Own digits power sum: Difference between revisions

=={{header|Delphi}}==

{{works with|Delphi|6.0}}

{{libheader|SysUtils,StdCtrls}}

Started with brute force method which took over a minute to do the 8-digit problem. Then borrowed ideas from everywhere, especially the XPL0 implementation.

<syntaxhighlight lang="Delphi">

{Table to speed up power(X,Y) calculation }

const PowerTable: array [0..9] of array [0..9] of integer = (

(1, 0, 0, 0, 0, 0, 0, 0, 0, 0),

(1, 1, 1, 1, 1, 1, 1, 1, 1, 1),

(1, 2, 4, 8, 16, 32, 64, 128, 256, 512),

(1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683),

(1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144),

(1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125),

(1, 6, 36, 216, 1296, 7776, 46656, 279936, 1679616, 10077696),

(1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, 40353607),

(1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 134217728),

(1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489)

);

procedure DigitsPowerSum(Memo: TMemo; var Number, DigitCount: integer; Level, Sum: integer);

{Recursively process DigitCount power}

var Digits: integer;

begin

{Finish when recursion = Level Zero}

if Level = 0 then

begin

for Digits:= 0 to 9 do

begin

{Test combinations of digits and previous sum against number}

if ((Sum + PowerTable[Digits, DigitCount]) = Number) and

(Number >= 100) then

begin

Memo.Lines.Add(IntToStr(DigitCount)+' '+IntToStr(Number));

end;

Inc(Number);

{Keep track of digit count - increases on even power of 10}

case Number of

10, 100, 1000, 10000, 100000,

1000000, 10000000, 100000000: Inc(DigitCount);

end;

end;

end

else for Digits:= 0 to 9 do

begin

{Recurse through all digits/levels}

DigitsPowerSum(Memo, Number, DigitCount,

Level-1, Sum + PowerTable[Digits, DigitCount]);

end;

end;

procedure ShowDigitsPowerSum(Memo: TMemo);

var Number, DigitCount: integer;

begin

Number:= 0;

DigitCount:= 1;

DigitsPowerSum(Memo, Number, DigitCount, 9-1, 0);

end;

</syntaxhighlight>

{{out}}

<pre>

3 153

3 370

3 371

3 407

4 1634

4 8208

4 9474

5 54748

5 92727

5 93084

6 548834

7 1741725

7 4210818

7 9800817

7 9926315

8 24678050

8 24678051

8 88593477

9 146511208

9 472335975

9 534494836

9 912985153

Elapsed Time: 3.058 Sec.

</pre>