Digital root/Multiplicative digital root: Difference between revisions
Digital root/Multiplicative digital root (view source)
Revision as of 11:33, 25 March 2017
, 7 years agoAdded Algol W
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(Added Algol W) |
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893: MDR: 2, MP: 3
899998: MDR: 0, MP: 2
MDR: [n0..n4]
=== ========
0: [0, 10, 20, 25, 30]
1: [1, 11, 111, 1111, 11111]
2: [2, 12, 21, 26, 34]
3: [3, 13, 31, 113, 131]
4: [4, 14, 22, 27, 39]
5: [5, 15, 35, 51, 53]
6: [6, 16, 23, 28, 32]
7: [7, 17, 71, 117, 171]
8: [8, 18, 24, 29, 36]
9: [9, 19, 33, 91, 119]
</pre>
=={{header|ALGOL W}}==
<lang algolw>begin
% calculate the Multiplicative Digital Root (mdr) and Multiplicative Persistence (mp) of n %
procedure getMDR ( integer value n
; integer result mdr, mp
) ;
begin
integer digitProduct;
mp := 0;
digitProduct := abs n;
while digitProduct > 9 do begin
integer v;
v := digitProduct;
digitProduct := 1;
while begin
digitProduct := digitProduct * ( v rem 10 );
v := v div 10;
v > 0
end do begin end;
mp := mp + 1;
end while_mdr_gt_9 ;
mdr := digitProduct
end MDR ;
% task test cases %
write( " N MDR MP" );
for n := 123321, 7739, 893, 899998 do begin
integer mdr, mp;
getMDR( n,mdr, mp );
write( s_w := 1, i_w := 8, n, i_w := 3, mdr, i_w := 2, mp )
end for_n ;
begin % find the first 5 numbers with each possible MDR %
integer requiredMdrs;
requiredMdrs := 5;
begin
integer array firstFew ( 0 :: 9, 1 :: requiredMdrs );
integer array mdrFOund ( 0 :: 9 );
integer totalFound, requiredTotal, n;
for i := 0 until 9 do mdrFound( i ) := 0;
totalFound := 0;
requiredMdrs := 5;
requiredTotal := 10 * requiredMdrs;
n := -1;
while totalFound < requiredTotal do begin
integer mdr, mp;
n := n + 1;
getMDR( n, mdr, mp );
if mdrFound( mdr ) < requiredMdrs then begin
% found another number with this MDR and haven't found enough yet %
totalFound := totalFound + 1;
mdrFound( mdr ) := mdrFound( mdr ) + 1;
firstFew( mdr, mdrFound( mdr ) ) := n
end if_found_another_MDR
end while_totalFound_lt_requiredTotal ;
% print the table of MDRs andnumbers %
write( "MDR: [n0..n4]" );
write( "=== ========" );
for v := 0 until 9 do begin
write( i_w := 3, s_w := 0, v, ": [" );
for foundPos := 1 until requiredMdrs do begin
if foundPos > 1 then writeon( s_w := 0, ", " );
writeon( i_w := 1, s_w := 0, firstFew( v, foundPos ) )
end for_foundPos ;
writeon( s_w := 0, "]" )
end for_v
end
end
end.</lang>
{{out}}
<pre>
N MDR MP
123321 8 3
7739 8 3
893 2 3
899998 0 2
MDR: [n0..n4]
=== ========
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