Digital root: Difference between revisions
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-- Test values. |
-- Test values. |
||
once |
once |
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Result := << |
Result := <<670033, 39390, 588225, 393900588225>> -- base 10 |
||
end |
end |
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| Line 580: | Line 580: | ||
-- Expected result values. |
-- Expected result values. |
||
once |
once |
||
Result := << |
Result := <<1, 6, 3, 9>> -- base 10 |
||
end |
end |
||
make |
make |
||
Revision as of 13:30, 17 November 2014
You are encouraged to solve this task according to the task description, using any language you may know.
The digital root, , of a number, , is calculated:
- find as the sum of the digits of
- find a new by summing the digits of , repeating until has only one digit.
The additive persistence is the number of summations required to obtain the single digit.
The task is to calculate the additive persistence and the digital root of a number, e.g.:
- has additive persistence and digital root of ;
- has additive persistence and digital root of ;
- has additive persistence and digital root of ;
- has additive persistence and digital root of ;
The digital root may be calculated in bases other than 10.
See:
- Casting out nines for this wiki's use of this procedure.
- Digital root/Multiplicative digital root
- Sum digits of an integer
- Digital root sequence on OEIS
- Additive persistence sequence on OEIS
- Iterated digits squaring
Ada
We first specify a Package "Generic_Root" with a generic procedure "Compute". The package is reduced for the implementation of multiplicative digital roots [[1]]. Further note the tunable parameter for the number base (default 10).
<lang Ada>package Generic_Root is
type Number is range 0 .. 2**63-1;
type Number_Array is array(Positive range <>) of Number;
type Base_Type is range 2 .. 16; -- any reasonable base to write down numb
generic
with function "&"(X, Y: Number) return Number;
-- instantiate with "+" for additive digital roots
-- instantiate with "*" for multiplicative digital roots
procedure Compute_Root(N: Number;
Root, Persistence: out Number;
Base: Base_Type := 10);
-- computes Root and Persistence of N;
end Generic_Root;</lang>
The implementation is straightforward: If the input N is a digit, then the root is N and the persistence is zero. Else, commute the digit-sum DS. The root of N is the root of DS, the persistence of N is 1 + (the persistence of DS).
<lang Ada>package body Generic_Root is
procedure Compute_Root(N: Number;
Root, Persistence: out Number;
Base: Base_Type := 10) is
function Digit_Sum(N: Number) return Number is
begin
if N < Number(Base) then
return N;
else
return (N mod Number(Base)) & Digit_Sum(N / Number(Base));
end if;
end Digit_Sum;
begin
if N < Number(Base) then
Root := N;
Persistence := 0;
else
Compute_Root(Digit_Sum(N), Root, Persistence, Base);
Persistence := Persistence + 1;
end if;
end Compute_Root;
end Generic_Root;</lang>
Finally the main program. The procedure "Print_Roots" is for our convenience.
<lang Ada>with Generic_Root, Ada.Text_IO; use Generic_Root;
procedure Digital_Root is
procedure Compute is new Compute_Root("+");
-- "+" for additive digital roots
package TIO renames Ada.Text_IO;
procedure Print_Roots(Inputs: Number_Array; Base: Base_Type) is
package NIO is new TIO.Integer_IO(Number);
Root, Pers: Number;
begin
for I in Inputs'Range loop
Compute(Inputs(I), Root, Pers, Base);
NIO.Put(Inputs(I), Base => Integer(Base), Width => 12);
NIO.Put(Root, Base => Integer(Base), Width => 9);
NIO.Put(Pers, Base => Integer(Base), Width => 12);
TIO.Put_Line(" " & Base_Type'Image(Base));
end loop;
end Print_Roots;
begin
TIO.Put_Line(" Number Root Persistence Base");
Print_Roots((961038, 923594037444, 670033, 448944221089), Base => 10);
Print_Roots((16#7e0#, 16#14e344#, 16#12343210#), Base => 16);
end Digital_Root;</lang>
- Output:
Number Root Persistence Base
961038 9 2 10
923594037444 9 2 10
670033 1 3 10
448944221089 1 3 10
16#7E0# 16#6# 16#2# 16
16#14E344# 16#F# 16#2# 16
16#12343210# 16#1# 16#2# 16
Applesoft BASIC
<lang ApplesoftBasic>1 GOSUB 430"BASE SETUP 2 FOR E = 0 TO 1 STEP 0 3 GOSUB 7"READ 4 ON E + 1 GOSUB 50, 10 5 NEXT E 6 END
7 READ N$ 8 E = N$ = "" 9 RETURN
10 GOSUB 7"READ BASE 20 IF E THEN RETURN 30 BASE = VAL(N$) 40 READ N$
50 GOSUB 100"DIGITAL ROOT 60 GOSUB 420: PRINT " HAS AD"; 70 PRINT "DITIVE PERSISTENCE"; 80 PRINT " "P" AND DIGITAL R"; 90 PRINT "OOT "X$";" : RETURN
REM DIGITAL ROOT OF N$, RETURNS X$ AND P
100 P = 0 : L = LEN(N$) 110 X$ = MID$(N$, 2, L - 1) 120 N = LEFT$(X$, 1) = "-" 130 IF NOT N THEN X$ = N$ 140 FOR P = 0 TO 1E38 150 L = LEN(X$) 160 IF L < 2 THEN RETURN 170 GOSUB 200"DIGIT SUM 180 X$ = S$ 190 NEXT P : STOP
REM DIGIT SUM OF X$, RETURNS S$
200 S$ = "0" 210 R$ = X$ 220 L = LEN(R$) 230 FOR L = L TO 1 STEP -1 240 E$ = "" : V$ = RIGHT$(R$, 1) 250 GOSUB 400 : S = LEN(S$) 260 ON R$ <> "0" GOSUB 300 270 R$ = MID$(R$, 1, L - 1) 280 NEXT L 290 RETURN
REM ADD V TO S$
300 FOR C = V TO 0 STEP 0 310 V$ = RIGHT$(S$, 1) 320 GOSUB 400 : S = S - 1 330 S$ = MID$(S$, 1, S) 340 V = V + C : C = V >= BASE 350 IF C THEN V = V - BASE 360 GOSUB 410 : E$ = V$ + E$ 370 IF S THEN NEXT C 380 IF C THEN S$ = "1" 390 S$ = S$ + E$ : RETURN
REM BASE VAL 400 V = V(ASC(V$)) : RETURN
REM BASE STR$ 410 V$ = V$(V) : RETURN
REM BASE DISPLAY 420 PRINT N$; 421 IF BASE = 10 THEN RETURN 422 PRINT "("BASE")"; 423 RETURN
REM BASE SETUP 430 IF BASE = 0 THEN BASE = 10 440 DIM V(127), V$(35) 450 FOR I = 0 TO 35 460 V = 55 + I - (I < 10) * 7 470 V$(I) = CHR$(V) 480 V(V) = I 490 NEXT I : RETURN
500 DATA627615,39390,588225 510 DATA393900588225 1000 DATA,30 1010 DATADIGITALROOT 63999DATA,</lang>
- Output:
627615 HAS ADDITIVE PERSISTENCE 2 AND DIGITAL ROOT 9; 39390 HAS ADDITIVE PERSISTENCE 2 AND DIGITAL ROOT 6; 588225 HAS ADDITIVE PERSISTENCE 2 AND DIGITAL ROOT 3; 393900588225 HAS ADDITIVE PERSISTENCE 2 AND DIGITAL ROOT 9; DIGITALROOT(30) HAS ADDITIVE PERSISTENCE 2 AND DIGITAL ROOT Q;
