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67
Task/Closest-pair-problem/Ada/closest-pair-problem.adb
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Task/Closest-pair-problem/Ada/closest-pair-problem.adb
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with Ada.Numerics.Generic_Elementary_Functions;
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with Ada.Text_IO;
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procedure Closest is
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package Math is new Ada.Numerics.Generic_Elementary_Functions (Float);
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Dimension : constant := 2;
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type Vector is array (1 .. Dimension) of Float;
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type Matrix is array (Positive range <>) of Vector;
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-- calculate the distance of two points
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function Distance (Left, Right : Vector) return Float is
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Result : Float := 0.0;
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Offset : Natural := 0;
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begin
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loop
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Result := Result + (Left(Left'First + Offset) - Right(Right'First + Offset))**2;
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Offset := Offset + 1;
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exit when Offset >= Left'Length;
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end loop;
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return Math.Sqrt (Result);
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end Distance;
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-- determine the two closest points inside a cloud of vectors
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function Get_Closest_Points (Cloud : Matrix) return Matrix is
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Result : Matrix (1..2);
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Min_Distance : Float;
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begin
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if Cloud'Length(1) < 2 then
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raise Constraint_Error;
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end if;
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Result := (Cloud (Cloud'First), Cloud (Cloud'First + 1));
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Min_Distance := Distance (Cloud (Cloud'First), Cloud (Cloud'First + 1));
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for I in Cloud'First (1) .. Cloud'Last(1) - 1 loop
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for J in I + 1 .. Cloud'Last(1) loop
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if Distance (Cloud (I), Cloud (J)) < Min_Distance then
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Min_Distance := Distance (Cloud (I), Cloud (J));
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Result := (Cloud (I), Cloud (J));
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end if;
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end loop;
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end loop;
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return Result;
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end Get_Closest_Points;
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Test_Cloud : constant Matrix (1 .. 10) := ( (5.0, 9.0), (9.0, 3.0),
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(2.0, 0.0), (8.0, 4.0),
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(7.0, 4.0), (9.0, 10.0),
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(1.0, 9.0), (8.0, 2.0),
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(0.0, 10.0), (9.0, 6.0));
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Closest_Points : Matrix := Get_Closest_Points (Test_Cloud);
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Second_Test : constant Matrix (1 .. 10) := ( (0.654682, 0.925557), (0.409382, 0.619391),
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(0.891663, 0.888594), (0.716629, 0.9962),
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(0.477721, 0.946355), (0.925092, 0.81822),
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(0.624291, 0.142924), (0.211332, 0.221507),
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(0.293786, 0.691701), (0.839186, 0.72826));
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Second_Points : Matrix := Get_Closest_Points (Second_Test);
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begin
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Ada.Text_IO.Put_Line ("Closest Points:");
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Ada.Text_IO.Put_Line ("P1: " & Float'Image (Closest_Points (1) (1)) & " " & Float'Image (Closest_Points (1) (2)));
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Ada.Text_IO.Put_Line ("P2: " & Float'Image (Closest_Points (2) (1)) & " " & Float'Image (Closest_Points (2) (2)));
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Ada.Text_IO.Put_Line ("Distance: " & Float'Image (Distance (Closest_Points (1), Closest_Points (2))));
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Ada.Text_IO.Put_Line ("Closest Points 2:");
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Ada.Text_IO.Put_Line ("P1: " & Float'Image (Second_Points (1) (1)) & " " & Float'Image (Second_Points (1) (2)));
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Ada.Text_IO.Put_Line ("P2: " & Float'Image (Second_Points (2) (1)) & " " & Float'Image (Second_Points (2) (2)));
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Ada.Text_IO.Put_Line ("Distance: " & Float'Image (Distance (Second_Points (1), Second_Points (2))));
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end Closest;
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@ -1,100 +1,90 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">bruteForceClosestPair</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span>
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<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">mind</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dy</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">minp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #0000FF;">{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #0000FF;">{</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
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<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x2</span>
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<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dx</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;"><</span><span style="color: #000000;">mind</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">dy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">y2</span>
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<span style="color: #000000;">dx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dy</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;"><</span><span style="color: #000000;">mind</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">mind</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dx</span>
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<span style="color: #000000;">minp</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mind</span><span style="color: #0000FF;">),</span><span style="color: #000000;">minp</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function bruteForceClosestPair(sequence s)
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atom {x1,y1} = s[1], {x2,y2} = s[2],
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dx = x1-x2, dy = y1-y2,
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mind = dx*dx+dy*dy
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sequence minp = s[1..2]
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for i,si in s to length(s)-1 do
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{x1,y1} = si
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for sj in s from i+1 do
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{x2,y2} = sj
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dx = x1-x2
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dx = dx*dx
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if dx<mind then
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dy = y1-y2
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dx += dy*dy
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if dx<mind then
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{mind,minp} = {dx,{si,sj}}
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end if
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end if
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end for
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end for
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minp = sort(minp) -- (see note below)
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return {sqrt(mind),minp}
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end function
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">testset</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_rnd</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">))</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
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<span style="color: #0000FF;">{</span><span style="color: #004080;">atom</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">points</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bruteForceClosestPair</span><span style="color: #0000FF;">(</span><span style="color: #000000;">testset</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- (Sorting the final point pair makes brute/dc more likely to tally. Note however
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-- when >1 equidistant pairs exist, brute and dc may well return different pairs;
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-- it is only a problem if they decide to return different minimum distances.)</span>
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">}}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">points</span><span style="color: #0000FF;">))</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
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sequence testset = sq_rnd(repeat({1,1},10000))
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atom t0 = time()
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atom {d, {{x1,y1},{x2,y2}}} = bruteForceClosestPair(testset)
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-- (Sorting the final point pair makes brute/dc more likely to tally. Note however
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-- when >1 equidistant pairs exist, brute and dc may well return different pairs;
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-- it is only a problem if they decide to return different minimum distances.)
