/* This program tries to guess the next number of a sequence given by the user using newton's forward difference formula. =============== NOTE:- The resulting solution may not appear to be satisfying to you, but would be mathematically logical --------------- INTPUT INSTRUCTIONS :- Enter first few digits of the sequence ( the more digits you input, more time the program will take to calculate the next number) SAMPLE INPUT :- 1 2 3 4 5 6 */ #include #include //////////// function declarations int newton_fwd_difference(std::vector); /////////// utility functions std::vector input(); int factorial(int); void display(std::vector &,int); //////////// The main() function int main() { std::vector v = input(); display(v,newton_fwd_difference(v)); } /////////// function definations int newton_fwd_difference(std::vector y) { int p = (y.size()+1)-y[0]; int res = y[0]; int counter = 0; while(y.size() > 1) { std::vector del_y; counter ++; for (long unsigned int i = 1; i < y.size(); ++i) { del_y.push_back(y[i]-y[i-1]); } y = del_y; int temp = 1; for (int i = 0; i < counter; ++i) { temp *= (p - i); } res += (temp*(y[0]/factorial(counter))); } return res; } std::vector input() { std::vector v; int ele; while(std::cin>>ele) { v.push_back(ele); } return v; } int factorial(int n) { int fact = 1; while(n > 0) { fact *= n; n--; } return fact; } void display(std::vector &v,int res) { std::cout<<"the given sequence is:-\n"; for(auto a : v) { std::cout<

Next number in sequence