AutoHotkey
<lang AutoHotkey>p := {} for key, val in [30,1597,381947,92524902,448944221089] {
n := val
while n > 9
{
m := 0
Loop, Parse, n
m += A_LoopField
n := m, i := A_Index
}
p[A_Index] := [val, n, i]
}
for key, val in p
Output .= val[1] ": Digital Root = " val[2] ", Additive Persistence = " val[3] "`n"
MsgBox, 524288, , % Output</lang>
- Output:
30: Digital Root = 3, Additive Persistence = 1
1597: Digital Root = 4, Additive Persistence = 2
381947: Digital Root = 5, Additive Persistence = 2
92524902: Digital Root = 6, Additive Persistence = 2
448944221089: Digital Root = 1, Additive Persistence = 3
AWK
<lang AWK># syntax: GAWK -f DIGITAL_ROOT.AWK BEGIN {
n = split("627615,39390,588225,393900588225,10,199",arr,",")
for (i=1; i<=n; i++) {
dr = digitalroot(arr[i],10)
printf("%12.0f has additive persistence %d and digital root of %d\n",arr[i],p,dr)
}
exit(0)
} function digitalroot(n,b) {
p = 0 # global
while (n >= b) {
p++
n = digitsum(n,b)
}
return(n)
} function digitsum(n,b, q,s) {
while (n != 0) {
q = int(n / b)
s += n - q * b
n = q
}
return(s)
}</lang>
- Output:
627615 has additive persistence 2 and digital root of 9
39390 has additive persistence 2 and digital root of 6
588225 has additive persistence 2 and digital root of 3
393900588225 has additive persistence 2 and digital root of 9
10 has additive persistence 1 and digital root of 1
199 has additive persistence 3 and digital root of 1
BASIC
This calculates the result "the hard way", but is limited to the limits of a 32-bit signed integer (+/-2,147,483,647) and therefore can't calculate the digital root of 393,900,588,225. <lang qbasic>DECLARE SUB digitalRoot (what AS LONG)
'test inputs: digitalRoot 627615 digitalRoot 39390 digitalRoot 588225
SUB digitalRoot (what AS LONG)
DIM w AS LONG, t AS LONG, c AS INTEGER
w = ABS(what)
IF w > 10 THEN
DO
c = c + 1
WHILE w
t = t + (w MOD (10))
w = w \ 10
WEND
w = t
t = 0
LOOP WHILE w > 9
END IF
PRINT what; ": additive persistance "; c; ", digital root "; w
END SUB</lang>
- Output:
627615 : additive persistance 2 , digital root 9 39390 : additive persistance 2 , digital root 6 588225 : additive persistance 2 , digital root 3
BBC BASIC
<lang bbcbasic> *FLOAT64
PRINT "Digital root of 627615 is "; FNdigitalroot(627615, 10, p) ;
PRINT " (additive persistence " ; p ")"
PRINT "Digital root of 39390 is "; FNdigitalroot(39390, 10, p) ;
PRINT " (additive persistence " ; p ")"
PRINT "Digital root of 588225 is "; FNdigitalroot(588225, 10, p) ;
PRINT " (additive persistence " ; p ")"
PRINT "Digital root of 393900588225 is "; FNdigitalroot(393900588225, 10, p) ;
PRINT " (additive persistence " ; p ")"
PRINT "Digital root of 9992 is "; FNdigitalroot(9992, 10, p) ;
PRINT " (additive persistence " ; p ")"
END
DEF FNdigitalroot(n, b, RETURN c)
c = 0
WHILE n >= b
c += 1
n = FNdigitsum(n, b)
ENDWHILE
= n
DEF FNdigitsum(n, b)
LOCAL q, s
WHILE n <> 0
q = INT(n / b)
s += n - q * b
n = q
ENDWHILE
= s</lang>
- Output:
Digital root of 627615 is 9 (additive persistence 2) Digital root of 39390 is 6 (additive persistence 2) Digital root of 588225 is 3 (additive persistence 2) Digital root of 393900588225 is 9 (additive persistence 2) Digital root of 9992 is 2 (additive persistence 3)
Bracmat
<lang bracmat> ( root
= sum persistence n d
. !arg:(~>9.?)
| !arg:(?n.?persistence)
& 0:?sum
& ( @( !n
: ?
(#%@?d&!d+!sum:?sum&~)
?
)
| root$(!sum.!persistence+1)
)
)
& ( 627615 39390 588225 393900588225 10 199
: ?
( #%@?N
& root$(!N.0):(?Sum.?Persistence)
& out
$ ( !N
"has additive persistence"
!Persistence
"and digital root of"
!Sum
)
& ~
)
?
| done
);</lang>
- Output:
627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9 10 has additive persistence 1 and digital root of 1 199 has additive persistence 3 and digital root of 1
C
<lang c>#include <stdio.h>
int droot(long long int x, int base, int *pers) { int d = 0; if (pers) for (*pers = 0; x >= base; x = d, (*pers)++) for (d = 0; x; d += x % base, x /= base); else if (x && !(d = x % (base - 1))) d = base - 1;
return d; }
int main(void) { int i, d, pers; long long x[] = {627615, 39390, 588225, 393900588225LL};
for (i = 0; i < 4; i++) { d = droot(x[i], 10, &pers); printf("%lld: pers %d, root %d\n", x[i], pers, d); }
return 0; }</lang>
C++
For details of SumDigits see: http://rosettacode.org/wiki/Sum_digits_of_an_integer <lang cpp>// Calculate the Digital Root and Additive Persistance of an Integer - Compiles with gcc4.7 // // Nigel Galloway. July 23rd., 2012 //
- include <iostream>
- include <cmath>
- include <tuple>
std::tuple<const unsigned long long int,int,int> DigitalRoot(const unsigned long long int digits, const int BASE = 10) {
int x = SumDigits(digits,BASE);
int ap = 1;
while (x >= BASE) {
x = SumDigits(x,BASE);
ap++;
}
return std::make_tuple(digits,ap,x);
}
int main() {
const unsigned long long int ip[] = {961038,923594037444,670033,448944221089};
for (auto i:ip){
auto res = DigitalRoot(i);
std::cout << std::get<0>(res) << " has digital root " << std::get<2>(res) << " and additive persistance " << std::get<1>(res) << "\n";
}
std::cout << "\n";
const unsigned long long int hip[] = {0x7e0,0x14e344,0xd60141,0x12343210};
for (auto i:hip){
auto res = DigitalRoot(i,16);
std::cout << std::hex << std::get<0>(res) << " has digital root " << std::get<2>(res) << " and additive persistance " << std::get<1>(res) << "\n";
}
return 0;
}</lang>
- Output:
961038 has digital root 9 and additive persistance 2 923594037444 has digital root 9 and additive persistance 2 670033 has digital root 1 and additive persistance 3 448944221089 has digital root 1 and additive persistance 3 7e0 has digital root 6 and additive persistance 2 14e344 has digital root f and additive persistance 2 d60141 has digital root a and additive persistance 2 12343210 has digital root 1 and additive persistance 2
Common Lisp
Using SUM-DIGITS from the task "Sum digits of an integer".