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printf(1,"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n",{x1,y2,x2,y2,d,time()-t0})
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<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">X</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">xP</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">testset</span><span style="color: #0000FF;">))</span>
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t0 = time()
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constant X = 1, Y = 2
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sequence xP = sort(deep_copy(testset)),
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yP = sort_columns(deep_copy(testset),{Y})
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<span style="color: #008080;">function</span> <span style="color: #000000;">byY</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">yP</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">custom_sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">routine_id</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"byY"</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">testset</span><span style="color: #0000FF;">))</span>
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function distsq(sequence p1,p2)
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atom {x1,y1} = p1, {x2,y2} = p2
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x1 -= x2
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y1 -= y2
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return x1*x1 + y1*y1
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">distsq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p2</span>
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<span style="color: #000000;">x1</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">x2</span>
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<span style="color: #000000;">y1</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">y2</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x1</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">y1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function closestPair(sequence xP, yP)
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-- where xP is P(1) .. P(N) sorted by x coordinate, and
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-- yP is P(1) .. P(N) sorted by y coordinate (ascending order)
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integer N = length(xP),
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midN = floor(N/2)
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assert(length(yP)=N)
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if N<=3 then
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return bruteForceClosestPair(xP)
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end if
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sequence xL = xP[1..midN],
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xR = xP[midN+1..N],
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yL = {},
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yR = {}
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atom xm = xP[midN][X]
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for yi in yP do
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if yi[X]<=xm then
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yL = append(yL,yi)
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else
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yR = append(yR,yi)
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end if
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end for
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{atom dmin, sequence pairMin} = min(closestPair(xL, yL),
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closestPair(xR, yR))
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sequence yS = {}
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for yi in yP do
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if abs(xm-yi[X])<dmin then
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yS = append(yS,yi)
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end if
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end for
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atom closest = dmin*dmin
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for i,yi in yS to length(yS)-1 do
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for yk in yS from i+1 do
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if yk[Y]-yi[Y]>=dmin then exit end if
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d = distsq(yk,yi)
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if d<closest then
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{closest, pairMin} = {d, {yk, yi}}
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end if
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end for
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end for
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pairMin = sort(pairMin) -- (see note above)
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return {sqrt(closest), pairMin}
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end function
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|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">closestPair</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">xP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">yP</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- where xP is P(1) .. P(N) sorted by x coordinate, and
|
||||
-- yP is P(1) .. P(N) sorted by y coordinate (ascending order)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xP</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">midN</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">N</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">N</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">bruteForceClosestPair</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xP</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">xL</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">midN</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">xR</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">midN</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">N</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">yL</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
|
||||
<span style="color: #000000;">yR</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">xm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">midN</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">yP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">]<=</span><span style="color: #000000;">xm</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">yL</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">yR</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yR</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #004080;">atom</span> <span style="color: #000000;">dL</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">pairL</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">closestPair</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">yL</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #004080;">atom</span> <span style="color: #000000;">dR</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">pairR</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">closestPair</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xR</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">yR</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #004080;">atom</span> <span style="color: #000000;">dmin</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">pairMin</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">({</span><span style="color: #000000;">dL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pairL</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">dR</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pairR</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">yS</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">-</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">X</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">dmin</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">yS</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">nS</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #004080;">atom</span> <span style="color: #000000;">closest</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">cPair</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">dmin</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pairMin</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nS</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">nS</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">dmin</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">distsq</span><span style="color: #0000FF;">(</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">closest</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">closest</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cPair</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">yS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]}}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">closest</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">cPair</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">points</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">closestPair</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xP</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yP</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">}}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">points</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- (see note above)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
|
||||
<!--
|
||||
{d,{{x1,y1},{x2,y2}}} = closestPair(xP,yP)
|
||||
printf(1,"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n",{x1,y2,x2,y2,d,time()-t0})
|
||||
|
|
|
|||
75
Task/Closest-pair-problem/Pluto/closest-pair-problem.pluto
Normal file
75
Task/Closest-pair-problem/Pluto/closest-pair-problem.pluto
Normal file
|
|
@ -0,0 +1,75 @@
|
|||
local fmt = require "fmt"
|
||||
|
||||
local distance = |p1, p2| -> math.hypot(p1[1] - p2[1], p1[2] - p2[2])
|
||||
|
||||
local function brute_force_closest_pair(p)
|
||||
local n = #p
|
||||
assert(n >= 2, "There must be at least two points.")
