 1ULL);
    assert(cn.get(2) == 2ULL);
    assert(cn.get(3) == 5ULL);
    assert(cn.get(4) == 14ULL);
    assert(cn.get(5) == 42ULL);
    assert(cn.get(6) == 132ULL);
    assert(cn.get(7) == 429ULL);
    assert(cn.get(8) == 1430ULL);
    assert(cn.get(9) == 4862ULL);
    assert(cn.get(10) == 16796ULL);
    assert(cn.get(11) == 58786ULL);
    assert(cn.get(12) == 208012ULL);
    assert(cn.get(13) == 742900ULL);
    assert(cn.get(14) == 2674440ULL);
    assert(cn.get(15) == 9694845ULL);
    assert(cn.get(16) == 35357670ULL);
    assert(cn.get(17) == 129644790ULL);
    assert(cn.get(18) == 477638700ULL);
    assert(cn.get(19) == 1767263190ULL);
    assert(cn.get(20) == 6564120420ULL);
}