<lang lisp>(defun digital-root (number &optional (base 10))
(loop for n = number then s
for ap = 1 then (1+ ap)
for s = (sum-digits n base)
when (< s base)
return (values s ap)))
(loop for (nr base) in '((627615 10) (393900588225 10) (#X14e344 16) (#36Rdg9r 36))
do (multiple-value-bind (dr ap) (digital-root nr base)
(format T "~vR (base ~a): additive persistence = ~a, digital root = ~vR~%"
base nr base ap base dr)))</lang>
- Output:
627615 (base 10): additive persistence = 2, digital root = 9 393900588225 (base 10): additive persistence = 2, digital root = 9 14E344 (base 16): additive persistence = 2, digital root = F DG9R (base 36): additive persistence = 2, digital root = U
D
<lang d>import std.stdio, std.typecons, std.conv, std.bigint, std.math,
std.traits;
Tuple!(uint, Unqual!T) digitalRoot(T)(in T inRoot, in uint base) pure nothrow in {
assert(base > 1);
} body {
Unqual!T root = inRoot.abs;
uint persistence = 0;
while (root >= base) {
auto num = root;
root = 0;
while (num != 0) {
root += num % base;
num /= base;
}
persistence++;
}
return typeof(return)(persistence, root);
}
void main() {
enum f1 = "%s(%d): additive persistance= %d, digital root= %d";
foreach (immutable b; [2, 3, 8, 10, 16, 36]) {
foreach (immutable n; [5, 627615, 39390, 588225, 393900588225])
writefln(f1, text(n, b), b, n.digitalRoot(b)[]);
writeln;
}
enum f2 = "(%d): additive persistance= %d, digital root= %d";
immutable n = BigInt("581427189816730304036810394583022044713" ~
"00738980834668522257090844071443085937");
foreach (immutable b; [2, 3, 8, 10, 16, 36])
writefln(f2, b, n.digitalRoot(b)[]); // Shortened output.
}</lang>
- Output:
101(2): additive persistance= 2, digital root= 1 10011001001110011111(2): additive persistance= 3, digital root= 1 1001100111011110(2): additive persistance= 3, digital root= 1 10001111100111000001(2): additive persistance= 3, digital root= 1 101101110110110010011011111110011000001(2): additive persistance= 3, digital root= 1 12(3): additive persistance= 2, digital root= 1 1011212221000(3): additive persistance= 3, digital root= 1 2000000220(3): additive persistance= 2, digital root= 2 1002212220010(3): additive persistance= 3, digital root= 1 1101122201121110011000000(3): additive persistance= 3, digital root= 1 5(8): additive persistance= 0, digital root= 5 2311637(8): additive persistance= 3, digital root= 2 114736(8): additive persistance= 3, digital root= 1 2174701(8): additive persistance= 3, digital root= 1 5566623376301(8): additive persistance= 3, digital root= 4 5(10): additive persistance= 0, digital root= 5 627615(10): additive persistance= 2, digital root= 9 39390(10): additive persistance= 2, digital root= 6 588225(10): additive persistance= 2, digital root= 3 393900588225(10): additive persistance= 2, digital root= 9 5(16): additive persistance= 0, digital root= 5 9939F(16): additive persistance= 2, digital root= 15 99DE(16): additive persistance= 2, digital root= 15 8F9C1(16): additive persistance= 2, digital root= 15 5BB64DFCC1(16): additive persistance= 2, digital root= 15 5(36): additive persistance= 0, digital root= 5 DG9R(36): additive persistance= 2, digital root= 30 UE6(36): additive persistance= 2, digital root= 15 CLVL(36): additive persistance= 2, digital root= 15 50YE8N29(36): additive persistance= 2, digital root= 25 <BIG>(2): additive persistance= 4, digital root= 1 <BIG>(3): additive persistance= 4, digital root= 1 <BIG>(8): additive persistance= 3, digital root= 3 <BIG>(10): additive persistance= 3, digital root= 4 <BIG>(16): additive persistance= 3, digital root= 7 <BIG>(36): additive persistance= 3, digital root= 17
Dc
Tested on GNU dc.
Procedure p is for breaking up the number into individual digits.
Procedure q is for summing all digits left by procedure p.
Procedure r is for overall control (when to stop).
<lang Dc>?[10~rd10<p]sp[+z1<q]sq[lpxlqxd10<r]dsrxp</lang>
Eiffel
<lang Eiffel> class APPLICATION
inherit ARGUMENTS
create make
feature {NONE} -- Initialization
digital_root_test_values: ARRAY [INTEGER_64] -- Test values. once Result := <<670033, 39390, 588225, 393900588225>> -- base 10 end
digital_root_expected_result: ARRAY [INTEGER_64] -- Expected result values. once Result := <<1, 6, 3, 9>> -- base 10 end
make local results: ARRAY [INTEGER_64] i: INTEGER do from i := 1 until i > digital_root_test_values.count loop results := compute_digital_root (digital_root_test_values [i], 10) if results [2] ~ digital_root_expected_result [i] then print ("%N" + digital_root_test_values [i].out + " has additive persistence " + results [1].out + " and digital root " + results [2].out) else print ("Error in the calculation of the digital root of " + digital_root_test_values [i].out + ". Expected value: " + digital_root_expected_result [i].out + ", produced value: " + results [2].out) end i := i + 1 end end
compute_digital_root (a_number: INTEGER_64; a_base: INTEGER): ARRAY [INTEGER_64] -- Returns additive persistence and digital root of `a_number' using `a_base'. require
valid_number: a_number >= 0
valid_base: a_base > 1
local
temp_num: INTEGER_64 do create Result.make_filled (0, 1, 2) from Result [2] := a_number until Result [2] < a_base loop from temp_num := Result [2] Result [2] := 0 until temp_num = 0 loop Result [2] := Result [2] + (temp_num \\ a_base) temp_num := temp_num // a_base end Result [1] := Result [1] + 1 end end </lang>
Erlang
Using Sum_digits_of_an_integer. <lang Erlang>-module( digital_root ).
-export( [task/0] ).
task() ->
Ns = [N || N <- [627615, 39390, 588225, 393900588225]],
Persistances = [persistance_root(X) || X <- Ns],
[io:fwrite("~p has additive persistence ~p and digital root of ~p~n", [X, Y, Z]) || {X, {Y, Z}} <- lists:zip(Ns, Persistances)].
persistance_root( X ) -> persistance_root( sum_digits:sum_digits(X), 1 ).
persistance_root( X, N ) when X < 10 -> {N, X}; persistance_root( X, N ) -> persistance_root( sum_digits:sum_digits(X), N + 1 ). </lang>
- Output:
11> digital_root:task(). 627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9
Fortran
<lang Fortran> program prec implicit none integer(kind=16) :: i i = 627615 call root_pers(i) i = 39390 call root_pers(i) i = 588225 call root_pers(i) i = 393900588225 call root_pers(i) end program
subroutine root_pers(i) implicit none integer(kind=16) :: N, s, a, i write(*,*) 'Number: ', i n = i a = 0 do while(n.ge.10)
a = a + 1 s = 0 do while(n.gt.0) s = s + n-int(real(n,kind=8)/10.0D0,kind=8) * 10_8 n = int(real(n,kind=16)/real(10,kind=8),kind=8) end do n = s
end do write(*,*) 'digital root = ', s write(*,*) 'additive persistance = ', a end subroutine </lang>
Number: 627615 digital root = 9 additive persistance = 2 Number: 39390 digital root = 6 additive persistance = 2 Number: 588225 digital root = 3 additive persistance = 2 Number: 393900588225 digital root = 9 additive persistance = 2
Forth
This is trivial to do in Forth, because radix control is one of its most prominent feature. The 32-bits version just takes two lines: <lang forth>: (Sdigit) 0 swap begin base @ /mod >r + r> dup 0= until drop ;
- digiroot 0 swap begin (Sdigit) >r 1+ r> dup base @ < until ;</lang>
This will take care of most numbers:
627615 digiroot . . 9 2 ok 39390 digiroot . . 6 2 ok 588225 digiroot . . 3 2 ok
For the last one we will need a "double number" version. MU/MOD is not available in some Forth implementations, but it is easy to define: <lang forth>[UNDEFINED] mu/mod [IF] : mu/mod >r 0 r@ um/mod r> swap >r um/mod r> ; [THEN]
- (Sdigit) 0. 2swap begin base @ mu/mod 2>r s>d d+ 2r> 2dup d0= until 2drop ;
- digiroot 0 -rot begin (Sdigit) 2>r 1+ 2r> 2dup base @ s>d d< until d>s ;</lang>
That one will take care of the last one:
393900588225. digiroot . . 9 2 ok
Go
With function Sum from Sum digits of an integer#Go.
