mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-02-03 18:46:50 +08:00
83 lines
2.4 KiB
C++
83 lines
2.4 KiB
C++
/**
|
|
* @file
|
|
* @brief 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/
|
|
*/
|
|
|
|
#include <cassert> /// for assert
|
|
#include <cstdint> /// for std::uint64_t
|
|
#include <cstdlib> /// for std::size_t
|
|
#include <functional> /// for std::plus & std::multiplies
|
|
#include <numeric> /// for std::transform_reduce
|
|
#include <vector> /// for std::vector
|
|
|
|
/**
|
|
* @brief computes and caches Catalan numbers
|
|
*/
|
|
class catalan_numbers {
|
|
using value_type = std::uint64_t;
|
|
std::vector<value_type> known{1, 1};
|
|
|
|
value_type compute_next() {
|
|
return std::transform_reduce(known.begin(), known.end(), known.rbegin(),
|
|
static_cast<value_type>(0), std::plus<>(),
|
|
std::multiplies<>());
|
|
}
|
|
|
|
void add() { known.push_back(this->compute_next()); }
|
|
|
|
public:
|
|
/**
|
|
* @brief computes the n-th Catalan number and updates the cache.
|
|
* @return the n-th Catalan number
|
|
*/
|
|
value_type get(std::size_t n) {
|
|
while (known.size() <= n) {
|
|
this->add();
|
|
}
|
|
return known[n];
|
|
}
|
|
};
|
|
|
|
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);
|
|
}
|
|
|
|
void test_catalan_numbers_25() {
|
|
// data verified with https://oeis.org/A000108/
|
|
catalan_numbers cn;
|
|
assert(cn.get(25) == 4861946401452ULL);
|
|
}
|
|
|
|
int main() {
|
|
test_catalan_numbers_up_to_20();
|
|
test_catalan_numbers_25();
|
|
}
|