% Lagrange Interpolation

clear all;
clc;

n = input('P(x) grade: ');

for i = 1 : n +1
    fprintf('x(%i): ', i);
    x(i) = input('');
end

for i = 1 : n +1
    fprintf('y(%i): ', i);
    y(i) = input('');
end

xo = input('Aprox. to evaluate: ');
sum = 0;

for i = 1 : n + 1
    prod = 1;

    for j = 1 : n + 1
        if j ~= i
            prod = prod * (xo - x(j))/(x(i) - x(j));
        end
    end

    sum = sum + y(i)*prod;
end

fprintf('R: %f \n', sum);