Population count: Difference between revisions
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The <code>system</code> unit in the RTL (run-time library) shipped with every FPC (Free Pascal compiler) distribution contains the function <code>popCnt</code>. |
The <code>system</code> unit in the RTL (run-time library) shipped with every FPC (Free Pascal compiler) distribution contains the function <code>popCnt</code>. |
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It accepts one integer parameter and is defined for all unsigned integer types. |
It accepts one integer parameter and is defined for all unsigned integer types. |
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Therefore its implementation is skipped. |
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<lang pascal>program populationCount(input, output, stdErr); |
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var |
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// general advice: iterator variables are _signed_ |
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iterator: int64; |
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// the variable we’d like to count the set bits in |
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number: qWord; |
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// how many evil numbers we’ve already found |
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evilCount: int64; |
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// odious numbers |
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odiousNumber: array[1..30] of qWord; |
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odiousIterator: int64; |
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begin |
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// population count for powers of three |
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for iterator := 0 to 29 do |
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begin |
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number := round(exp(ln(3) * iterator)); |
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write(popCnt(number):3); |
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end; |
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writeLn(); |
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// evil numbers |
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// (while preserving calculated odious numbers for next sub-task) |
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evilCount := 0; |
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odiousIterator := low(odiousNumber); |
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// for-loop: because we (pretend to) don’t know, |
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// when and where we’ve found the first 30 numbers of each |
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for iterator := 0 to high(iterator) do |
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begin |
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// implicit typecast: popCnt only accepts _un_-signed integers |
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number := iterator; |
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if odd(popCnt(number)) then |
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begin |
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if odiousIterator <= high(odiousNumber) then |
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begin |
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odiousNumber[odiousIterator] := number; |
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inc(odiousIterator); |
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end; |
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end |
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else |
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begin |
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if evilCount < 30 then |
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begin |
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write(number:20); |
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inc(evilCount); |
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end; |
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end; |
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if evilCount + odiousIterator > 60 then |
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begin |
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break; |
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end; |
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end; |
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writeLn(); |
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// odious numbers |
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for number in odiousNumber do |
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begin |
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write(number:20); |
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end; |
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writeLn(); |
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end.</lang> |
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{{out}} |
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<pre> 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 |
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0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 |
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1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59</pre> |
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=={{header|Gambas}}== |
=={{header|Gambas}}== |
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Revision as of 16:14, 9 September 2019
You are encouraged to solve this task according to the task description, using any language you may know.
The population count is the number of 1s (ones) in the binary representation of a non-negative integer.
Population count is also known as pop count, popcount, sideways sum, and Hamming weight.
- For example, 5 (which is 101 in binary) has a population count of 2.
Evil numbers are non-negative integers that have an even population count.
Odious numbers are positive integers that have an odd population count.
- Task
- write a function (or routine) to return the population count of a non-negative integer.
- all computation of the lists below should start with 0 (zero indexed).
- display the pop count of the 1st thirty powers of 3 (30, 31, 32, 33, 34, ∙∙∙ 329).
- display the 1st thirty evil numbers.
- display the 1st thirty odious numbers.
- display each list of integers on one line (which may or may not include a title), each set of integers being shown should be properly identified.
- See also
- The On-Line Encyclopedia of Integer Sequences: A000069 odious numbers.
- The On-Line Encyclopedia of Integer Sequences: A001969 evil numbers.
360 Assembly
Use of the old " Unnormalized Double Floating Point" feature, a bit forgotten, to have 56-bit integers. And also use of ICM (Insert Characters Under Mask) and TM (Test under Mask) to handle bits.
Let's note:
- in Normalized Double Floating Point, one is implemented X'4110000000000000'
- in Unnormalized Double Floating Point, one is implemented X'4E00000000000001'
<lang 360asm>* Population count 09/05/2019
POPCNT CSECT
USING POPCNT,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
