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part 2
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src/day9/part2.pas
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120
src/day9/part2.pas
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program day9part1;
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{$INCLUDE 'polynomial.pas'}
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function lagrange(x, y: array of int64; l: int64 = 0): polynomial;
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var
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new: polynomial;
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idx: int64;
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i: int64;
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begin
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lagrange := constant(c_fraction(0, 1));
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if l = 0 then
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begin
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case length(x) > length(y) of
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true: l := length(y);
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false: l := length(x);
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end;
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end;
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for idx := 0 to l - 1 do
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begin
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new := constant(c_fraction((y[idx]), 1));
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for i := 0 to l - 1 do
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begin
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if i = idx then
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continue;
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new := new * binomial(c_fraction(1, 1), c_fraction(- x[i], 1));
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new := new * constant(c_fraction(1, (x[idx] - x[i])));
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end;
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lagrange := lagrange + new;
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end;
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end;
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var
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{ couldn't have done that with a for loop }
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x: array[0..100] of int64 = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100);
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y: array[0..100] of int64;
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file_: text;
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str: string;
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negative, number: int64;
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c: char;
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count, b: int64;
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sum: fraction;
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p: polynomial;
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f: fraction;
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begin
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assign(file_, 'resources/day9.txt');
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reset(file_);
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sum := c_fraction(0, 1);
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while not EOF(file_) do
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begin
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readln(file_, str);
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count := 0;
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number := 0;
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negative := 1;
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for c in str do
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begin
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if c = '-' then
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negative := -1
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else if (('0' <= c) and (c <= '9')) then
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begin
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//add number to number
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val(c, b);
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number := number * 10 + b;
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end
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else
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begin
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y[count] := number * negative;
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count := count + 1;
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number := 0;
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negative := 1;
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end;
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end;
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y[count] := number * negative;
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p := simplify_poly(lagrange(x, y, count + 1));
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print_polynomial(p);
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write(' at ');
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write(-1);
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write(' is ');
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f := simplify(eval_polynomial(p, -1));
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print_fraction(f);
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sum := sum + f;
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writeln();
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end;
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write('The final sum is: ');
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print_fraction(sum);
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end.
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