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Task/Babbage-problem/SQL/babbage-problem.sql

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+/*
+This code is an implementation of Babbage Problem in SQL ORACLE 19c
+p_ziel  -- the substring to search for, which can start with leading zeros
+p_max   -- upper bound of the cycle
+v_max   -- safe determination of the upper bound of the cycle
+v_start -- safe starting point
+*/
+with
+  function babbage(p_ziel in varchar2, p_max integer) return varchar2 is
+    v_max    integer := greatest(p_max,to_number('1E+'||length(to_char(p_ziel))));
+    v_start  number := case when substr(p_ziel,1,1)='0' then ceil(sqrt('1'||p_ziel)) else ceil(sqrt(p_ziel)) end;
+    v_length number := to_number('1E+'||length(to_char(p_ziel)));
+  begin
+    -- first check
+    if substr(p_ziel,-1) in (2,3,7,8) then
+      return 'The exact square of an integer cannot end with '''||substr(p_ziel,-1)||''', so there is no such smallest number whose square ends in '''||p_ziel||'''';
+    end if;
+    -- second check
+    if regexp_count(p_ziel,'([^0]0{1,}$)')=1 and mod(regexp_count(regexp_substr(p_ziel,'(0{1,}$)'),'0'),2)=1 then
+      return 'An exact square of an integer cannot end with an odd number of zeros, so there is no such smallest number whose square ends in '''||p_ziel||'''';
+    end if;
+    -- main cycle
+    while v_start < v_max loop
+      exit when mod(v_start**2,v_length) = p_ziel;
+      v_start := v_start + 1;
+    end loop;
+    -- output
+    if v_start = v_max then
+      return 'There is no such smallest number before '||v_max||' whose square ends in '''||p_ziel||'''';
+    else
+      return ''||v_start||' is the smallest number, whose square '||regexp_replace(to_char(v_start**2),'(\d{1,})('||p_ziel||')','\1''\2''')||' ends in '''||p_ziel||'''';
+    end if;
+    --
+  end;
+
+--Test
+select babbage('222',100000) as res from dual
+union all
+select babbage('33',100000) as res from dual
+union all
+select babbage('17',100000) as res from dual
+union all
+select babbage('888',100000) as res from dual
+union all
+select babbage('1000',100000) as res from dual
+union all
+select babbage('000',100000) as res from dual
+union all
+select babbage('269696',100000) as res from dual -- strict Babbage Problem
+union all
+select babbage('269696',10) as res from dual
+union all
+select babbage('169696',10) as res from dual
+union all
+select babbage('19696',100000) as res from dual
+union all
+select babbage('04',100000) as res from dual;