57 lines
1.1 KiB
ObjectPascal
57 lines
1.1 KiB
ObjectPascal
uses NumLibABC;
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var
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p := Dict((1, 0));
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lvl := Lst(Lst(word(1)));
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function tofraction(s: string): fraction;
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begin
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var period := s.IndexOf('.');
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if period = -1 then result := Frc(s.ToBigInteger)
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else result := Frc(s.Remove(period, 1).ToBigInteger, Power(10bi, s.Length - period - 1));
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end;
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function path(n: word): List<word>;
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begin
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result := new List<word>;
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if n = 0 then exit;
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while not p.ContainsKey(n) do
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begin
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var q := new List<word>;
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foreach var x in lvl[0] do
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foreach var y in path(x) do
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begin
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if (x + y) in p then break;
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p[x + y] := x;
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q.add(x + y);
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end;
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lvl[0] := q;
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end;
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result := path(p[n]) + Lst(n);
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end;
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function treePow(x: real; n: word): Fraction;
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begin
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var frac := tofraction(FloatToStr(x));
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var r := Dict((0, Frc(1)), (1, frac));
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var p := 0;
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foreach var i in path(n) do
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begin
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r[i] := r[i - p] * r[p];
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p := i;
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end;
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result := r[n];
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end;
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procedure showPow(x: real; n: word);
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begin
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writeln(n, ': ', path(n));
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writeln(x, '^', n, ' = ', treePow(x, n), #10);
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end;
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begin
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for var n := 0 to 17 do showPow(2, n);
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showPow(1.1, 81);
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showPow(3, 191);
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end.
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