SAVE (14,12) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LD F0,UN 1
STD F0,BB bb=1
MVC PG(7),=C'pow 3:' init buffer
L R10,NN nn
BCTR R10,0 nn-1
LA R9,PG+7 @pg
LA R6,0 i=0
DO WHILE=(CR,R6,LE,R10) do i=0 to nn-1
LM R0,R1,BB r0r1=bb
BAL R14,POPCOUNT call popcount(bb)
LR R1,R0 popcount(bb)
XDECO R1,XDEC edit popcount(bb)
MVC 0(3,R9),XDEC+9 output popcount(bb)
LD F0,BB bb
AW F0,BB bb*2
AW F0,BB bb*3
STD F0,BB bb=bb*3
LA R9,3(R9) @pg
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
SR R7,R7 j=0
DO WHILE=(C,R7,LE,=F'1') do j=0 to 1
MVC PG,=CL132' ' clear buffer
IF LTR,R7,Z,R7 THEN if j=0 then
MVC PG(7),=C'evil: ' init buffer
ELSE , else
MVC PG(7),=C'odious:' init buffer
ENDIF , endif
LA R9,PG+7 @pg
SR R8,R8 n=0
SR R6,R6 i=0
DO WHILE=(C,R8,LT,NN) do i=0 by 1 while(n<nn)
XR R0,R0 r0=0
LR R1,R6 r1=i
BAL R14,POPCOUNT r0=popcount(i)
SRDA R0,32 ~
D R0,=F'2' popcount(i)/2
IF CR,R0,EQ,R7 THEN if popcount(i)//2=j then
LA R8,1(R8) n=n+1
XDECO R6,XDEC edit i
MVC 0(3,R9),XDEC+9 output i
LA R9,3(R9) @pg
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
LA R7,1(R7) j++
ENDDO , enddo j
L R13,4(0,R13) restore previous savearea pointer
RETURN (14,12),RC=0 restore registers from calling sav
- ------- ---- ------------------
POPCOUNT EQU * popcount(x)
ICM R0,B'1000',=X'00' zap exponant part
XR R3,R3 y=0
LA R4,56 mantissa size = 56
LOOP STC R1,CC do i=1 to 56
TM CC,X'01' if bit(x,i)=1
BNO NOTONE then{
LA R3,1(R3) y++}
NOTONE SRDA R0,1 shift right double arithmetic
BCT R4,LOOP enddo i
LR R0,R3 return(y)
BR R14 return
- ------- ---- ------------------
NN DC F'30' nn=30 BB DS D bb UN DC X'4E00000000000001' un=1 (unnormalized) PG DC CL132' ' buffer XDEC DS CL12 temp for xdeco CC DS C
REGEQU
END POPCNT </lang>
- Output:
pow 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Ada
Specification and implementation of an auxiliary package "Population_Count". The same package is used for Pernicious numbers#Ada
<lang ada>with Interfaces;
package Population_Count is
subtype Num is Interfaces.Unsigned_64; function Pop_Count(N: Num) return Natural;
end Population_Count;</lang>
<lang Ada>package body Population_Count is
function Pop_Count(N: Num) return Natural is
use Interfaces;
K5555: constant Unsigned_64 := 16#5555555555555555#;
K3333: constant Unsigned_64 := 16#3333333333333333#;
K0f0f: constant Unsigned_64 := 16#0f0f0f0f0f0f0f0f#;
K0101: constant Unsigned_64 := 16#0101010101010101#;
X: Unsigned_64 := N;
begin
X := X - (Shift_Right(X, 1) and k5555);
X := (X and k3333) + (Shift_Right(X, 2) and k3333);
X := (X + (Shift_Right(X, 4)) and K0f0f);
X := Shift_Right((x * k0101), 56);
return Natural(X);
end Pop_Count;
end Population_Count;</lang>
The main program:
<lang Ada>with Ada.Text_IO, Population_Count; use Ada.Text_IO; use Population_Count;
procedure Test_Pop_Count is
X: Num; use type Num;
begin
Put("Pop_Cnt(3**i):"); -- print pop_counts of powers of three
X := 1; -- X=3**0
for I in 1 .. 30 loop
Put(Natural'Image(Pop_Count(X)));
X := X * 3;
end loop;
New_Line;
Put("Evil: "); -- print first thirty evil numbers
X := 0;
for I in 1 .. 30 loop
while Pop_Count(X) mod 2 /= 0 loop -- X is not evil
X := X + 1;
end loop;
Put(Num'Image(X));
X := X + 1;
end loop;
New_Line;
Put("Odious: "); -- print thirty oudous numbers
X := 1;
for I in 1 .. 30 loop
while Pop_Count(X) mod 2 /= 1 loop -- X is not odious
X := X + 1;
end loop;
Put(Num'Image(X));
X := X + 1;
end loop;
New_Line;
end Test_Pop_Count;</lang>
- Output:
Pop_Cnt(3**i): 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
ALGOL 68
<lang algol68># returns the population count (number of bits on) of the non-negative #
- integer n #
PROC population count = ( LONG INT n )INT:
BEGIN
LONG INT number := n;
INT result := 0;
WHILE number > 0 DO
IF ODD number THEN result +:= 1 FI;
number OVERAB 2
OD;
result
END # population # ;
- population count of 3^0, 3^1, 3*2, ..., 3^29 #
LONG INT power of three := 1; print( ( "3^x pop counts:" ) ); FOR power FROM 0 TO 29 DO
print( ( " ", whole( population count( power of three ), 0 ) ) ); power of three *:= 3
OD; print( ( newline ) );
- print the first thirty evil numbers (even population count) #
INT evil count := 0; print( ( "evil numbers :" ) ); FOR n FROM 0 WHILE evil count < 30 DO
IF NOT ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
evil count +:= 1
FI
OD; print( ( newline ) );
- print the first thirty odious numbers (odd population count) #
INT odious count := 0; print( ( "odious numbers:" ) ); FOR n WHILE odious count < 30 DO
IF ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
odious count +:= 1
FI
OD; print( ( newline ) ) </lang>
- Output:
3^x pop counts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil numbers : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
ALGOL W
<lang algolw>begin
% returns the population count (number of bits on) of the non-negative integer n %
integer procedure populationCount( integer value n ) ;
begin
integer v, count;
v := n;
count := 0;
while v > 0 do begin
if odd( v ) then count := count + 1;
v := v div 2
end while_v_gt_0 ;
count
end populationCount ;
% returns the sum of population counts of the elements of the array n %
% the bounds of n must be 1 :: length %
integer procedure arrayPopulationCount( integer array n ( * ); integer value length ) ;
begin
integer count;
count := 0;
for i := 1 until length do count := count + populationCount( n( i ) );
count
end arrayPopulationCount ;
begin %task requirements %
integer array power( 1 :: 8 );
integer n, count, carry;
% population counts of the first 30 powers of three %
% Algol W integers are 32-bit, so we simulate 64-bit with an array of integers %
% the only operation we need is multiplication by 3 %
% we use 8 bits of each number %
% start with 3^0, which is 1 %
for i := 1 until 8 do power( i ) := 0;
power( 1 ) := 1;
write( i_w := 1, s_w := 0, "3^x population: ", arrayPopulationCount( power, 8 ) );
for p := 1 until 29 do begin
carry := 0;
for b := 1 until 8 do begin
integer bValue;
bValue := ( power( b ) * 3 ) + carry;
carry := bValue div 256;
power( b ) := bValue rem 256
end for_b ;
writeon( i_w := 1, s_w := 0, " ", arrayPopulationCount( power, 8 ) )
end for_p ;
% evil numbers (even population count) %
write( "evil numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if not odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_not_odd_populationCount ;
n := n + 1
end evil_numbers_loop ;
% odious numbers (odd population count %
write( "odious numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_odd_populationCount ;
n := n + 1
end odious_numbers_loop
end
end.</lang>
- Output:
3^x population: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
AppleScript
<lang AppleScript>-- popCount :: Int -> Int on popCount(n)
script bitSum
on |λ|(a, x)
a + (x as integer)
end |λ|
end script
foldl(bitSum, 0, characters of showIntAtBase(n, 2))
end popCount
-- TEST -----------------------------------------------------------------------
on run
script powerOfThreePopCount
on |λ|(x)
popCount(3 ^ x)
end |λ|
end script
script popCountisEven
on |λ|(x)
popCount(x) mod 2 = 0
end |λ|
end script
{popCounts:¬
map(powerOfThreePopCount, enumFromTo(0, 30)), evenThenOdd:¬
partition(popCountisEven, enumFromTo(0, 59))}
end run
-- GENERIC FUNCTIONS ----------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- partition :: predicate -> List -> (Matches, nonMatches) -- partition :: (a -> Bool) -> [a] -> ([a], [a]) on partition(f, xs)
tell mReturn(f)
