main.cpp

#include <iostream>
#include "main.h"

using std::cin;
using std::cout;


// Global Variables
int d;
double xi, * fi, h;


int main() {
  char s[256];
  int i;
  double x;

  cout << "Number of cases: ";
  cin >> d;
  fi = new double[d];
  d--;

  cout << "\nEnter x0: ";
  cin >> xi;
  cout << "Enter h: ";
  cin >> h;
  cout << "\n";
  for (i = 0; i <= d; i++) {
    cout << "Enter f" << i << ": ";
    cin >> fi[i];
  }
  while (1) {
    cout << "\nFind f(x) at x: ";
    cin >> x;
    cout << "f(" << x << ") = " << p(x) << "\n";
    cout << "Stop? ";
    cin >> s;
    if (s[0] == 'y' || s[0] == 'Y')break;
  }

  delete fi;
  return 0;
}


double f(int j, double k) {
  if (j > 0) return f(j-1, k+0.5) - f(j-1, k-0.5);
  return fi[d/2 + (int)k];
}


double p(double x) {
  int i;
  double k, kstart;
  double r, fc = 0, fp = 1, a = 1, ans = 0;

  kstart = d - (d / 2);
  r = (x - (xi + d * h)) / h;
  for (i = 0, k = kstart; i <= d; i++, k -= 0.5) {
    ans += a * f(i, k) / fp;
    a *= r;
    r++;
    fc++;
    fp *= fc;
  }
  return ans;
}