FindMissingBinom, C++ (gcc)

FindMissingBinom

//g++  7.4.0
//Interpolation: Binomial Expansion Method
//code is created by Rezaul Hoque on January 12,2021
//please contact at jewelmrh@yahoo.com
// if x advances by equal interval and corresponding x value for the value of y to be interpolated is one of the class limits of x series then binomial expansion method is suitable for interpolation
 #include <iostream>
using namespace std;

int main()
{
int n=6;
int x[n]={1982,1983,1984,1985,1986,1987};
int y[n]={150,235,365,000,525,780};
//Detecting the missing value 
for (int i=0; i<n; i++)
if(y[i]==000) cout<<"The missing value is at "<<i<<endl;

//Since number of known value is 5, leading 5 differences will be zero.
// Based on y[i]-i*y[i-1]+(i*(i-1)*y[i-2])/factorial (2)-(i*(i-1)*(i-2)*y[i-3])/factorial(3)+(i*(i-1)*(i-2)*(i-3)*y[i-4])/factorial(4)-(i*(i-1)*(i-2)*(i-3)*(i-4)*y[i-5])/factorial(5)+(i-1)*(i-2)*(i-3)*(i-4)*(i-5)*y[i-6])/factorial(6);
//

//  So y[5]-5*y[4]+10*y[3]-10*y[2]+5*y[1]-y[0]=0;
y[3]=(y[0]-5*y[1]+10*y[2]+5*y[4]-y[5])/10;
 cout<<"The missing value is :\t"<<y[3];
return 0;
}


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