set lst to {{}, {}}
repeat with x in xs
set v to contents of x
set end of item ((|λ|(v) as integer) + 1) of lst to v
end repeat
end tell
{item 2 of lst, item 1 of lst}
end partition
-- showIntAtBase :: Int -> Int -> String on showIntAtBase(n, base)
if base > 1 then
if n > 0 then
set m to n mod base
set r to n - m
if r > 0 then
set prefix to showIntAtBase(r div base, base)
else
set prefix to ""
end if
if m < 10 then
set baseCode to 48 -- "0"
else
set baseCode to 55 -- "A" - 10
end if
prefix & character id (baseCode + m)
else
"0"
end if
else
missing value
end if
end showIntAtBase</lang>
- Output:
<lang AppleScript>{popCounts: {1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25}, evenThenOdd: {{0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58}, {1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59}}}</lang>
AutoHotkey
<lang AutoHotkey>Loop, 30 Out1 .= PopCount(3 ** (A_Index - 1)) " " Loop, 60 i := A_Index - 1 , PopCount(i) & 0x1 ? Out3 .= i " " : Out2 .= i " " MsgBox, % "3^x:`t" Out1 "`nEvil:`t" Out2 "`nOdious:`t" Out3
PopCount(x) { ;https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation x -= (x >> 1) & 0x5555555555555555 , x := (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333) , x := (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f return (x * 0x0101010101010101) >> 56 }</lang>
- Output:
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
C
<lang c>#include <stdio.h>
int main() {
{
unsigned long long n = 1;
for (int i = 0; i < 30; i++) {
// __builtin_popcount() for unsigned int
// __builtin_popcountl() for unsigned long
// __builtin_popcountll() for unsigned long long
printf("%d ", __builtin_popcountll(n));
n *= 3;
}
printf("\n");
}
int od[30];
int ne = 0, no = 0;
printf("evil : ");
for (int n = 0; ne+no < 60; n++) {
if ((__builtin_popcount(n) & 1) == 0) {
if (ne < 30) {
printf("%d ", n); ne++;
}
} else {
if (no < 30) {
od[no++] = n;
}
}
}
printf("\n");
printf("odious: ");
for (int i = 0; i < 30; i++) {
printf("%d ", od[i]);
}
printf("\n");
return 0;
}</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
GCC's builtin doesn't exist prior to 3.4, and the LL version is broken in 3.4 to 4.1. In 4.2+, if the platform doesn't have a good popcount instruction or isn't enabled (e.g. not compiled with -march=native), it typically emits unoptimized code which is over 2x slower than the C below. Alternative:
<lang c>#if defined(__POPCNT__) && defined(__GNUC__) && (__GNUC__> 4 || (__GNUC__== 4 && __GNUC_MINOR__> 1))
- define HAVE_BUILTIN_POPCOUNTLL
- endif
static uint64_t bitcount64(uint64_t b) {
b -= (b >> 1) & 0x5555555555555555; b = (b & 0x3333333333333333) + ((b >> 2) & 0x3333333333333333); b = (b + (b >> 4)) & 0x0f0f0f0f0f0f0f0f; return (b * 0x0101010101010101) >> 56;
} /* For 32-bit, an 8-bit table may or may not be a little faster */ static uint32_t bitcount32(uint32_t b) {
b -= (b >> 1) & 0x55555555; b = (b & 0x33333333) + ((b >> 2) & 0x33333333); b = (b + (b >> 4)) & 0x0f0f0f0f; return (b * 0x01010101) >> 24;
}</lang>
C++
<lang cpp>#include <iostream>
- include <bitset>
- include <climits>
size_t popcount(unsigned long long n) {
return std::bitset<CHAR_BIT * sizeof n>(n).count();
}
int main() {
{
unsigned long long n = 1;
for (int i = 0; i < 30; i++) {
std::cout << popcount(n) << " ";
n *= 3;
}
std::cout << std::endl;
}
int od[30];
int ne = 0, no = 0;
std::cout << "evil : ";
for (int n = 0; ne+no < 60; n++) {
if ((popcount(n) & 1) == 0) {
if (ne < 30) {
std::cout << n << " "; ne++;
}
} else {
if (no < 30) {
od[no++] = n;
}
}
}
std::cout << std::endl;
std::cout << "odious: ";
for (int i = 0; i < 30; i++) {
std::cout << od[i] << " ";
}
std::cout << std::endl;
return 0;
}</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
C#
<lang csharp> using System; using System.Linq;
namespace PopulationCount {
class Program
{
private static int PopulationCount(long n)
{
string binaryn = Convert.ToString(n, 2);
return binaryn.ToCharArray().Where(t => t == '1').Count();
}
static void Main(string[] args)
{
Console.WriteLine("Population Counts:");
Console.Write("3^n : ");
int count = 0;
while (count < 30)
{
double n = Math.Pow(3f, (double)count);
int popCount = PopulationCount((long)n);
Console.Write(string.Format("{0} ", popCount));
count++;
}
Console.WriteLine();
Console.Write("Evil: ");
count = 0;
int i = 0;
while (count < 30)
{
int popCount = PopulationCount(i);
if (popCount % 2 == 0)
{
count++;
Console.Write(string.Format("{0} ", i));
}
i++;
}
Console.WriteLine();
Console.Write("Odious: ");
count = 0;
i = 0;
while (count < 30)
{
int popCount = PopulationCount(i);
if (popCount % 2 != 0)
{
count++;
Console.Write(string.Format("{0} ", i));
}
i++;
}
Console.ReadKey();
}
}
} </lang>
- Output:
Population Counts: 3^n : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Common Lisp
<lang lisp>(format T "3^x: ~{~a ~}~%"
(loop for i below 30
collect (logcount (expt 3 i))))
(multiple-value-bind
(evil odious)
(loop for i below 60
if (evenp (logcount i)) collect i into evil
else collect i into odious
finally (return (values evil odious)))
(format T "evil: ~{~a ~}~%" evil)
(format T "odious: ~{~a ~}~%" odious))</lang>
- Output:
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
D
<lang d>void main() {
import std.stdio, std.algorithm, std.range, core.bitop;
enum pCount = (ulong n) => popcnt(n & uint.max) + popcnt(n >> 32);
writefln("%s\nEvil: %s\nOdious: %s",
uint.max.iota.map!(i => pCount(3L ^^ i)).take(30),
uint.max.iota.filter!(i => pCount(i) % 2 == 0).take(30),
uint.max.iota.filter!(i => pCount(i) % 2).take(30));
}</lang>
- Output:
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] Evil: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] Odious: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Elixir
<lang elixir>defmodule Population do
def count(n), do: count(<<n :: integer>>, 0)
defp count(<<>>, acc), do: acc
defp count(<<bit :: integer-1, rest :: bitstring>>, sum), do: count(rest, sum + bit) def evil?(n), do: n >= 0 and rem(count(n),2) == 0 def odious?(n), do: n >= 0 and rem(count(n),2) == 1
end
IO.puts "Population count of the first thirty powers of 3:" IO.inspect Stream.iterate(1, &(&1*3)) |> Enum.take(30) |> Enum.map(&Population.count(&1)) IO.puts "first thirty evil numbers:" IO.inspect Stream.iterate(0, &(&1+1)) |> Stream.filter(&Population.evil?(&1)) |> Enum.take(30) IO.puts "first thirty odious numbers:" IO.inspect Stream.iterate(0, &(&1+1)) |> Stream.filter(&Population.odious?(&1)) |> Enum.take(30)</lang>
- Output:
Population count of the first thirty powers of 3: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] first thirty evil numbers: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] first thirty odious numbers: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Erlang
<lang erlang>-module(population_count). -export([popcount/1]).
-export([task/0]).
popcount(N) ->
popcount(N,0).
popcount(0,Acc) ->
Acc;
popcount(N,Acc) ->
popcount(N div 2, Acc + N rem 2).
threes(_,0,Acc) ->
lists:reverse(Acc);
threes(Threes,N,Acc) ->
threes(Threes * 3, N-1, [popcount(Threes)|Acc]).
threes(N) ->
threes(1,N,[]).
evil(_,0,Acc) ->
lists:reverse(Acc);
evil(N,Count,Acc) ->
case popcount(N) rem 2 of
0 ->
evil(N+1,Count-1,[N|Acc]);
1 ->
evil(N+1,Count,Acc)
end.
evil(Count) ->
evil(0,Count,[]).
odious(_,0,Acc) ->
lists:reverse(Acc);
odious(N,Count,Acc) ->
case popcount(N) rem 2 of
1 ->
odious(N+1,Count-1,[N|Acc]);
0 ->
odious(N+1,Count,Acc)
end.
odious(Count) ->
odious(1,Count,[]).
