Question: Challenge: Number of Palindromic Numbers
Challenge: provide the implementation of a custom Delphi function to locate all palindromic numbers from 1 to maxNumber and return the number of found palindromes as a result of the function.
The code is submitted for the Number of Palindromic Numbers Delphi Challenge
Answer: Number of palindromic numbers entry by Boris Novgorodov (Russia):
function BorisNovgorodov_NumberOfPalindromes(const MaxNumber: Int64): Int64;
const
TenPowers: array[0..9] of Int64 =
(1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000) ;
function PalBeforeTenPower(Pow: Integer): Int64;
begin
if Pow = 0 then
Result := 1
else if Odd(Pow) then
Result := 11 * TenPowers[Pow div 2] - 2
else
Result := 2 * TenPowers[Pow div 2] - 2;
end;
var
DigCnt, HalfCnt: Integer;
AStart, ARevStart, AEnd, AMed, OddityMul, StartMul: Int64;
begin
DigCnt := 0;
AStart := MaxNumber;
while AStart > 0 do
begin
AStart := AStart div 10;
Inc(DigCnt) ;
end;
if DigCnt <= 1 then
begin
Result := MaxNumber;
Exit;
end;
HalfCnt := DigCnt div 2;
AStart := MaxNumber div TenPowers[HalfCnt];
AEnd := MaxNumber mod TenPowers[HalfCnt];
if Odd(DigCnt) then
begin
AMed := AStart mod 10;
AStart := AStart div 10;
OddityMul := 10;
end
else
begin
AMed := 0;
OddityMul := 1;
end;
StartMul := AStart - TenPowers[HalfCnt - 1];
ARevStart := 0;
while AStart > 0 do
begin
ARevStart := ARevStart * 10 + AStart mod 10;
AStart := AStart div 10;
end;
if ARevStart <= AEnd then Inc(AMed) ;
Result := PalBeforeTenPower(DigCnt - 1) + StartMul * OddityMul + AMed;
end;
Test data: MAXNUMBER = 10 000 000
Boris's speed result: 1689 nanoseconds.
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