<lang go>package main
import ( "fmt" "log" "strconv" )
func Sum(i uint64, base int) (sum int) { b64 := uint64(base) for ; i > 0; i /= b64 { sum += int(i % b64) } return }
func DigitalRoot(n uint64, base int) (persistence, root int) { root = int(n) for x := n; x >= uint64(base); x = uint64(root) { root = Sum(x, base) persistence++ } return }
// Normally the below would be moved to a *_test.go file and // use the testing package to be runnable as a regular test.
var testCases = []struct { n string base int persistence int root int }{ {"627615", 10, 2, 9}, {"39390", 10, 2, 6}, {"588225", 10, 2, 3}, {"393900588225", 10, 2, 9}, {"1", 10, 0, 1}, {"11", 10, 1, 2}, {"e", 16, 0, 0xe}, {"87", 16, 1, 0xf}, // From Applesoft BASIC example: {"DigitalRoot", 30, 2, 26}, // 26 is Q base 30 // From C++ example: {"448944221089", 10, 3, 1}, {"7e0", 16, 2, 0x6}, {"14e344", 16, 2, 0xf}, {"d60141", 16, 2, 0xa}, {"12343210", 16, 2, 0x1}, // From the D example: {"1101122201121110011000000", 3, 3, 1}, }
func main() { for _, tc := range testCases { n, err := strconv.ParseUint(tc.n, tc.base, 64) if err != nil { log.Fatal(err) } p, r := DigitalRoot(n, tc.base) fmt.Printf("%12v (base %2d) has additive persistence %d and digital root %s\n", tc.n, tc.base, p, strconv.FormatInt(int64(r), tc.base)) if p != tc.persistence || r != tc.root { log.Fatalln("bad result:", tc, p, r) } } }</lang>
- Output:
627615 (base 10) has additive persistence 2 and digital root 9
39390 (base 10) has additive persistence 2 and digital root 6
588225 (base 10) has additive persistence 2 and digital root 3
393900588225 (base 10) has additive persistence 2 and digital root 9
1 (base 10) has additive persistence 0 and digital root 1
11 (base 10) has additive persistence 1 and digital root 2
e (base 16) has additive persistence 0 and digital root e
87 (base 16) has additive persistence 1 and digital root f
DigitalRoot (base 30) has additive persistence 2 and digital root q
448944221089 (base 10) has additive persistence 3 and digital root 1
7e0 (base 16) has additive persistence 2 and digital root 6
14e344 (base 16) has additive persistence 2 and digital root f
d60141 (base 16) has additive persistence 2 and digital root a
12343210 (base 16) has additive persistence 2 and digital root 1
1101122201121110011000000 (base 3) has additive persistence 3 and digital root 1
Haskell
<lang haskell>import Data.List (unfoldr)
digSum base = sum . unfoldr f where
f 0 = Nothing
f n = Just (r,q) where (q,r) = n `divMod` base
digRoot base = head . dropWhile ((>= base).snd) . zip [0..] . iterate (digSum base)
main = do putStrLn "in base 10:" mapM_ print $ map (\x -> (x, digRoot 10 x)) [627615, 39390, 588225, 393900588225]</lang>
- Output:
in base 10: (627615,(2,9)) (39390,(2,6)) (588225,(2,3)) (393900588225,(2,9))
<lang haskell>import Data.List (elemIndex, unfoldr) import Data.Maybe (fromJust) import Numeric (readInt, showIntAtBase)
-- Return a pair consisting of the additive persistence and digital root of a -- base b number. digRoot :: Integer -> Integer -> (Integer, Integer) digRoot b = find . zip [0..] . iterate (sum . toDigits b)
where find = head . dropWhile ((>= b) . snd)
-- Print the additive persistence and digital root of a base b number (given as -- a string). printDigRoot :: Integer -> String -> IO () printDigRoot b s = do
let (p, r) = digRoot b $ strToInt b s putStrLn $ s ++ ": additive persistence " ++ show p ++ ", digital root " ++ intToStr b r
-- -- Utility methods for dealing with numbers in different bases. --
-- Convert a base b number to a list of digits, from least to most significant. toDigits :: Integral a => a -> a -> [a] toDigits b = unfoldr f
where f 0 = Nothing
f n = Just (r,q) where (q,r) = n `quotRem` b
-- A list of digits, for bases up to 36. digits :: String digits = ['0'..'9'] ++ ['A'..'Z']
-- Return a number's base b string representation. intToStr :: (Integral a, Show a) => a -> a -> String intToStr b n | b < 2 || b > 36 = error "intToStr: base must be in [2..36]"
| otherwise = showIntAtBase b (digits !!) n ""
-- Return the number for the base b string representation. strToInt :: Integral a => a -> String -> a strToInt b = fst . head . readInt b (`elem` digits)
(fromJust . (`elemIndex` digits))
main :: IO () main = do
printDigRoot 2 "1001100111011110" printDigRoot 3 "2000000220" printDigRoot 8 "5566623376301" printDigRoot 10 "39390" printDigRoot 16 "99DE" printDigRoot 36 "50YE8N29" printDigRoot 36 "37C71GOYNYJ25M3JTQQVR0FXUK0W9QM71C1LVN"</lang>
- Output:
1001100111011110: additive persistence 3, digital root 1 2000000220: additive persistence 2, digital root 2 5566623376301: additive persistence 3, digital root 4 39390: additive persistence 2, digital root 6 99DE: additive persistence 2, digital root F 50YE8N29: additive persistence 2, digital root P 37C71GOYNYJ25M3JTQQVR0FXUK0W9QM71C1LVN: additive persistence 2, digital root N
Icon and Unicon
The following works in both languages: <lang unicon>procedure main(A)
every m := n := integer(!A) do {
ap := 0
while (*n > 1) do (ap +:= 1, n := sumdigits(n))
write(m," has additive persistence of ",ap," and digital root of ",n)
}
end
procedure sumdigits(n)
s := 0 n ? while s +:= move(1) return s
end</lang>
- Sample run:
->dr 627615 39390 588225 393900588225 627615 has additive persistence of 2 and digital root of 9 39390 has additive persistence of 2 and digital root of 6 588225 has additive persistence of 2 and digital root of 3 393900588225 has additive persistence of 2 and digital root of 9 ->
J
<lang J>digrot=: +/@(#.inv~&10)^:_ addper=: _1 + [: # +/@(#.inv~&10)^:a:</lang>
Example use:
<lang J> (, addper, digrot)&> 627615 39390 588225 393900588225
627615 2 9
39390 2 6
588225 2 3
393900588225 2 9</lang>
Here's an equality operator for comparing these digital roots:
<lang J>equals=: =&(9&|)"0</lang>
table of results:
<lang J> equals table i. 10 ┌──────┬───────────────────┐ │equals│0 1 2 3 4 5 6 7 8 9│ ├──────┼───────────────────┤ │0 │1 0 0 0 0 0 0 0 0 1│ │1 │0 1 0 0 0 0 0 0 0 0│ │2 │0 0 1 0 0 0 0 0 0 0│ │3 │0 0 0 1 0 0 0 0 0 0│ │4 │0 0 0 0 1 0 0 0 0 0│ │5 │0 0 0 0 0 1 0 0 0 0│ │6 │0 0 0 0 0 0 1 0 0 0│ │7 │0 0 0 0 0 0 0 1 0 0│ │8 │0 0 0 0 0 0 0 0 1 0│ │9 │1 0 0 0 0 0 0 0 0 1│ └──────┴───────────────────┘</lang>
If digital roots other than 10 are desired, the modifier ~&10 can be removed from the above definitions, and the base can be supplied as a left argument. Since this is a simplification, these definitions are shown here:
<lang J>digrt=: +/@(#.inv)^:_ addpr=: _1 + [: # +/@(#.inv)^:a:</lang>
Note that these routines merely calculate results, which are numbers. If you want the result to be displayed in some other base converting the result from numbers to character strings needs an additional step. Since that's currently not a part of the task, this is left as an exercise for the reader.
