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: 6
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:
Below is the implementation of the above approach:
C++
// C++ implementation to find the // Nth Central Binomial Coefficient#include<bits/stdc++.h> using 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 Code int 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 Code public 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 Code public 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
<script>// Javascript implementation to find the // Nth Central Binomial Coefficient// Function to find the value of // Nth Central Binomial Coefficientfunction binomialCoeff(n, k) { var C = Array.from(Array(n+1),()=> Array(k+1)); var 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 Code var n = 3;var k = n;n = 2*n;document.write( binomialCoeff(n, k)); </script> |
Output:
20
Time Complexity: O(N * K)
Auxiliary Space: O(N * K)
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