# Lobb Number in C++

In this article, we will learn about Lobb Numbers and how to find Lobb Number of m,n in C++.

## What is Lobb Number?

Lobb number (Lm,n) calculates the number of ways that n+m open parentheses and n-m close parentheses can be positioned to form the start of a valid sequence of balanced parentheses. Lobb number is defined by two non-negative integers m and n, where n ≥ m ≥ 0. (m, n)th Lobb number is given by the equation.

## Lobb Number in C++

1. Create a function binomialCoeff to calculate the binomial coefficient(2*n, m+n).

2. Now Directly apply the formula ((2*m+1) * binomialCoeff(2*n, m+n))/(m+n+1);

#include <bits/stdc++.h> using namespace std; int binomialCoeff(int n, int k){ int coeff[n+1][k+1]; for (int i=0;i<=n;i++){ for (int j =0;j<=min(i, k);j++){ if (j == 0 || j == i) coeff[i][j] = 1; else coeff[i][j] = coeff[i-1][j-1] + coeff[i-1][j]; } } return coeff[n][k]; } int lobb_number(int n, int m){ return ((2*m+1) * binomialCoeff(2*n, m+n))/(m+n+1); } int main(){ int m, n; cout<<"Enter the n value: "; cin>>n; cout<<"Enter the m value: "; cin>>m; cout<<lobb_number(n, m)<<endl; return 0; }

Output

Enter the n value: 6 Enter the m value: 4 54 Enter the n value: 10 Enter the m value: 5 10659

Also, read

## Leave a Reply