Java
- Code:
<lang java>import java.math.BigInteger;
class DigitalRoot {
public static int[] calcDigitalRoot(String number, int base)
{
BigInteger bi = new BigInteger(number, base);
int additivePersistence = 0;
if (bi.signum() < 0)
bi = bi.negate();
BigInteger biBase = BigInteger.valueOf(base);
while (bi.compareTo(biBase) >= 0)
{
number = bi.toString(base);
bi = BigInteger.ZERO;
for (int i = 0; i < number.length(); i++)
bi = bi.add(new BigInteger(number.substring(i, i + 1), base));
additivePersistence++;
}
return new int[] { additivePersistence, bi.intValue() };
}
public static void main(String[] args)
{
for (String arg : args)
{
int[] results = calcDigitalRoot(arg, 10);
System.out.println(arg + " has additive persistence " + results[0] + " and digital root of " + results[1]);
}
}
}</lang>
- Example:
java DigitalRoot 627615 39390 588225 393900588225 627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9
jq
digital_root(n) is defined here for decimals and strings representing decimals. <lang jq>def do_until(condition; next):
def u: if condition then . else (next|u) end; u;
- n may be a decimal number or a string representing a decimal number
def digital_root(n):
# string-only version
def dr:
# state: [mdr, persist]
do_until( .[0] | length == 1;
[ (.[0] | explode | map(.-48) | add | tostring), .[1] + 1 ]
);
[n|tostring, 0] | dr | .[0] |= tonumber;
def neatly:
. as $in | range(0;length) | "\(.): \($in[.])";
def rjust(n): tostring | (n-length)*" " + .;</lang> Examples: <lang jq>(
" i : [DR, P]", (961038, 923594037444, 670033, 448944221089 ) as $i | "\($i|rjust(12)): \(digital_root($i))"
),
"", "digital_root(\"1\" * 100000) => \(digital_root( "1" * 100000))"</lang>
- Output:
<lang sh>$ jq -M -n -r -c -f Digital_root.jq
i : [DR, P]
961038: [9,2]
923594037444: [9,2]
670033: [1,3]
448944221089: [1,3]
digital_root("1" * 100000) => [1,2]</lang>
Lua
With function sum_digits from [2] <lang lua>function digital_root(n, base)
p = 0
while n > 9.5 do
n = sum_digits(n, base)
p = p + 1
end
return n, p
end
print(digital_root(627615, 10)) print(digital_root(39390, 10)) print(digital_root(588225, 10)) print(digital_root(393900588225, 10))</lang>
- Output:
9 2 6 2 3 2 9 2
Mathematica
<lang Mathematica>seq[n_, b_] := FixedPointList[Total[IntegerDigits[#, b]] &, n]; root[n_Integer, base_: 10] := If[base == 10, #, BaseForm[#, base]] &[Last[seq[n, base]]] persistance[n_Integer, base_: 10] := Length[seq[n, base]] - 2;</lang>
- Output:
root /@ {627615, 39390, 588225 , 393900, 588225, 670033, 448944221089}
{9, 6, 3, 6, 3, 1, 1}
persistance /@ {627615, 39390, 588225 , 393900, 588225, 670033, 448944221089}
{2, 2, 2, 2, 2, 3, 3}
root[16^^14E344, 16]
f
16NetRexx
<lang NetRexx>/* NetRexx ************************************************************
- Test digroot
- /
Say 'number -> digital_root persistence' test_digroot(7 ,7, 0) test_digroot(627615 ,9, 2) test_digroot(39390 ,6, 2) test_digroot(588225 ,3, 2) test_digroot(393900588225,9, 2) test_digroot(393900588225,9, 3) /* test error case */
method test_digroot(n,dx,px) static res=digroot(n) Parse res d p If d=dx & p=px Then tag='ok'
Else tag='expected:' dx px
Say n '->' d p tag
method digroot(n) static /**********************************************************************
- Compute the digital root and persistence of the given decimal number
- 19.08.2012 Walter Pachl derived from Rexx
- Bottom of Data **************************/
p=0 /* persistence */ Loop While n.length()>1 /* more than one digit in n */
s=0 /* initialize sum */ p=p+1 /* increment persistence */ Loop while n<> /* as long as there are digits */ Parse n c +1 n /* pick the first one */ s=s+c /* add to the new sum */ End n=s /* the 'new' number */ End
return n p /* return root and persistence */</lang>
- Output:
number -> digital_root persistence 7 -> 7 0 ok 627615 -> 9 2 ok 39390 -> 6 2 ok 588225 -> 3 2 ok 393900588225 -> 9 2 ok 393900588225 -> 9 2 expected: 9 3
Nimrod
<lang nimrod>import strutils
proc droot(n: int64): auto =
var x = @[n]
while x[x.high] > 10:
var s = 0'i64
for dig in $x[x.high]:
s += parseInt("" & dig)
x.add s
return (x.len - 1, x[x.high])
for n in [627615'i64, 39390'i64, 588225'i64, 393900588225'i64]:
let (a, d) = droot(n) echo align($n, 12)," has additive persistance ",a," and digital root of ",d</lang>
- Output:
627615 has additive persistance 2 and digital root of 9
39390 has additive persistance 2 and digital root of 6
588225 has additive persistance 2 and digital root of 3
393900588225 has additive persistance 2 and digital root of 9Pascal
<lang Pascal>program DigitalRoot;
{$mode objfpc}{$H+}
uses
{$IFDEF UNIX}{$IFDEF UseCThreads}
cthreads,
{$ENDIF}{$ENDIF}
SysUtils, StrUtils;
// FPC has no Big mumbers implementation, Int64 will suffice.
procedure GetDigitalRoot(Value: Int64; Base: Byte; var DRoot, Pers: Integer); var
i: Integer; DigitSum: Int64;
begin
Pers := 0;
repeat
Inc(Pers);
DigitSum := 0;
while Value > 0 do
begin
Inc(DigitSum, Value mod Base);
Value := Value div Base;
end;
Value := DigitSum;
until Value < Base;
DRoot := Value;
End;
function IntToStrBase(Value: Int64; Base: Byte):String; const
// usable up to 36-Base DigitSymbols = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXY';
begin
Result := ; while Value > 0 do begin Result := DigitSymbols[Value mod Base+1] + Result; Value := Value div Base; End;
End;
procedure Display(const Value: Int64; Base: Byte = 10); var
DRoot, Pers: Integer; StrValue: string;
begin
GetDigitalRoot(Value, Base, DRoot, Pers);
WriteLn(Format('%s(%d) has additive persistence %d and digital root %d.',
[IntToStrBase(Value, Base), Base, Pers, DRoot]));
End;
begin
WriteLn('--- Examples in 10-Base ---');
Display(627615);
Display(39390);
Display(588225);
Display(393900588225);
WriteLn('--- Examples in 16-Base ---');
Display(627615, 16);
Display(39390, 16);
Display(588225, 16);
Display(393900588225, 16);
ReadLn;
End.</lang>
- Output:
--- Examples in 10-Base --- 627615(10) has additive persistence 2 and digital root 9. 39390(10) has additive persistence 2 and digital root 6. 588225(10) has additive persistence 2 and digital root 3. 393900588225(10) has additive persistence 2 and digital root 9. --- Examples in 16-Base --- 9939F(16) has additive persistence 2 and digital root 15. 99DE(16) has additive persistence 2 and digital root 15. 8F9C1(16) has additive persistence 2 and digital root 15. 5BB64DFCC1(16) has additive persistence 2 and digital root 15.
