begin
clrscr;
writeln('N = ', n);
{}
for i := 0 to n do
begin
write('x[', i, '] := ');
readln(x[i]);
write('y[', i, '] := ');
readln(y[i]);
writeln;
end;
write('Vvedite X: ');
readln(Xx); {Xx - tochka gde nado naiti znachenie S(x)}
{/} {sdelali vvod elementov}

for i := 1 to n do {nahodim shagi mezhdu x[i]}
h[i] := x[i] - x[i - 1];

for i := 1 to n - 1 do {nahodim vektor F, A*X = F}
F[i] := 6 * ( (y[i+1] - y[i])/h[i+1] - (y[i] - y[i-1])/h[i] );

{}
for i := 1 to n - 1 do
_b[i] := 2 * (h[i] + h[i+1]);

for i := 1 to n - 2 do
_c[i] := - h[i + 1];

for i := 1 to n - 2 do
_a[i] := - h[i];
{/} {zapolnili linii treh diagonalei}

{}
alpha[1] := _c[1] / _b[1];
betta[1] := F[1] / _b[1];
for i := 2 to n - 1 do
begin
alpha[i] := _c[i] / (_b[i] - _a[i] * alpha[i - 1]);
betta[i] := (F[i] + _a[i] * betta[i - 1]) /
(_b[i] - _a[i] * alpha[i - 1]);
end;
{/} {pryamoi hod}

{}
C[n] := 0;
for i := n - 1 downto 1 do
C[i] := alpha[i] * C[i + 1] + betta[i];
{/} {obratnii hod}

for i := 1 to n do {nashli nomer (i) otrezka, gde nahoditsya Xx}
if x[i] >= Xx then break;
{}
d := (c[i] - c[i - 1]) / h[i]; {vichislyaem po formulam koeff}
b := h[i]*C[i]/2 - h[i]*h[i]*d/6 + (y[i] - y[i-1])/h[i];

spl := y[i] + b*(Xx-x[i]) + (C[i]*sqr(Xx-x[i]))/2 +
d*(sqr(Xx-x[i]))*(Xx-x[i])/6; {sam mnogochlen kubich. splaina}

writeln('S(x) = ', spl:3:4);
{/} {formula splaina}

readkey;
end.

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