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f = fopen('CubicSpline_in.txt', 'r');
n = fscanf(f, '%d', 1);
n = n-1;

x = zeros(1,n+1);
y = zeros(1,n+1);

for i=1:n+1
    x(i) = fscanf(f, '%f', 1);
    y(i) = fscanf(f, '%f', 1);
end

fclose(f);

a = y;
h = x(2:n+1)-x(1:n);

A = zeros(n+1,n+1);
rhs = zeros(n+1,1);
A(1,1)=1; A(n+1,n+1)=1;
for i=2:n
    A(i,i)=2*(h(i-1)+h(i));
    A(i,i-1)=h(i-1);
    A(i,i+1)=h(i);
    rhs(i)=3/h(i) * (a(i+1)-a(i)) - 3/h(i-1) * (a(i)-a(i-1));
end

c = (A \ rhs)';
b = zeros(1,n);
d = zeros(1,n);

for i=1:n
    b(i)=(a(i+1)-a(i))/h(i) - (2*c(i)+c(i+1))/3 * h(i);
    d(i)=(c(i+1)-c(i))/3/h(i);
end

coefs = [a(1:n);b;c(1:n);d]';
for i=1:n
    fprintf("%f ",coefs(i,:))
    fprintf("\n");
end

nPoints = 30;
colors = ['k','b','r','c','m'];
figure
hold on
for ind=1:n
    tx = x(ind):((x(ind+1)-x(ind))/nPoints):x(ind+1);
    tx = tx-x(ind);
    ty = d(ind)*tx.^3 + c(ind)*tx.^2 + b(ind)*tx + a(ind);
   
    plot(tx+x(ind), ty, colors(1+mod(ind, length(colors))))
    scatter(x, y, '.k')
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        Backtrace
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