PARI/GP
<lang parigp>dsum(n)=my(s); while(n, s+=n%10; n\=10); s additivePersistence(n)=my(s); while(n>9, s++; n=dsum(n)); s digitalRoot(n)=if(n, (n-1)%9+1, 0)</lang>
Perl
<lang perl>#!perl use strict; use warnings; use List::Util qw(sum);
my @digit = (0..9, 'a'..'z'); my %digit = map { +$digit[$_], $_ } 0 .. $#digit;
sub base {
my ($n, $b) = @_;
$b ||= 10;
die if $b > @digit;
my $result = ;
while( $n ) {
$result .= $digit[ $n % $b ];
$n = int( $n / $b );
}
reverse($result) || '0';
}
sub digi_root {
my ($n, $b) = @_;
my $inbase = base($n, $b);
my $additive_persistance = 0;
while( length($inbase) > 1 ) {
++$additive_persistance;
$n = sum @digit{split //, $inbase};
$inbase = base($n, $b);
}
$additive_persistance, $n;
}
MAIN: {
my @numbers = (5, 627615, 39390, 588225, 393900588225); my @bases = (2, 3, 8, 10, 16, 36); my $fmt = "%25s(%2s): persistance = %s, root = %2s\n";
if( eval { require Math::BigInt; 1 } ) {
push @numbers, Math::BigInt->new("5814271898167303040368".
"1039458302204471300738980834668522257090844071443085937");
}
for my $base (@bases) {
for my $num (@numbers) {
my $inbase = base($num, $base);
$inbase = 'BIG' if length($inbase) > 25;
printf $fmt, $inbase, $base, digi_root($num, $base);
}
print "\n";
}
}</lang>
- Output:
101( 2): persistance = 2, root = 1
10011001001110011111( 2): persistance = 3, root = 1
1001100111011110( 2): persistance = 3, root = 1
10001111100111000001( 2): persistance = 3, root = 1
BIG( 2): persistance = 3, root = 1
BIG( 2): persistance = 4, root = 1
12( 3): persistance = 2, root = 1
1011212221000( 3): persistance = 3, root = 1
2000000220( 3): persistance = 2, root = 2
1002212220010( 3): persistance = 3, root = 1
1101122201121110011000000( 3): persistance = 3, root = 1
BIG( 3): persistance = 4, root = 1
5( 8): persistance = 0, root = 5
2311637( 8): persistance = 3, root = 2
114736( 8): persistance = 3, root = 1
2174701( 8): persistance = 3, root = 1
5566623376301( 8): persistance = 3, root = 4
BIG( 8): persistance = 3, root = 3
5(10): persistance = 0, root = 5
627615(10): persistance = 2, root = 9
39390(10): persistance = 2, root = 6
588225(10): persistance = 2, root = 3
393900588225(10): persistance = 2, root = 9
BIG(10): persistance = 3, root = 4
5(16): persistance = 0, root = 5
9939f(16): persistance = 2, root = 15
99de(16): persistance = 2, root = 15
8f9c1(16): persistance = 2, root = 15
5bb64dfcc1(16): persistance = 2, root = 15
BIG(16): persistance = 3, root = 7
5(36): persistance = 0, root = 5
dg9r(36): persistance = 2, root = 30
ue6(36): persistance = 2, root = 15
clvl(36): persistance = 2, root = 15
50ye8n29(36): persistance = 2, root = 25
BIG(36): persistance = 3, root = 17
Perl 6
<lang perl6>sub digroot ($r, :$base = 10) {
my $root = $r.base($base);
my $persistence = 0;
while $root.chars > 1 {
$root = [+]($root.comb.map({:36($_)})).base($base);
$persistence++;
}
$root, $persistence;
}
my @testnums =
627615, 39390, 588225, 393900588225, 58142718981673030403681039458302204471300738980834668522257090844071443085937;
for 10, 8, 16, 36 -> $b {
for @testnums -> $n {
printf ":$b\<%s>\ndigital root %s, persistence %s\n\n",
$n.base($b), digroot $n, :base($b);
}
}</lang>
- Output:
:10<627615> digital root 9, persistence 2 :10<39390> digital root 6, persistence 2 :10<588225> digital root 3, persistence 2 :10<393900588225> digital root 9, persistence 2 :10<58142718981673030403681039458302204471300738980834668522257090844071443085937> digital root 4, persistence 3 :8<2311637> digital root 2, persistence 3 :8<114736> digital root 1, persistence 3 :8<2174701> digital root 1, persistence 3 :8<5566623376301> digital root 4, persistence 3 :8<10021347156245115014463623107370014314341751427033746320331121536631531505161175135161> digital root 3, persistence 3 :16<9939F> digital root F, persistence 2 :16<99DE> digital root F, persistence 2 :16<8F9C1> digital root F, persistence 2 :16<5BB64DFCC1> digital root F, persistence 2 :16<808B9CDCA526832679323BE018CC70FA62E1BF3341B251AF666B345389F4BA71> digital root 7, persistence 3 :36<DG9R> digital root U, persistence 2 :36<UE6> digital root F, persistence 2 :36<CLVL> digital root F, persistence 2 :36<50YE8N29> digital root P, persistence 2 :36<37C71GOYNYJ25M3JTQQVR0FXUK0W9QM71C1LVNCBWNRVNOJYPD> digital root H, persistence 3
Or if you are more inclined to the functional programming persuasion, you can use the ... sequence operator to calculate the values without side effects: <lang perl6>sub digroot ($r, :$base = 10) {
my &sum = { [+](.comb.map({:36($_)})).base($base) }
return .[*-1], .elems-1
given $r.base($base), &sum ... { .chars == 1 }
}</lang>
PicoLisp
<lang PicoLisp>(for N (627615 39390 588225 393900588225)
(for ((A . I) N T (sum format (chop I)))
(T (> 10 I)
(prinl N " has additive persistance " (dec A) " and digital root of " I ";") ) ) )</lang>
- Output:
627615 has additive persistance 2 and digital root of 9; 39390 has additive persistance 2 and digital root of 6; 588225 has additive persistance 2 and digital root of 3; 393900588225 has additive persistance 2 and digital root of 9;
PL/I
<lang pli> digrt: Proc Options(main);
/* REXX *************************************************************** * Test digroot **********************************************************************/
Call digrtst('7');
Call digrtst('627615');
Call digrtst('39390');
Call digrtst('588225');
Call digrtst('393900588225');
digrtst: Proc(n); Dcl n Char(100) Var; Dcl dr Pic'9'; Dcl p Dec Fixed(5); Call digroot(n,dr,p); Put Edit(n,dr,p)(skip,a,col(20),f(1),f(3)); End;
digroot: Proc(n,dr,p);
/**********************************************************************
* Compute the digital root and persistence of the given decimal number
* 27.07.2012 Walter Pachl (derived from REXX)
**********************************************************************/
Dcl n Char(100) Var;
Dcl dr Pic'9';
Dcl p Dec Fixed(5);
Dcl s Pic'(14)Z9';
Dcl v Char(100) Var;
p=0;
v=strip(n); /* copy the number */
If length(v)=1 Then
dr=v;
Else Do;
Do While(length(v)>1); /* more than one digit in v */
s=0; /* initialize sum */
p+=1; /* increment persistence */
Do i=1 To length(v); /* loop over all digits */
dig=substr(v,i,1); /* pick a digit */
s=s+dig; /* add to the new sum */
End;
/*Put Skip Data(v,p,s);*/
v=strip(s); /* the 'new' number */
End;
dr=Decimal(s,1,0);
End;
Return;
End;
strip: Proc(x) Returns(Char(100) Var);
Dcl x Char(*);
Dcl res Char(100) Var Init();
Do i=1 To length(x);
If substr(x,i,1)>' ' Then
res=res||substr(x,i,1);
End;
Return(res);
End;
End;</lang>
- Output:
7 7 0 627615 9 2 39390 6 2 588225 3 2 393900588225 9 2
Alternative: <lang PL/I>digital: procedure options (main); /* 29 April 2014 */
declare 1 pict union,
2 x picture '9999999999999',
2 d(13) picture '9';
declare ap fixed, n fixed (15);
do n = 5, 627615, 39390, 588225, 393900588225, 99999999999;
x = n;
do ap = 1 by 1 until (x < 10);
x = sum(d);
end;