task() ->
io:format("Powers of 3: ~p~n",[threes(30)]),
io:format("Evil:~p~n",[evil(30)]),
io:format("Odious:~p~n",[odious(30)]).</lang>
- Output:
<lang erlang>61> population_count:task(). Powers of 3: [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,
25]
Evil:[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,
51,53,54,57,58]
Odious:[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,
50,52,55,56,59]
ok</lang>
Factor
<lang factor>USING: formatting kernel lists lists.lazy math math.bits math.functions namespaces prettyprint.config sequences ; IN: rosetta-code.population-count
- pop-count ( n -- m ) make-bits [ t = ] count ;
- 3^n ( obj -- obj' ) [ 3 swap ^ pop-count ] lmap-lazy ;
- evil ( obj -- obj' ) [ pop-count even? ] lfilter ;
- odious ( obj -- obj' ) [ pop-count odd? ] lfilter ;
- pop-count-demo ( -- )
100 margin set 0 lfrom [ 3^n ] [ evil ] [ odious ] tri [ 30 swap ltake list>array ] tri@ "3^n: %u\nEvil: %u\nOdious: %u\n" printf ;
MAIN: pop-count-demo</lang>
- Output:
3^n: { 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 }
Evil: { 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 }
Odious: { 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59 }
Forth
<lang Forth>: popcnt ( n -- u) 0 swap
BEGIN dup WHILE tuck 1 AND + swap 1 rshift REPEAT DROP ;
- odious? ( n -- t|f) popcnt 1 AND ;
- evil? ( n -- t|f) odious? 0= ;
CREATE A 30 ,
- task1 1 0 ." 3**i popcnt: "
BEGIN dup A @ < WHILE
over popcnt . 1+ swap 3 * swap
REPEAT DROP DROP CR ;
- task2 0 0 ." evil : "
BEGIN dup A @ < WHILE
over evil? IF over . 1+ THEN swap 1+ swap
REPEAT DROP DROP CR ;
- task3 0 0 ." odious : "
BEGIN dup A @ < WHILE
over odious? IF over . 1+ THEN swap 1+ swap
REPEAT DROP DROP CR ;
task1 task2 task3 BYE</lang>
- Output:
3**i popcnt: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Fortran
<lang fortran>program population_count
implicit none
integer, parameter :: i64 = selected_int_kind(18) integer(i64) :: x integer :: i, n x = 1 write(*, "(a8)", advance = "no") "3**i :" do i = 1, 30 write(*, "(i3)", advance = "no") popcnt(x) x = x * 3 end do
write(*,*)
write(*, "(a8)", advance = "no") "Evil :"
n = 0
x = 0
do while(n < 30)
if(mod(popcnt(x), 2) == 0) then
n = n + 1
write(*, "(i3)", advance = "no") x
end if
x = x + 1
end do
write(*,*)
write(*, "(a8)", advance = "no") "Odious :"
n = 0
x = 0
do while(n < 30)
if(mod(popcnt(x), 2) /= 0) then
n = n + 1
write(*, "(i3)", advance = "no") x
end if
x = x + 1
end do
contains
integer function popcnt(x)
integer(i64), intent(in) :: x integer :: i
popcnt = 0 do i = 0, 63 if(btest(x, i)) popcnt = popcnt + 1 end do
end function end program</lang>
- Output:
3**i : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Free Pascal
The system unit in the RTL (run-time library) shipped with every FPC (Free Pascal compiler) distribution contains the function popCnt.
It accepts one integer parameter and is defined for all unsigned integer types.
Therefore its implementation is skipped.
<lang pascal>program populationCount(input, output, stdErr);
var
// general advice: iterator variables are _signed_
iterator: int64;
// the variable we’d like to count the set bits in
number: qWord;
// how many evil numbers we’ve already found
evilCount: int64;
// odious numbers
odiousNumber: array[1..30] of qWord;
odiousIterator: int64;
begin
// population count for powers of three
for iterator := 0 to 29 do
begin
number := round(exp(ln(3) * iterator));
write(popCnt(number):3);
end;
writeLn();
// evil numbers // (while preserving calculated odious numbers for next sub-task) evilCount := 0; odiousIterator := low(odiousNumber);
// for-loop: because we (pretend to) don’t know, // when and where we’ve found the first 30 numbers of each for iterator := 0 to high(iterator) do begin // implicit typecast: popCnt only accepts _un_-signed integers number := iterator; if odd(popCnt(number)) then begin if odiousIterator <= high(odiousNumber) then begin odiousNumber[odiousIterator] := number; inc(odiousIterator); end; end else begin if evilCount < 30 then begin write(number:20); inc(evilCount); end; end;
if evilCount + odiousIterator > 60 then begin break; end; end; writeLn();
// odious numbers for number in odiousNumber do begin write(number:20); end; writeLn(); end.</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Gambas
Click this link to run this code <lang gambas>Public Sub Main() Dim sEvil, sOdious As String 'To store the output for printing Evil and Odious Dim iCount, iEvil, iOdious As Integer 'Counters
Print "First 30 numbers ^3\t"; 'Print title
For iCount = 0 To 29 'Count 30 times
Print Len(Replace(Bin(3 ^ iCount), "0", ""));; 'Get the Bin of the number, take out the '0's and the remaining
Next 'length is the Population count e.g. 3^2=9, Bin=1001, remove '0's='11', length=2
iCount = 0 'Reset iCount
Repeat 'Repeat/Until loop
If Even(Len(Replace(Bin(iCount), "0", ""))) Then 'If (as above) the result is Even then sEvil &= Str(icount) & " " 'Add it to sEvil Inc iEvil 'Increase iEvil End If If Odd(Len(Replace(Bin(iCount), "0", ""))) Then 'If (as above) the result is Odd then sOdious &= Str(icount) & " " 'Add it to sOdious Inc iOdious 'Increase iOdious End If Inc iCount 'Increase iCount
Until iEvil = 30 And iOdious = 30 'Until both iEvil and iOdious = 30 then exit the loop
Print "\n1st 30 Evil numbers =\t" & sEvil 'Print Evil Print "1st 30 Odious numbers =\t" & sOdious 'Print Odious
End</lang> Output:
First 30 numbers ^3 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 1st 30 Evil numbers = 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 1st 30 Odious numbers = 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Go
Standard Library
As of Go 1.9, this function is in the standard Library. <lang go>package main
import (
"fmt" "math/bits"
)
func main() {
fmt.Println("Pop counts, powers of 3:")
n := uint64(1) // 3^0
for i := 0; i < 30; i++ {
fmt.Printf("%d ", bits.OnesCount64(n))
n *= 3
}
fmt.Println()
fmt.Println("Evil numbers:")
var od [30]uint64
var ne, no int
for n = 0; ne+no < 60; n++ {
if bits.OnesCount64(n)&1 == 0 {
if ne < 30 {
fmt.Printf("%d ", n)
ne++
}
} else {
if no < 30 {
od[no] = n
no++
}
}
}
fmt.Println()
fmt.Println("Odious numbers:")
for _, n := range od {
fmt.Printf("%d ", n)
}
fmt.Println()
}</lang>
- Output:
Pop counts, powers of 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Implementation
Method of WP example popcount_3: <lang go>func pop64(w uint64) int {
const (
ff = 1<<64 - 1
mask1 = ff / 3
mask3 = ff / 5
maskf = ff / 17
maskp = maskf >> 3 & maskf
)
w -= w >> 1 & mask1
w = w&mask3 + w>>2&mask3
w = (w + w>>4) & maskf
return int(w * maskp >> 56)
}</lang> Method of WP example popcount_4: <lang go>func pop64(w uint64) (c int) {
for w != 0 {
w &= w - 1
c++
}
return
}</lang>
Haskell
<lang haskell>import Data.Bits (popCount)
printPops :: (Show a, Integral a) => String -> [a] -> IO () printPops title counts = putStrLn $ title ++ show (take 30 counts)
main :: IO () main = do
printPops "popcount " $ map popCount $ iterate (*3) (1 :: Integer) printPops "evil " $ filter (even . popCount) ([0..] :: [Integer]) printPops "odious " $ filter ( odd . popCount) ([0..] :: [Integer])</lang>
- Output:
