Data update

Task/Longest-increasing-subsequence/Ada/longest-increasing-subsequence.ada

@@ -0,0 +1,51 @@
+with Ada.Text_IO;
+
+procedure Longest_Increasing_Subsequence is
+   type Sequence is array (Positive range <>) of Integer;
+
+   Seq1 : constant Sequence :=
+     (3, 2, 6, 4, 5, 1);
+   Seq2 : constant Sequence :=
+     (0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15);
+
+   function Lis (Seq : Sequence) return Sequence is
+      Best : Sequence (Seq'Range) := (others => 1);
+      Pred : Sequence (Seq'Range) := (others => 0);
+      Best_Idx, Max_Len : Natural := 0;
+   begin
+      --  Calculate LIS length for every end point
+      for I in Seq'Range loop
+         for J in 1 .. I - 1 loop
+            if Seq (J) < Seq (I) and then
+               Best (I) < 1 + Best (J) then
+               Best (I) := 1 + Best (J);
+               Pred (I) := J;
+            end if;
+         end loop;
+      end loop;
+
+      --  Find tail of global LIS
+      for I in Best'Range loop
+         if Best (I) > Max_Len then
+            Best_Idx := I;
+            Max_Len := Best (I);
+         end if;
+      end loop;
+
+      --  Trace sequence
+      declare
+         Lis : Sequence (1 .. Max_Len);
+      begin
+         for I in reverse 1 .. Max_Len loop
+            Lis (I) := Seq (Best_Idx);
+            Best_Idx := Pred (Best_Idx);
+         end loop;
+
+         return Lis;
+      end;
+   end Lis;
+
+begin
+   Ada.Text_IO.Put_Line (Lis (Seq1)'Image);
+   Ada.Text_IO.Put_Line (Lis (Seq2)'Image);
+end Longest_Increasing_Subsequence;

Task/Longest-increasing-subsequence/DuckDB/longest-increasing-subsequence.duckdb

@@ -0,0 +1,31 @@
+# Return a list - just one in the case of a tie
+create or replace function longest_increasing_subsequence(lst) as (
+
+  -- Add a flag to signal the start of a new subsequence
+  with flagged as (
+    select *, if(id = 1, 0, if(c > (lag(c) over ()), 0, 1)) as flag
+    from (select generate_subscripts(lst,1) as id,
+                 unnest(lst) as c)
+  ),
+  partitions as (
+    select *, sum(flag) over (order by id) as partition_number
+    from (select *, if(id=1 or (c > (lag(c) over ())), 1, 0) as flag
+          from flagged)
+    order by id asc
+  ),
+  subseq_number as (
+    select max_by(partition_number, ncount) as n
+      from (select partition_number, count(*) as ncount
+            from partitions
+            group by partition_number)
+  )
+  select array_agg(c order by id)
+        from partitions, subseq_number
+        where partition_number = subseq_number.n
+);
+
+# Examples;
+select l as list, longest_increasing_subsequence(l) as lis
+  from (select [3,2,6,4,5,1] as l union all
+        select [0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15] as l union all
+        select [0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15,20] as l);