Catalan_Triangle_Row — Sequences

Computes the row of the given order in Catalan's triangle.

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View versions (2)

Interface

#include <codecogs/maths/combinatorics/sequences/catalan_triangle_row.h>

using namespace Maths::Combinatorics::Sequences;

std::vector<int> catalan_triangle_row(int n, bool first = true)

The recurrent formula used to generate Catalan's triangle is

$$C(0, 0) = 1 \qquad C(i, 0) = 1 \qquad C(i, j) = 0, \quad \forall i < j$$

(1)

$$C(i, j) = C(i, j - 1) + C(i - 1, j)$$

(2)

The number found at $C(i, i)$ represents the Catalan number of order $i$.

Parameters

the order of the row requested

first

internal flag selecting which code path builds the row; leave this at its default value of true when calling this function directly

Returns

the row of order n in Catalan's triangle, as a standard C++ vector

Example:

#include <codecogs/maths/combinatorics/sequences/catalan_triangle_row.h>
#include <iostream>
int main() {
  std::vector<int> row = Maths::Combinatorics::Sequences::catalan_triangle_row(6);
  std::cout << "Length of row: " << row.size() << std::endl;
  for (int i = 0; i < row.size(); i++)
    std::cout << row[i] << "  ";
  std::cout << std::endl;
  return 0;
}

Output:

Length of row: 7
1  6  20  48  90  132  132

References

SUBSET, a combinatorial functions library created in C++, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html