popcount [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25] evil [0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58] odious [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Or, if we want to write our own popCount, perhaps something like:
<lang haskell>import Data.List (partition, unfoldr) import Data.Bifoldable (biList) import Data.Tuple (swap) import Data.Bool (bool)
-- POPCOUNT ------------------------------------------------------------- popCount :: Int -> Int popCount =
sum . unfoldr ((bool Nothing . Just . swap . flip quotRem 2) <*> (0 <))
-- TEST ----------------------------------------------------------------- main :: IO () main =
mapM_ putStrLn $
zipWith
(\k xs -> k ++ ":\n" ++ show xs ++ "\n")
["Population count of powers of 3", "evil", "odious"]
((popCount . (3 ^) <$> [0 .. 29]) :
biList (partition (even . popCount) [0 .. 59]))</lang>
- Output:
Population count of powers of 3: [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25] evil: [0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58] odious: [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Idris
<lang Idris>module Main import Data.Vect
isOdd : (x : Int) -> Bool isOdd x = case mod x 2 of
0 => False
1 => True
popcnt : Int -> Int popcnt 0 = 0 popcnt x = case isOdd x of
False => popcnt (shiftR x 1) True => 1 + popcnt (shiftR x 1)
isOdious : Int -> Bool isOdious k = isOdd (popcnt k)
isEvil : Int -> Bool isEvil k = not (isOdious k)
filterUnfoldN : (n : Nat) ->
(pred : Int -> Bool) -> (f : Int -> a) ->
(next : Int -> Int) -> (seed : Int) ->
Vect n a
filterUnfoldN Z pred f next seed = [] filterUnfoldN (S k) pred f next seed =
if pred seed then (f seed) :: filterUnfoldN k pred f next (next seed) else filterUnfoldN (S k) pred f next (next seed)
printCompact : (Show a) => Vect n a -> IO () printCompact v = putStrLn (unwords (map show (toList v)))
main : IO () main = do putStr "popcnt(3**i): "
printCompact (filterUnfoldN 30 (\_ => True) popcnt (3 *) 1)
putStr "Evil: "
printCompact (filterUnfoldN 30 isEvil id (1 +) 0)
putStr "Odious: "
printCompact (filterUnfoldN 30 isOdious id (1 +) 0)</lang>
- Output:
popcnt(3**i): 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
J
Implementation:
<lang J>countPopln=: +/"1@#: isOdd=: 1 = 2&| isEven=: 0 = 2&|</lang>
Task:
<lang J> countPopln 3^i.30x 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
30{.(#~ isOdd@countPopln) i. 100 NB. odd population count (aka "ODious numbers")
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
30{.(#~ isEven@countPopln) i. 100 NB. even population count (aka "EVil numbers")
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58</lang>
Java
<lang java>import java.math.BigInteger;
public class PopCount {
public static void main(String[] args) {
{ // with int System.out.print("32-bit integer: "); int n = 1; for (int i = 0; i < 20; i++) { System.out.printf("%d ", Integer.bitCount(n)); n *= 3; } System.out.println(); } { // with long System.out.print("64-bit integer: "); long n = 1; for (int i = 0; i < 30; i++) { System.out.printf("%d ", Long.bitCount(n)); n *= 3; } System.out.println(); } { // with BigInteger System.out.print("big integer : "); BigInteger n = BigInteger.ONE; BigInteger three = BigInteger.valueOf(3); for (int i = 0; i < 30; i++) { System.out.printf("%d ", n.bitCount()); n = n.multiply(three); } System.out.println(); }
int[] od = new int[30]; int ne = 0, no = 0; System.out.print("evil : "); for (int n = 0; ne+no < 60; n++) { if ((Integer.bitCount(n) & 1) == 0) { if (ne < 30) { System.out.printf("%d ", n); ne++; } } else { if (no < 30) { od[no++] = n; } } } System.out.println(); System.out.print("odious : "); for (int n : od) { System.out.printf("%d ", n); } System.out.println();
}
}</lang>
- Output:
32-bit integer: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 64-bit integer: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 big integer : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
JavaScript
ES6
<lang JavaScript>(() => {
// popCount :: Int -> Int
const popCount = n =>
foldl(
(a, x) => a + (x === '1' ? 1 : 0),
0,
splitOn(, showIntAsBinary(n))
);
// GENERIC FUNCTIONS ------------------------------------------------------
// (++) :: [a] -> [a] -> [a] const append = (xs, ys) => xs.concat(ys);
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// foldl :: (b -> a -> b) -> b -> [a] -> b const foldl = (f, a, xs) => xs.reduce(f, a);
// length :: [a] -> Int const length = xs => xs.length;
// map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f);
// raise :: Num -> Int -> Num const raise = Math.pow;
// showIntAsBinary :: Int -> String const showIntAsBinary = n => n.toString(2);
// splitOn :: String -> String -> [String] const splitOn = (cs, xs) => xs.split(cs);
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = (p, f, x) => {
let v = x;
while (!p(v)) v = f(v);
return v;
}
// TEST -------------------------------------------------------------------
// { popCounts : [Int], evenThenOdd : ([Int], [Int]) }
return {
popCounts: map(x => popCount(raise(3, x)), enumFromTo(0, 30)),
evenThenOdd: until(
m => length(m.evenOdd[0]) >= 30 && length(m.evenOdd[1]) >= 30,
m => ({
x: m.x + 1,
evenOdd: popCount(m.x) % 2 === 0 ? (
[append(m.evenOdd[0], m.x), m.evenOdd[1]]
) : [m.evenOdd[0], append(m.evenOdd[1], m.x)]
}), {
x: 0,
evenOdd: [
[],
[]
]
}
)
.evenOdd
};
})();</lang>
- Output:
<lang JavaScript>{"popCounts":[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25], "evenThenOdd":[ [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58], [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]]}</lang>
jq
<lang jq>def popcount:
def bin: recurse( if . == 0 then empty else ./2 | floor end ) % 2; [bin] | add;
def firstN(count; condition):
if count > 0 then if condition then ., (1+.| firstN(count-1; condition)) else (1+.) | firstN(count; condition) end else empty end;
def task:
def pow(n): . as $m | reduce range(0;n) as $i (1; . * $m);
"The pop count of the first thirty powers of 3:", [range(0;30) as $n | 3 | pow($n) | popcount],
"The first thirty evil numbers:", [0 | firstN(30; (popcount % 2) == 0)],
"The first thirty odious numbers:", [0 | firstN(30; (popcount % 2) == 1)]
task</lang>
- Output:
$ jq -n -r -c -f Population_count.jq The pop count of the first thirty powers of 3: [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25] The first thirty evil numbers: [0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58] The first thirty odious numbers: [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Julia
<lang julia>popcount(n) = sum(digits(n, 2))
println("First 3 ^ i, up to 29 pop. counts: ", join((popcount(3 ^ n) for n in 0:29), ", ")) println("Evil numbers: ", join(filter(x -> iseven(popcount(x)), 0:59), ", ")) println("Odious numbers: ", join(filter(x -> isodd(popcount(x)), 0:59), ", "))</lang>
- Output:
First 3 ^ i, up to 29 pop. counts: 1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25 Evil numbers: 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58 Odious numbers: 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59
Kotlin
<lang scala>// version 1.0.6
fun popCount(n: Long) = when {
n < 0L -> throw IllegalArgumentException("n must be non-negative")
else -> java.lang.Long.bitCount(n)
}
fun main(args: Array<String>) {
println("The population count of the first 30 powers of 3 are:")
var pow3 = 1L