put skip data (n, x, ap);
end;
end digital;</lang> Results:
N= 5 PICT.X=0000000000005 AP= 1; N= 627615 PICT.X=0000000000009 AP= 2; N= 39390 PICT.X=0000000000006 AP= 2; N= 588225 PICT.X=0000000000003 AP= 2; N= 393900588225 PICT.X=0000000000009 AP= 2; N= 99999999999 PICT.X=0000000000009 AP= 3;
PowerShell
Uses the recursive function from the 'Sum Digits of an Integer' task. <lang Powershell>function Get-DigitalRoot ($n) {
function Get-Digitalsum ($n)
{
if ($n -lt 10) {$n}
else {
($n % 10) + (Get-DigitalSum ([math]::Floor($n / 10)))
}
}
$ap = 0
do {$n = Get-DigitalSum $n; $ap++}
until ($n -lt 10)
$DigitalRoot = [pscustomobject]@{
'Sum' = $n
'Additive Persistence' = $ap
}
$DigitalRoot
}</lang> Command:
Get-DigitalRoot 65536
- Output:
Sum Additive Persistence --- -------------------- 7 2
PureBasic
<lang purebasic>; if you just want the DigitalRoot
- Procedure.q DigitalRoot(N.q) apparently will do
- i must have missed something because it seems too simple
- http://en.wikipedia.org/wiki/Digital_root#Congruence_formula
Procedure.q DigitalRoot(N.q) Protected M.q=N%9 if M=0:ProcedureReturn 9 Else :ProcedureReturn M:EndIf EndProcedure
- there appears to be a proof guarantying that Len(N$)<=1 for some X
- http://en.wikipedia.org/wiki/Digital_root#Proof_that_a_constant_value_exists
Procedure.s DigitalRootandPersistance(N.q) Protected r.s,t.s,X.q,M.q,persistance,N$=Str(N) M=DigitalRoot(N.q) ; just a test to see if we get the same DigitalRoot via the Congruence_formula
Repeat X=0:Persistance+1
For i=1 to Len(N$) ; finding X as the sum of the digits of N X+Val(Mid(N$,i,1)) Next
N$=Str(X) If Len(N$)<=1:Break:EndIf ; If Len(N$)<=1:Break:EndIf Forever
If Not (X-M)=0:t.s=" Error in my logic":else:t.s=" ok":EndIf
r.s=RSet(Str(N),15)+" has additive persistance "+Str(Persistance) r.s+" and digital root of X(slow) ="+Str(X)+" M(fast) ="+Str(M)+t.s ProcedureReturn r.s EndProcedure
NewList Nlist.q() AddElement(Nlist()) : Nlist()=627615 AddElement(Nlist()) : Nlist()=39390 AddElement(Nlist()) : Nlist()=588225 AddElement(Nlist()) : Nlist()=393900588225
FirstElement(Nlist())
ForEach Nlist() N.q=Nlist()
- cw(DigitalRootandPersistance(N))
Debug DigitalRootandPersistance(N) Next</lang>
- Output:
627615 has additive persistance 2 and digital root of X(slow) =9 M(fast) =9 ok
39390 has additive persistance 2 and digital root of X(slow) =6 M(fast) =6 ok
588225 has additive persistance 2 and digital root of X(slow) =3 M(fast) =3 ok
393900588225 has additive persistance 2 and digital root of X(slow) =9 M(fast) =9 ok
Python
<lang python>def droot (n):
x = [n]
while x[-1] > 10:
x.append(sum(int(dig) for dig in str(x[-1])))
return len(x) - 1, x[-1]
for n in [627615, 39390, 588225, 393900588225]:
a, d = droot (n)
print "%12i has additive persistance %2i and digital root of %i" % (
n, a, d)</lang>
- Output:
627615 has additive persistance 2 and digital root of 9
39390 has additive persistance 2 and digital root of 6
588225 has additive persistance 2 and digital root of 3
393900588225 has additive persistance 2 and digital root of 9Racket
<lang racket>#lang racket (define/contract (additive-persistence/digital-root n (ap 0))
(->* (natural-number/c) (natural-number/c) (values natural-number/c natural-number/c))
(define/contract (sum-digits x (acc 0))
(->* (natural-number/c) (natural-number/c) natural-number/c)
(if (= x 0)
acc
(let-values (((q r) (quotient/remainder x 10)))
(sum-digits q (+ acc r)))))
(if (< n 10)
(values ap n)
(additive-persistence/digital-root (sum-digits n) (+ ap 1))))
(module+ test
(require rackunit)
(for ((n (in-list '(627615 39390 588225 393900588225)))
(ap (in-list '(2 2 2 2)))
(dr (in-list '(9 6 3 9))))
(call-with-values
(lambda () (additive-persistence/digital-root n))
(lambda (a d)
(check-equal? a ap)
(check-equal? d dr)
(printf ":~a has additive persistence ~a and digital root of ~a;~%" n a d)))))</lang>
- Output:
627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9
REXX
version 1
<lang rexx>/* REXX ***************************************************************
- Test digroot
- /
/* n r p */
say right(7 ,12) digroot(7 ) /* 7 7 0 */ say right(627615 ,12) digroot(627615 ) /* 627615 9 2 */ say right(39390 ,12) digroot(39390 ) /* 39390 6 2 */ say right(588225 ,12) digroot(588225 ) /* 588225 3 2 */ say right(393900588225,12) digroot(393900588225) /*393900588225 9 2 */
Exit
digroot: Procedure /**********************************************************************
- Compute the digital root and persistence of the given decimal number
- 25.07.2012 Walter Pachl
- Bottom of Data **************************/
Parse Arg n /* the number */ p=0 /* persistence */ Do While length(n)>1 /* more than one digit in n */
s=0 /* initialize sum */ p=p+1 /* increment persistence */ Do while n<> /* as long as there are digits */ Parse Var n c +1 n /* pick the first one */ s=s+c /* add to the new sum */ End n=s /* the 'new' number */ End
return n p /* return root and persistence */</lang>
version 2
<lang rexx>/*REXX program calculates the digital root and additive persisteance. */ numeric digits 1000 /*lets handle biguns.*/ say 'digital' /*part of the header.*/ say ' root persistence' center('number',81) /* " " " " */ say '═══════ ═══════════' center( ,81,'═') /* " " " " */ call digRoot 627615 call digRoot 39390 call digRoot 588225 call digRoot 393900588225 call digRoot 899999999999999999999999999999999999999999999999999999999999999999999999999999999 exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────DIGROOT subroutine──────────────────*/ digRoot: procedure; parse arg x 1 ox /*get the num, save as original. */
do pers=0 while length(x)\==1; r=0 /*keep summing until digRoot=1dig*/
do j=1 for length(x) /*add each digit in the number. */
r=r+substr(x,j,1) /*add a digit to the digital root*/
end /*j*/
x=r /*'new' num, it may be multi-dig.*/
end /*pers*/
say center(x,7) center(pers,11) ox /*show a nicely formatted line. */ return</lang>
- Output:
digital root persistence number ═══════ ═══════════ ═════════════════════════════════════════════════════════════════════════════════ 9 2 627615 6 2 39390 3 2 588225 9 2 393900588225 8 3 899999999999999999999999999999999999999999999999999999999999999999999999999999999
version 3
This subroutine version can handle numbers with signs, blanks, and/or decimal points. <lang rexx> ∙
∙ ∙
/*──────────────────────────────────DIGROOT subroutine──────────────────*/ digRoot: procedure; parse arg x 1 ox /*get the num, save as original. */
do pers=0 while length(x)\==1; r=0 /*keep summing until digRoot=1dig*/
do j=1 for length(x) /*add each digit in the number. */
?=substr(x,j,1) /*pick off a char, maybe a dig ? */
if datatype(?,'W') then r=r+? /*add a digit to the digital root*/
end /*j*/
x=r /*'new' num, it may be multi-dig.*/
end /*pers*/
say center(x,7) center(pers,11) ox /*show a nicely formatted line. */
return</lang>
output is the same as the 2nd version.
