69 lines
2.1 KiB
Ada
69 lines
2.1 KiB
Ada
with Ada.Text_IO; use Ada.Text_IO;
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procedure Pyramid_of_Numbers is
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B_X, B_Y, B_Z : Integer := 0; -- Unknown variables
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type Block_Value is record
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Known : Integer := 0;
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X, Y, Z : Integer := 0;
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end record;
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X : constant Block_Value := (0, 1, 0, 0);
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Y : constant Block_Value := (0, 0, 1, 0);
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Z : constant Block_Value := (0, 0, 0, 1);
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procedure Add (L : in out Block_Value; R : Block_Value) is
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begin -- Symbolically adds one block to another
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L.Known := L.Known + R.Known;
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L.X := L.X + R.X - R.Z; -- Z is excluded as n(Y - X - Z) = 0
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L.Y := L.Y + R.Y + R.Z;
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end Add;
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procedure Add (L : in out Block_Value; R : Integer) is
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begin -- Symbolically adds a value to the block
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L.Known := L.Known + R;
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end Add;
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function Image (N : Block_Value) return String is
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begin -- The block value, when X,Y,Z are known
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return Integer'Image (N.Known + N.X * B_X + N.Y * B_Y + N.Z * B_Z);
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end Image;
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procedure Solve_2x2 (A11, A12, B1, A21, A22, B2 : Integer) is
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begin -- Don't care about things, supposing an integer solution exists
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if A22 = 0 then
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B_X := B2 / A21;
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B_Y := (B1 - A11*B_X) / A12;
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else
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B_X := (B1*A22 - B2*A12) / (A11*A22 - A21*A12);
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B_Y := (B1 - A11*B_X) / A12;
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end if;
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B_Z := B_Y - B_X;
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end Solve_2x2;
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B : array (1..5, 1..5) of Block_Value; -- The lower triangle contains blocks
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begin
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-- The bottom blocks
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Add (B(5,1),X); Add (B(5,2),11); Add (B(5,3),Y); Add (B(5,4),4); Add (B(5,5),Z);
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-- Upward run
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for Row in reverse 1..4 loop
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for Column in 1..Row loop
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Add (B (Row, Column), B (Row + 1, Column));
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Add (B (Row, Column), B (Row + 1, Column + 1));
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end loop;
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end loop;
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-- Now have known blocks 40=(3,1), 151=(1,1) and Y=X+Z to determine X,Y,Z
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Solve_2x2
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( B(1,1).X, B(1,1).Y, 151 - B(1,1).Known,
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B(3,1).X, B(3,1).Y, 40 - B(3,1).Known
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);
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-- Print the results
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for Row in 1..5 loop
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New_Line;
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for Column in 1..Row loop
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Put (Image (B(Row,Column)));
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end loop;
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end loop;
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end Pyramid_of_Numbers;
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