Related Articles

# Central binomial coefficient

• Last Updated : 28 Jun, 2021

Given an integer N, the task is to find the Central binomial coefficient
The first few Central binomial coefficients for N = 0, 1, 2, 3… are

1, 2, 6, 20, 70, 252, 924, 3432…..

Examples:

Input: N = 3
Output: 20
Explanation: Central Binomial Coefficient =   = 20
Input: N = 2
Output:

Approach: The central binomial coefficient is a binomial coefficient of the form . The Binomial Coefficient can be computed using this approach for a given value N using Dynamic Programming.
For Example:

Central binomial coefficient of N = 3 is given by:   = 20

Below is the implementation of the above approach:

## C++

 // C++ implementation to find the// Nth Central Binomial Coefficient #includeusing namespace std; // Function to find the value of// Nth Central Binomial Coefficientint binomialCoeff(int n, int k){    int C[n + 1][k + 1];    int i, j;     // Calculate value of Binomial    // Coefficient in bottom up manner    for (i = 0; i <= n; i++)    {        for (j = 0; j <= min(i, k); j++)        {            // Base Cases            if (j == 0 || j == i)                C[i][j] = 1;             // Calculate value            // using previously            // stored values            else                C[i][j] = C[i - 1][j - 1] +                        C[i - 1][j];        }    }     return C[n][k];} // Driver Codeint main(){    int n = 3;    int k = n;    n = 2*n;    cout << binomialCoeff(n, k);}

## Java

 // Java implementation to find the// Nth Central Binomial Coefficientclass GFG{     // Function to find the value of// Nth Central Binomial Coefficientstatic int binomialCoeff(int n, int k){    int[][] C = new int[n + 1][k + 1];    int i, j;     // Calculate value of Binomial    // Coefficient in bottom up manner    for(i = 0; i <= n; i++)    {       for(j = 0; j <= Math.min(i, k); j++)       {                      // Base Cases          if (j == 0 || j == i)              C[i][j] = 1;                     // Calculate value          // using previously          // stored values          else              C[i][j] = C[i - 1][j - 1] +                        C[i - 1][j];       }    }    return C[n][k];} // Driver Codepublic static void main(String[] args){    int n = 3;    int k = n;    n = 2 * n;         System.out.println(binomialCoeff(n, k));}} // This code is contributed by Ritik Bansal

## Python3

 # C# implementation to find the# Nth Central Binomial Coefficient # Function to find the value of# Nth Central Binomial Coefficientdef binomialCoeff(n, k):         C = [[0 for j in range(k + 1)]            for i in range(n + 1)]         i = 0    j = 0         # Calculate value of Binomial    # Coefficient in bottom up manner    for i in range(n + 1):        for j in range(min(i, k) + 1):                         # Base Cases            if j == 0 or j == i:                C[i][j] = 1                             # Calculate value            # using previously            # stored values            else:                C[i][j] = (C[i - 1][j - 1] +                           C[i - 1][j])         return C[n][k]     # Driver codeif __name__=='__main__':         n = 3    k = n    n = 2 * n         print(binomialCoeff(n, k))         # This code is contributed by rutvik_56

## C#

 // C# implementation to find the// Nth Central Binomial Coefficientusing System;class GFG{     // Function to find the value of// Nth Central Binomial Coefficientstatic int binomialCoeff(int n, int k){    int [,]C = new int[n + 1, k + 1];    int i, j;     // Calculate value of Binomial    // Coefficient in bottom up manner    for(i = 0; i <= n; i++)    {       for(j = 0; j <= Math.Min(i, k); j++)       {                      // Base Cases          if (j == 0 || j == i)              C[i, j] = 1;                         // Calculate value          // using previously          // stored values          else              C[i, j] = C[i - 1, j - 1] +                        C[i - 1, j];       }    }    return C[n, k];} // Driver Codepublic static void Main(){    int n = 3;    int k = n;    n = 2 * n;         Console.Write(binomialCoeff(n, k));}} // This code is contributed by Code_Mech

## Javascript

 
Output:
20

Time Complexity: O(N * K)
Auxiliary Space: O(N * K)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up