- Related Questions & Answers
- Add minimum number to an array so that the sum becomes even in C programming
- C Program for Tower of Hanoi
- C++ Program for Dijkstra’s shortest path algorithm?
- C Program to Multiply two Floating Point Numbers?
- C program to find the length of a string?
- C Program to Check if all digits of a number divide it
- C Program to Check if a Given String is a Palindrome?
- Concatenate a string given number of times in C++ programming
- Write a program to Delete a Tree in C programming
- Write a C program to print “ Tutorials Point ” without using a semicolon
- Superperfect Number in C programming
- Sum of the nodes of a Singly Linked List in C Program
- Sum of first n natural numbers in C Program
- HTML DOM Input Number value Property
- HTML DOM Input Number type Property

Catalan numbers are a sequence of numbers. Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

C

_{n}is the number of Dyck words of length 2n. A Dyck word is a string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's. For example, the following are the Dyck words of length 6

XXXYYY XYXXYY XYXYXY XXYYXY XXYXYY.

Re-interpreting the symbol X as an open parenthesis and Y as a close parenthesis, C

_{n}counts the number of expressions containing n pairs of parentheses which are correctly matched

((())) ()(()) ()()() (())() (()())

C

_{n}is the number of different ways n + 1 factors can be completely parenthesized (or the number of ways of associating n applications of a binary operator). For n = 3, for example, we have the following five different parenthesizations of four factors:

((ab)c)d (a(bc))d (ab)(cd) a((bc)d) a(b(cd))

Successive applications of a binary operator can be represented in terms of a full binary tree. (A rooted binary tree is full if every vertex has either two children or no children.) It follows that C

_{n}is the number of full binary trees with n + 1 leaves:

**Input** - 6**Output **- 1 1 2 5 14 42

Explanation

The first Catalan numbers for n = 0, 1, 2, 3,4,5,6,7,8,9,10, ... are

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862,

#include<iostream> using namespace std; long int catalan( int n) { if (n <= 1){ return 1; } long int result = 0; for (int i=0; i<n; i++){ result += catalan(i)*catalan(n-i-1); } return result; } int main(){ for (int i=0; i<6; i++) cout << catalan(i) << " "; return 0; }

1 1 2 5 14 42

Advertisements