for (i in 1..30) {
print("${popCount(pow3)} ")
pow3 *= 3L
}
println("\n")
println("The first thirty evil numbers are:")
var count = 0
var i = 0
while (true) {
val pc = popCount(i.toLong())
if (pc % 2 == 0) {
print("$i ")
if (++count == 30) break
}
i++
}
println("\n")
println("The first thirty odious numbers are:")
count = 0
i = 1
while (true) {
val pc = popCount(i.toLong())
if (pc % 2 == 1) {
print("$i ")
if (++count == 30) break
}
i++
}
println()
}</lang>
- Output:
The population count of the first 30 powers of 3 are: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 The first thirty evil numbers are: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 The first thirty odious numbers are: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Lua
<lang Lua>-- Take decimal number, return binary string function dec2bin (n)
local bin, bit = ""
while n > 0 do
bit = n % 2
n = math.floor(n / 2)
bin = bit .. bin
end
return bin
end
-- Take decimal number, return population count as number function popCount (n)
local bin, count = dec2bin(n), 0
for pos = 1, bin:len() do
if bin:sub(pos, pos) == "1" then count = count + 1 end
end
return count
end
-- Implement task requirements function firstThirty (mode)
local numStr, count, n, remainder = "", 0, 0
if mode == "Evil" then remainder = 0 else remainder = 1 end
while count < 30 do
if mode == "3^x" then
numStr = numStr .. popCount(3 ^ count) .. " "
count = count + 1
else
if popCount(n) % 2 == remainder then
numStr = numStr .. n .. " "
count = count + 1
end
n = n + 1
end
end
print(mode .. ":" , numStr)
end
-- Main procedure firstThirty("3^x") firstThirty("Evil") firstThirty("Odious")</lang>
- Output:
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Mathematica
<lang Mathematica>popcount[n_Integer] := IntegerDigits[n, 2] // Total Print["population count of powers of 3"] popcount[#] & /@ (3^Range[0, 30]) (*******) evilQ[n_Integer] := popcount[n] // EvenQ evilcount = 0; evillist = {}; i = 0; While[evilcount < 30,
If[evilQ[i], AppendTo[evillist, i]; evilcount++]; i++ ]
Print["first thirty evil numbers"] evillist (*******) odiousQ[n_Integer] := popcount[n] // OddQ odiouscount = 0; odiouslist = {}; i = 0; While[odiouscount < 30,
If[odiousQ[i], AppendTo[odiouslist, i]; odiouscount++]; i++ ]
Print["first thirty odious numbers"] odiouslist</lang>
- Output:
population count of powers of 3
{1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25}
first thirty evil numbers
{0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58}
first thirty odious numbers
{1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59}
min
<lang min>(2 over over mod 'div dip) :divmod2
(
:n () =list (n 0 >) (n divmod2 list append #list @n) while list (1 ==) filter size
) :pop-count
(:n 0 () (over swap append 'succ dip) n times) :iota
"3^n: " print! 30 iota (3 swap pow int pop-count) map puts! 60 iota (pop-count odd?) partition "Evil: " print! puts! "Odious: " print! puts!</lang>
- Output:
3^n: (1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25) Evil: (0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58) Odious: (1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
Oforth
<lang oforth>: popcount(n)
0 while ( n ) [ n isOdd + n bitRight(1) ->n ] ;
- test
| i count |
30 seq map(#[ 3 swap 1- pow ]) map(#popcount) println 0 ->count 0 while( count 30 <> ) [ dup popcount isEven ifTrue: [ dup . count 1+ ->count ] 1+ ] drop printcr
0 ->count 0 while( count 30 <> ) [ dup popcount isOdd ifTrue: [ dup . count 1+ ->count ] 1+ ] drop ;</lang>
- Output:
>test [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59 ok
PARI/GP
<lang parigp>vector(30,n,hammingweight(3^(n-1))) od=select(n->hammingweight(n)%2,[0..100]); ev=setminus([0..100],od); ev[1..30] od[1..30]</lang>
- Output:
%1 = [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] %2 = [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] %3 = [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Pascal
Like Ada a unit is used. <lang pascal>unit popcount; {$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,ASMCSE,CSE,PEEPHOLE}
{$Smartlink OFF}
{$ENDIF}
interface
function popcnt(n:Uint64):integer;overload; function popcnt(n:Uint32):integer;overload; function popcnt(n:Uint16):integer;overload; function popcnt(n:Uint8):integer;overload;
implementation const //K1 = $0101010101010101;
K33 = $3333333333333333; K55 = $5555555555555555; KF1 = $0F0F0F0F0F0F0F0F; KF2 = $00FF00FF00FF00FF; KF4 = $0000FFFF0000FFFF; KF8 = $00000000FFFFFFFF;
{ function popcnt64(n:Uint64):integer; begin
n := n- (n shr 1) AND K55; n := (n AND K33)+ ((n shr 2) AND K33); n := (n + (n shr 4)) AND KF1; n := (n*k1) SHR 56; result := n;
end; } function popcnt(n:Uint64):integer;overload; // on Intel Haswell 2x faster for fpc 32-Bit begin
n := (n AND K55)+((n shr 1) AND K55); n := (n AND K33)+((n shr 2) AND K33); n := (n AND KF1)+((n shr 4) AND KF1); n := (n AND KF2)+((n shr 8) AND KF2); n := (n AND KF4)+((n shr 16) AND KF4); n := (n AND KF8)+ (n shr 32); result := n;
end;
function popcnt(n:Uint32):integer;overload; var
c,b : NativeUint;
begin
b := n; c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C; c := ((b shr 2) AND NativeUint(K33));b := (b AND NativeUint(K33))+C; c:= ((b shr 4) AND NativeUint(KF1)); b := (b AND NativeUint(KF1))+c; c := ((b shr 8) AND NativeUint(KF2));b := (b AND NativeUint(KF2))+c; c := b shr 16; b := (b AND NativeUint(KF4))+ C; result := b;
end;
function popcnt(n:Uint16):integer;overload; var
c,b : NativeUint;
begin
b := n; c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C; c :=((b shr 2) AND NativeUint(K33)); b := (b AND NativeUint(K33))+C; c:= ((b shr 4) AND NativeUint(KF1)); b := (b AND NativeUint(KF1))+c; c := b shr 8; b := (b AND NativeUint(KF2))+c; result := b;
end;
function popcnt(n:Uint8):integer;overload; var
c,b : NativeUint;
begin
b := n; c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C; c :=((b shr 2) AND NativeUint(K33));b := (b AND NativeUint(K33))+C; c:= b shr 4; result := (b AND NativeUint(KF1))+c;
end;
Begin End.</lang> The program <lang pascal>program pcntTest; uses
sysutils,popCount;
function Odious(n:Uint32):boolean;inline; Begin
Odious := boolean(PopCnt(n) AND 1)
end;
function EvilNumber(n:Uint32):boolean;inline; begin
EvilNumber := boolean(NOT(PopCnt(n)) AND 1);
end;
var
s : String; i : Uint64; k : LongWord;
Begin
s :='PopCnt 3^i :'; i:= 1; For k := 1 to 30 do Begin s := s+InttoStr(PopCnt(i)) +' '; i := 3*i; end; writeln(s);writeln;
s:='Evil numbers :';i := 0;k := 0;
repeat
IF EvilNumber(i) then
Begin
inc(k);s := s+InttoStr(i) +' ';
end;
inc(i);
until k = 30;
writeln(s);writeln;s:=;
s:='Odious numbers :';i := 0;k := 0;
repeat
IF Odious(i) then
Begin
inc(k);s := s+InttoStr(i) +' ';
end;
inc(i);
until k = 30;
writeln(s);
end.</lang>
- Output
PopCnt 3^i :1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil numbers :0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious numbers :1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Some processors define the card function, which can be used in conjunction with sets:
<lang pascal>var
i: integer;
f: set of 0..(bitSizeOf(i)-1) absolute i; // same address as i, but different interpretation
begin
writeLn(card(f));
end;</lang>
Perl
We'll emulate infinite lists with closures.