Ruby
<lang ruby>class String
def digroot_persistence(base=10)
num = self.to_i(base)
persistence = 0
until num < base do
num = num.to_s(base).each_char.reduce(0){|m, c| m + c.to_i(base) }
persistence += 1
end
[num.to_s(base), persistence]
end
end
puts "--- Examples in 10-Base ---" %w(627615 39390 588225 393900588225).each do |str|
puts "%12s has a digital root of %s and a persistence of %s." % [str, *str.digroot_persistence]
end puts "\n--- Examples in other Base ---" format = "%s base %s has a digital root of %s and a persistence of %s." [["101101110110110010011011111110011000001", 2],
[ "5BB64DFCC1", 16], ["5", 8], ["50YE8N29", 36]].each do |(str, base)| puts format % [str, base, *str.digroot_persistence(base)]
end</lang>
- Output:
--- Examples in 10-Base ---
627615 has a digital root of 9 and a persistence of 2.
39390 has a digital root of 6 and a persistence of 2.
588225 has a digital root of 3 and a persistence of 2.
393900588225 has a digital root of 9 and a persistence of 2.
--- Examples in other Base ---
101101110110110010011011111110011000001 base 2 has a digital root of 1 and a persistence of 3.
5BB64DFCC1 base 16 has a digital root of f and a persistence of 2.
5 base 8 has a digital root of 5 and a persistence of 0.
50YE8N29 base 36 has a digital root of p and a persistence of 2.
Run BASIC
<lang runbasic>print "Digital root of 627615 is "; digitRoot$(627615, 10) print "Digital root of 39390 is "; digitRoot$(39390, 10) print "Digital root of 588225 is "; digitRoot$(588225, 10) print "Digital root of 393900588225 is "; digitRoot$(393900588225, 10) print "Digital root of 9992 is "; digitRoot$(9992, 10) END
function digitRoot$(n,b) WHILE n >= b
c = c + 1 n = digSum(n, b)
wend digitRoot$ = n;" persistance is ";c end function
function digSum(n, b) WHILE n <> 0
q = INT(n / b) s = s + n - q * b n = q
wend digSum = s end function</lang>
- Output:
Digital root of 627615 is 9 persistance is 2 Digital root of 39390 is 6 persistance is 2 Digital root of 588225 is 3 persistance is 2 Digital root of 393900588225 is 9 persistance is 2 Digital root of 9992 is 2 persistance is 3
Scala
<lang scala>def digitalRoot(x:BigInt, base:Int=10):(Int,Int) = {
def sumDigits(x:BigInt):Int=x.toString(base) map (_.asDigit) sum def loop(s:Int, c:Int):(Int,Int)=if (s < 10) (s, c) else loop(sumDigits(s), c+1) loop(sumDigits(x), 1)
}
Seq[BigInt](627615, 39390, 588225, BigInt("393900588225")) foreach {x =>
var (s, c)=digitalRoot(x)
println("%d has additive persistance %d and digital root of %d".format(x,c,s))
} var (s, c)=digitalRoot(0x7e0, 16) println("%x has additive persistance %d and digital root of %d".format(0x7e0,c,s))</lang>
- Output:
627615 has additive persistance 2 and digital root of 9 39390 has additive persistance 2 and digital root of 6 588225 has additive persistance 2 and digital root of 3 393900588225 has additive persistance 2 and digital root of 9 7e0 has additive persistance 2 and digital root of 6
Seed7
<lang seed7>$ include "seed7_05.s7i";
include "bigint.s7i";
const func bigInteger: digitalRoot (in var bigInteger: num, in bigInteger: base, inout bigInteger: persistence) is func
result
var bigInteger: sum is 0_;
begin
persistence := 0_;
while num >= base do
sum := 0_;
while num > 0_ do
sum +:= num rem base;
num := num div base;
end while;
num := sum;
incr(persistence);
end while;
end func;
const proc: main is func
local
var bigInteger: num is 0_;
var bigInteger: root is 0_;
var bigInteger: persistence is 0_;
begin
for num range [] (627615_, 39390_, 588225_, 393900588225_) do
root := digitalRoot(num, 10_, persistence);
writeln(num <& " has additive persistence " <& persistence <& " and digital root of " <& root);
end for;
end func;</lang>
- Output:
627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9
Tcl
<lang tcl>package require Tcl 8.5 proc digitalroot num {
for {set p 0} {[string length $num] > 1} {incr p} {
set num [::tcl::mathop::+ {*}[split $num ""]]
} list $p $num
}
foreach n {627615 39390 588225 393900588225} {
lassign [digitalroot $n] p r puts [format "$n has additive persistence $p and digital root of $r"]
}</lang>
- Output:
627615 has additive persistence 2 and digital root of 9 39390 has additive persistence 2 and digital root of 6 588225 has additive persistence 2 and digital root of 3 393900588225 has additive persistence 2 and digital root of 9
Wortel
<lang wortel>@let {
sumDigits ^(@sum @arr) drootl &\@rangef [. sumDigits ^(\~>1 #@arr)] droot ^(@last drootl) apers ^(#-drootl)
[
!console.log "[number]: [digital root] [additive persistence] [intermediate sums]"
~@each [627615 39390 588225 393900588225]
&n !console.log "{n}: {!droot n} {!apers n} {@str !drootl n}"
]
}</lang>
- Output:
[number]: [digital root] [additive persistence] [intermediate sums] 627615: 9 2 [627615 27 9] 39390: 6 2 [39390 24 6] 588225: 3 2 [588225 30 3] 393900588225: 9 2 [393900588225 54 9]
XPL0
Since integers are only 32 bits, floating point is used to get the extra precision needed.
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations
func DRoot(N, B, P); \Return digital root and persistance P real N, B; int P; int S; [P(0):= 0; while N >= B do
[S:= 0;
repeat S:= S + fix(Mod(N,B)); \sum last digit
N:= N/B; \remove last digit
N:= N - Mod(N,1.);
until N < 0.1; \(beware of rounding errors)
P(0):= P(0)+1; \increment persistance
N:= float(S);
];
return fix(N); ];
real Tbl; int I, Root, Pers; [Tbl:= [627615., 39390., 588225., 393900588225.]; for I:= 0 to 4-1 do
[Root:= DRoot(Tbl(I), 10., @Pers);
IntOut(0, Pers); ChOut(0, ^ ); IntOut(0, Root); CrLf(0);
];
]</lang>
- Output:
2 9 2 6 2 3 2 9
zkl
<lang zkl>fcn sum(n,b){ n.split(b).sum(0) } fcn droot(n,b=10,X=0) // -->(digital root, additive persistence)
{ if(n<b)return(n,X); return(self.fcn(sum(n,b),b,X+1)) }</lang>
<lang zkl>droot(627615) droot(39390) droot(588225) droot(393900588225) droot(7,2) droot(0x7e0,16)</lang>
- Output:
L(9,2) //627615 L(6,2) //39390 L(3,2) //588225 L(9,2) //393900588225 L(1,3) //111 base 2: 111-->11-->10-->1 L(6,2) //7e0 base 16: 0x7e0-->0x15-->0x6
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