Data update

Task/Palindromic-gapful-numbers/00-TASK.txt

@@ -1,24 +1,18 @@
-Numbers   (positive integers expressed in base ten)   that are (evenly) divisible by the number formed by the
-first and last digit are known as   '''gapful numbers'''.
+For this task, a ''number'' is to be understood as a positive integer expressed in base ten,
+and a ''palindromic'' number is one that is equal to the integer formed by reversing its decimal digits.
 
+A number that is evenly divisible by the number formed by concatenating its
+first and last digits in that order is known as a '''gapful number'''.
+All one─ and two─digit numbers have this property and accordingly only
+numbers greater than or equal to '''100''' should be considered for this Rosetta Code task.
 
-''Evenly divisible''   means divisible with   no   remainder.
-
-
-All   one─   and two─digit   numbers have this property and are trivially excluded.   Only
-numbers &nbsp; <big> &ge; </big> '''100''' &nbsp; will be considered for this Rosetta Code task.
-
+(''Evenly divisible'' here means divisible with no remainder.)
 
 ;Example:
 <big>'''1037'''</big> &nbsp; is a &nbsp; '''gapful''' &nbsp; number because it is evenly divisible by the
 number &nbsp; <big>'''17'''</big> &nbsp; which is formed by the first and last decimal digits
 of &nbsp; <big> '''<u>1</u>03<u>7</u>'''. </big>
 
-
-A palindromic number is &nbsp; (for this task, a positive integer expressed in base ten), &nbsp; when the number is 
-reversed, &nbsp; is the same as the original number.
-
-
 ;Task:
 :* &nbsp; Show &nbsp; (nine sets) &nbsp; the first &nbsp; '''20''' &nbsp; palindromic gapful numbers that &nbsp; ''end'' &nbsp; with:
 :::* &nbsp; the digit &nbsp; '''1'''

Task/Palindromic-gapful-numbers/Jq/palindromic-gapful-numbers.jq

@@ -0,0 +1,68 @@
+### Generic functions
+def power($a;$b): reduce range(0;$b) as $i (1; . * $a);
+
+# Emit the reverse of the string $s
+def reverse($s):
+  $s | tostring | split("") | reverse | join("");
+
+def skip($n; stream):
+  foreach stream as $s (-1;
+      if . == $n then . else .+1 end;
+      select(. == $n) | $s);
+
+### Palindromic gapful numbers
+
+# Output: a stream of non-trivial palindromic gapful numbers ending in the specified digit
+def palindromicgapfuls($digit):
+  {emit: null,
+   dd: (11 * $digit),                             # digit gapful divisor: 11, 22,...88, 99
+   power: 1}
+  | foreach range(0; infinite) as $_ (.;
+      .power += 1
+      | (power(10; .power / 2 | floor)) as $base  # value of middle digit position: 10..
+      | ($base * 11) as $base11                   # value of middle two digits positions: 110..
+      | ($base * $digit) as $this_lo              # starting half for this digit: 10.. to  90..
+      | ($base * ($digit + 1)) as $next_lo        # starting half for next digit: 20.. to 100..
+
+      | foreach range($this_lo; $next_lo; 10) as $front_half (.;  # d_00; d_10; d_20; ...
+          ($front_half|tostring) as $left_half
+          | reverse($left_half) as $right_half
+          | if .power%2 == 1
+            then .palindrome = (($left_half + $right_half) | tonumber)
+            | foreach range(0;10) as $i (.;
+                .emit = if .palindrome % .dd == 0
+                        then .palindrome
+                        else null
+                        end
+                | .palindrome += $base11 )
+            else .palindrome = ((($left_half[:-1]) + $right_half) | tonumber)
+            | foreach range(0;10) as $i (.;
+                .emit = if .palindrome % .dd == 0
+                        then .palindrome
+                        else null
+                        end
+                | .palindrome += $base )
+            end ) )
+  | select(.emit).emit ;
+
+def palindromicgapfuls($count; $keep):
+  range(1; 10) as $digit
+  | "\($digit) : \([limit($keep; skip($count - $keep; palindromicgapfuls($digit)))])" ;
+
+def task:
+  "First 20 non-trivial palindromic gapful numbers ending with:",
+   palindromicgapfuls(20; 20),
+
+  "\nLast 15 of first 100 non-trivial palindromic gapful numbers ending in:",
+   palindromicgapfuls(100; 15),
+
+  "\nLast 10 of first 1000 non-trivial palindromic gapful numbers ending in:",
+   palindromicgapfuls(1000; 10),
+
+  "\n100,000th non-trivial palindromic gapful number ending with:",
+   palindromicgapfuls(100000; 1),
+
+  "\n1,000,000th non-trivial palindromic gapful number ending with:",
+   palindromicgapfuls(1000000; 1);
+
+task