<lang perl>use strict; use warnings;
sub population_count {
my $n = shift;
die "argument can't be negative" if $n < 0;
my $c;
for ($c = 0; $n; $n >>= 1) {
$c += $n & 1;
}
$c;
}
print join ' ', map { population_count(3**$_) } 0 .. 30 - 1; print "\n"; sub evil {
my $i = 0;
sub { $i++ while population_count($i) % 2; $i++ }
} sub odious {
my $i = 0;
sub { $i++ until population_count($i) % 2; $i++ }
}
my ($evil, $odious) = (evil, odious); my (@evil, @odious); for (1 .. 30) {
push @evil, $evil->(); push @odious, $odious->();
}
printf "Evil : %s\n", join ' ', @evil; printf "Odious: %s\n", join ' ', @odious;</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
A faster population count can be done with pack/unpack:
<lang>say unpack("%b*",pack "J*", 1234567); # J = UV</lang>
Various modules can also perform a population count, with the first of these being faster than the pack/unpack builtins. The first three easily support bigints, the last will with some adjustment. <lang perl>use ntheory qw/hammingweight/; say hammingweight(1234567);
use Math::GMPz qw/Rmpz_popcount/; say Rmpz_popcount(Math::GMPz->new(1234567));
use Math::BigInt; say 0 + (Math::BigInt->new(1234567)->as_bin() =~ tr/1//);
use Bit::Vector; say Bit::Vector->new_Dec(64,1234567)->Norm;</lang>
Perl 6
<lang perl6>sub population-count(Int $n where * >= 0) { [+] $n.base(2).comb }
say map &population-count, 3 «**« ^30; say "Evil: ", (grep { population-count($_) %% 2 }, 0 .. *)[^30]; say "Odious: ", (grep { population-count($_) % 2 }, 0 .. *)[^30];</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
That's the convenient way to write it, but the following avoids string processing and is therefore about twice as fast: <lang perl6>sub population-count(Int $n is copy where * >= 0) {
loop (my $c = 0; $n; $n +>= 1) {
$c += $n +& 1;
}
$c;
}</lang>
Phix
<lang Phix>function pop_count(atom n)
if n<0 then ?9/0 end if
integer res = 0
while n!=0 do
res += and_bits(n,1)
n = floor(n/2)
end while
return res
end function
sequence s = {} for i=0 to 29 do
s &= pop_count(power(3,i))
end for puts(1,"3^x pop_counts:") ?s
procedure eo(integer b0, string name)
integer k=0, l=1
while l<=30 do
if and_bits(pop_count(k),1)=b0 then
s[l] = k
l += 1
end if
k += 1
end while
puts(1,name&" numbers:") ?s
end procedure eo(0," evil") eo(1,"odious")</lang>
- Output:
3^x pop_counts:{1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25}
evil numbers:{0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58}
odious numbers:{1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59}
PicoLisp
<lang PicoLisp>(de popz (N)
(cnt
'((N) (= "1" N))
(chop (bin N)) ) )
(println
'pops:
(mapcar
'((N) (popz (** 3 N)))
(range 0 29) ) )
(setq N -1) (println
'evil:
(make
(for (C 0 (> 30 C))
(unless (bit? 1 (popz (inc 'N)))
(link N)
(inc 'C) ) ) ) )
(setq N -1) (println
'odio:
(make
(for (C 0 (> 30 C))
(when (bit? 1 (popz (inc 'N)))
(link N)
(inc 'C) ) ) ) )</lang>
- Output:
pops: (1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25) evil: (0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58) odio: (1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
PHP
<lang PHP> function convertToBinary($integer) {
$binary = "";
do {
$quotient = (int) ($integer / 2);
$binary .= $integer % 2;
$integer = $quotient;
} while ($quotient > 0);
return $binary;
}
function getPopCount($integer) {
$binary = convertToBinary($integer); $offset = 0; $popCount = 0;
do {
$pos = strpos($binary, "1", $offset);
if($pos !== FALSE) $popCount++;
$offset = $pos + 1;
} while ($pos !== FALSE);
return $popCount;
}
function print3PowPopCounts() {
for ($p = 0; $p < 30; $p++) {
echo " " . getPopCount(3 ** $p);
}
}
function printFirst30Evil() {
$counter = 0; $pops = 0;
while ($pops < 30) {
$popCount = getPopCount($counter);
if ($popCount % 2 == 0) {
echo " " . $counter;
$pops++;
}
$counter++;
}
}
function printFirst30Odious() {
$counter = 1; $pops = 0;
while ($pops < 30) {
$popCount = getPopCount($counter);
if ($popCount % 2 != 0) {
echo " " . $counter;
$pops++;
}
$counter++;
}
}
echo "3 ^ x pop counts:"; print3PowPopCounts();
echo "\nfirst 30 evil numbers:"; printFirst30Evil();
echo "\nfirst 30 odious numbers:"; printFirst30Odious(); </lang>
- Output:
03 ^ x pop counts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 first 30 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 first 30 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
PowerShell
<lang PowerShell> function pop-count($n) {
(([Convert]::ToString($n, 2)).toCharArray() | where {$_ -eq '1'}).count
} "pop_count 3^n: $(1..29 | foreach -Begin {$n = 1; (pop-count $n)} -Process {$n = 3*$n; (pop-count $n)} )" "even pop_count: $($m = $n = 0; while($m -lt 30) {if(0 -eq ((pop-count $n)%2)) {$m += 1; $n}; $n += 1} )" "odd pop_count: $($m = $n = 0; while($m -lt 30) {if(1 -eq ((pop-count $n)%2)) {$m += 1; $n}; $n += 1} )" </lang> Output:
pop_count 3^n: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 even pop_count: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odd pop_count: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Python
Procedural
<lang python>>>> def popcount(n): return bin(n).count("1") ... >>> [popcount(3**i) for i in range(30)] [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] >>> evil, odious, i = [], [], 0 >>> while len(evil) < 30 or len(odious) < 30: ... p = popcount(i) ... if p % 2: odious.append(i) ... else: evil.append(i) ... i += 1 ... >>> evil[:30] [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] >>> odious[:30] [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59] >>> </lang>
Composition of pure functions
<lang python>Population count
from functools import reduce
- popCount :: Int -> Int
def popCount(n):
The count of non-zero digits in the binary
representation of the positive integer n.