|
||||
local min_points = {p[1], p[2]}
|
||||
local min_dist = distance(p[1], p[2])
|
||||
for i = 1, n - 1 do
|
||||
for j = i + 1, n do
|
||||
local dist = distance(p[i], p[j])
|
||||
if dist < min_dist then
|
||||
min_dist = dist
|
||||
min_points = {p[i], p[j]}
|
||||
end
|
||||
end
|
||||
end
|
||||
return min_dist, min_points
|
||||
end
|
||||
|
||||
local function optimized_closest_pair(xp, yp)
|
||||
local n = #xp
|
||||
if n <= 3 then return brute_force_closest_pair(xp) end
|
||||
local hn = n // 2
|
||||
local xl = xp:slice(1, hn)
|
||||
local xr = xp:slice(hn + 1)
|
||||
local xm = xp[hn][1]
|
||||
local yl = yp:filtered(|p| -> p[1] <= xm):reorder()
|
||||
local yr = yp:filtered(|p| -> p[1] > xm):reorder()
|
||||
local dl, pair_l = optimized_closest_pair(xl, yl)
|
||||
local dr, pair_r = optimized_closest_pair(xr, yr)
|
||||
local dmin = dr
|
||||
local pair_min = pair_r
|
||||
if dl < dr then
|
||||
dmin = dl
|
||||
pair_min = pair_l
|
||||
end
|
||||
local ys = yp:filtered(|p| -> math.abs(xm - p[1]) < dmin):reorder()
|
||||
local ns = #ys
|
||||
local closest = dmin
|
||||
local closest_pair = pair_min
|
||||
for i = 1, ns - 1 do
|
||||
local k = i + 1
|
||||
while k <= ns and (ys[k][2] - ys[i][2] < dmin) do
|
||||
local dist = distance(ys[k], ys[i])
|
||||
if dist < closest then
|
||||
closest = dist
|
||||
closest_pair = {ys[k], ys[i]}
|
||||
end
|
||||
k += 1
|
||||
end
|
||||
end
|
||||
return closest, closest_pair
|
||||
end
|
||||
|
||||
local points = {
|
||||
{ {5, 9}, {9, 3}, {2, 0}, {8, 4}, {7, 4}, {9, 10}, {1, 9}, {8, 2}, {0, 10}, {9, 6} },
|
||||
|
||||
{
|
||||
{0.654682, 0.925557}, {0.409382, 0.619391}, {0.891663, 0.888594},
|
||||
{0.716629, 0.996200}, {0.477721, 0.946355}, {0.925092, 0.818220},
|
||||
{0.624291, 0.142924}, {0.211332, 0.221507}, {0.293786, 0.691701},
|
||||
{0.839186, 0.728260}
|
||||
}
|
||||
}
|
||||
|
||||
for points as p do
|
||||
local dist, pair = brute_force_closest_pair(p)
|
||||
fmt.print($"Closest pair (brute force) is %,s and %,s, distance %s", pair[1], pair[2], dist)
|
||||
local xp = p:sorted(|x, y| -> x[1] < y[1])
|
||||
local yp = p:sorted(|x, y| -> x[2] < y[2])
|
||||
dist, pair = optimized_closest_pair(xp, yp)
|
||||
fmt.print("Closest pair (optimized) is %,s and %,s, distance %s\n", pair[1], pair[2], dist)
|
||||
end
|
||||
Loading…
Add table
Add a link
Reference in a new issue