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.

nCr = 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;
}

Output

If we run the above code it will generate the following output −

Maximum Coefficient: 3