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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, …., nCr, …., nCn-2, nCn-1, nCn
find the maximum value of nCr.
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
#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
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