Maximum binomial coefficient term value in C

We are given with a positive integer ‘N’. We have to find the maximum coefficient term in all binomial coefficients.

The binomial coefficient series is _nC₀, _nC₁, _nC₂, …., _nC_r, …., _nC_n-2, _nC_n-1, _nC_n

find the maximum value of _nC_r.

_nC_r = n! / r! * (n - r)!

Input − N=4

Output − Maximum Coefficient − 6

Explanation − ₄C₀= 1, ₄C₁ = 4, ₄C₂ = 6, ₄C₃ = 4, ₄C₄ = 1

Therefore, the maximum coefficient is 6 in this case.

Input − N=5

Output − Maximum Coefficient − 10

Explanation − ₅C₀= 1, ₅C₁ = 5, ₅C₂ =10, ₅C₃ = 10, ₅C₄ = 5, ₅C₅ = 1

Therefore, the maximum coefficient is 10 in this case.

Approach used in the below program is as follows

We take input from the user for N.
Function maxCoeff(int n) takes one parameter ‘n’ and return the maximum coefficient found so far stored in C[n+1][n+1]
Initialize the min and max variables with 0. ‘min’ is used to traverse the C[][] array and ‘max’ is used to store the maximum coefficient value found.
For loop from i=0 to n is used to initialize the C[][] array.
Now inside another for loop traverse till ‘i’ or ‘n’ whichever is minimum.
If i==j. C[i][j]==1. else C[i][j] = C[i-1][j-1] + C[i-1][j];
Now traverse the whole C[][] again and store maximum coefficient in max.
Return the result.

Example

Live Demo

#include <stdio.h>
int maxCoeff(int n){
   int C[n+1][n+1];
   int max=0,min=0;
   // Calculate value of Binomial Coefficient in
   for (int i = 0; i <= n; i++){
      min=i<n?i:n;
      for (int j = 0; j <= min; j++){
         if (j == 0 || j == i)
            C[i][j] = 1;
         else
            C[i][j] = C[i-1][j-1] + C[i-1][j];
      }
   }
   for (int i = 0; i <= n; i++){
      max = max> C[n][i] ? max: C[n][i];
   }
   return max;
}
int main(){
   int N = 3;
   printf("Maximum Coefficient :%d", maxCoeff(N) );
   return 0;
}