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: 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:
= = = 20
Below is the implementation of the above approach:
C++
#include<bits/stdc++.h>
using namespace std;
int binomialCoeff( int n, int k)
{
int C[n + 1][k + 1];
int i, j;
for (i = 0; i <= n; i++)
{
for (j = 0; j <= min(i, k); j++)
{
if (j == 0 || j == i)
C[i][j] = 1;
else
C[i][j] = C[i - 1][j - 1] +
C[i - 1][j];
}
}
return C[n][k];
}
int main()
{
int n = 3;
int k = n;
n = 2*n;
cout << binomialCoeff(n, k);
}
|
Java
class GFG{
static int binomialCoeff( int n, int k)
{
int [][] C = new int [n + 1 ][k + 1 ];
int i, j;
for (i = 0 ; i <= n; i++)
{
for (j = 0 ; j <= Math.min(i, k); j++)
{
if (j == 0 || j == i)
C[i][j] = 1 ;
else
C[i][j] = C[i - 1 ][j - 1 ] +
C[i - 1 ][j];
}
}
return C[n][k];
}
public static void main(String[] args)
{
int n = 3 ;
int k = n;
n = 2 * n;
System.out.println(binomialCoeff(n, k));
}
}
|
Python3
def binomialCoeff(n, k):
C = [[ 0 for j in range (k + 1 )]
for i in range (n + 1 )]
i = 0
j = 0
for i in range (n + 1 ):
for j in range ( min (i, k) + 1 ):
if j = = 0 or j = = i:
C[i][j] = 1
else :
C[i][j] = (C[i - 1 ][j - 1 ] +
C[i - 1 ][j])
return C[n][k]
if __name__ = = '__main__' :
n = 3
k = n
n = 2 * n
print (binomialCoeff(n, k))
|
C#
using System;
class GFG{
static int binomialCoeff( int n, int k)
{
int [,]C = new int [n + 1, k + 1];
int i, j;
for (i = 0; i <= n; i++)
{
for (j = 0; j <= Math.Min(i, k); j++)
{
if (j == 0 || j == i)
C[i, j] = 1;
else
C[i, j] = C[i - 1, j - 1] +
C[i - 1, j];
}
}
return C[n, k];
}
public static void Main()
{
int n = 3;
int k = n;
n = 2 * n;
Console.Write(binomialCoeff(n, k));
}
}
|
Javascript
<script>
function binomialCoeff(n, k)
{
var C = Array.from(Array(n+1),()=> Array(k+1));
var i, j;
for (i = 0; i <= n; i++)
{
for (j = 0; j <= Math.min(i, k); j++)
{
if (j == 0 || j == i)
C[i][j] = 1;
else
C[i][j] = C[i - 1][j - 1] +
C[i - 1][j];
}
}
return C[n][k];
}
var n = 3;
var k = n;
n = 2*n;
document.write( binomialCoeff(n, k));
</script>
|
Time Complexity: O(N * K)
Auxiliary Space: O(N * K)
Like Article
Suggest improvement
Share your thoughts in the comments
Please Login to comment...