def go(x):
return Just(divmod(x, 2)) if 0 < x else Nothing()
return sum(unfoldl(go)(n))
- TEST ----------------------------------------------------
def main():
Tests
print('Population count of first 30 powers of 3:')
print(
[popCount(pow(3, x)) for x in enumFromTo(0)(29)]
)
evilNums, odiousNums = partition(
compose(even)(popCount)
)(enumFromTo(0)(59))
print("\nFirst thirty 'evil' numbers:")
print(evilNums)
print("\nFirst thirty 'odious' numbers:")
print(odiousNums)
- GENERIC -------------------------------------------------
- Just :: a -> Maybe a
def Just(x):
Constructor for an inhabited Maybe (option type) value.
return {'type': 'Maybe', 'Nothing': False, 'Just': x}
- Nothing :: Maybe a
def Nothing():
Constructor for an empty Maybe (option type) value.
return {'type': 'Maybe', 'Nothing': True}
- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
Right to left function composition. return lambda f: lambda x: g(f(x))
- enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
Integer enumeration from m to n. return lambda n: list(range(m, 1 + n))
- even :: Int -> Bool
def even(x):
True if x is a
multiple of two.
return 0 == x % 2
- partition :: (a -> Bool) -> [a] -> ([a], [a])
def partition(p):
The pair of lists of those elements in xs
which respectively, do and don't
satisfy the predicate p.
def go(a, x):
ts, fs = a
return (ts + [x], fs) if p(x) else (ts, fs + [x])
return lambda xs: reduce(go, xs, ([], []))
- unfoldl(lambda x: Just(((x - 1), x)) if 0 != x else Nothing())(10)
- -> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
- unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
Dual to reduce or foldr.
Where catamorphism reduces a list to a summary value,
the anamorphic unfoldr builds a list from a seed value.
As long as f returns Just(a, b), a is prepended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.
def go(xr):
mb = f(xr[0])
if mb.get('Nothing'):
return []
else:
y, r = mb.get('Just')
return go((y, r)) + [r]
return lambda x: go((x, x))
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Population count of first 30 powers of 3: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] First thirty 'evil' numbers: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] First thirty 'odious' numbers: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Racket
<lang racket>#lang racket
- Positive version from "popcount_4" in
- https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
- negative version follows R6RS definition documented in
- http://docs.racket-lang.org/r6rs/r6rs-lib-std/r6rs-lib-Z-H-12.html?q=bitwise-bit#node_idx_1074
(define (population-count n)
(if (negative? n)
(bitwise-not (population-count (bitwise-not n)))
(let inr ((x n) (rv 0))
(if (= x 0) rv (inr (bitwise-and x (sub1 x)) (add1 rv))))))
(define (evil? x)
(and (not (negative? x))
(even? (population-count x))))
(define (odious? x)
(and (positive? x)
(odd? (population-count x))))
(define tasks
(list "display the pop count of the 1st thirty powers of 3 (3^0, 3^1, 3^2, 3^3, 3^4, ...)." (for/list ((i (in-range 30))) (population-count (expt 3 i))) "display the 1st thirty evil numbers." (for/list ((_ (in-range 30)) (e (sequence-filter evil? (in-naturals)))) e) "display the 1st thirty odious numbers." (for/list ((_ (in-range 30)) (o (sequence-filter odious? (in-naturals)))) o)))
(for-each displayln tasks)
(module+ test
(require rackunit) (check-equal? (for/list ((p (sequence-map population-count (in-range 16)))) p) '(0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4)) (check-true (evil? 0) "0 has just *got* to be evil") (check-true (evil? #b011011011) "six bits... truly evil") (check-false (evil? #b1011011011) "seven bits, that's odd!") (check-true (odious? 1) "the least odious number") (check-true (odious? #b1011011011) "seven (which is odd) bits") (check-false (odious? #b011011011) "six bits... is evil"))</lang>
- Output:
display the pop count of the 1st thirty powers of 3 (3^0, 3^1, 3^2, 3^3, 3^4, ...). (1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25) display the 1st thirty evil numbers. (0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58) display the 1st thirty odious numbers. (1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
REXX
<lang rexx>/*REXX program counts the number of "one" bits in the binary version of a decimal number*/ /*─────────────────── and also generates a specific number of EVIL and ODIOUS numbers.*/ parse arg N B . /*get optional arguments from the C.L. */ if N== | N=="," then N=30 /*N not specified? Then use default. */ if B== | B=="," then B= 3 /*B " " " " " */ numeric digits 2000 /*be able to handle gihugeic numbers.*/ numeric digits max(20, length(B**N) ) /*whittle the precision down to size.*/ $= /* [↑] a little calculation for sizing*/
do j=0 for N; $=$ popcount(B**j) /*generate N popCounts for some powers.*/
end /*j*/ /* [↑] append popCount to the $ list. */
/* [↓] display popcounts of "3" powers*/
call showList 'popcounts of the powers of' B /*display the list with a header/title.*/
do j=0 until #>=N /*generate N evil numbers. */
if popCount(j) // 2 then iterate /*if odd population count, skip it. */
#=# + 1; $=$ j /*bump evil # count; add it to $ list.*/
end /*j*/ /* [↑] build a list of evil numbers. */
/* [↓] display the evil number list. */
call showList 'evil numbers' /*display the $ list with a header. */
do j=0 until #>=N /*generate N odious numbers. */
if popCount(j) // 2 ==0 then iterate /*if even population count, then skip. */
#=# + 1; $=$ j /*bump odious # count; add to $ list. */
end /*j*/ /* [↑] build a list of odious numbers.*/
/* [↓] display the odious number list.*/
call showList 'odious numbers' /*display the $ list with a header. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ d2b: return word( strip( x2b( d2x( arg(1) ) ), 'L', 0) 0, 1) /*dec ──► bin.*/ popCount: return length( space( translate( d2b(arg(1) ), , 0), 0) ) /*count ones. */ showList: say; say 'The 1st' N arg(1)':'; say strip($); #=0; $=; return</lang>
- output when using the default input:
The 1st 30 popcounts of the powers of 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 The 1st 30 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 The 1st 30 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Ring
<lang ring>
- Project : Population count
load "stdlib.ring" n = 0 neven = 0 nodd = 0 binodd = [] bineven = [] binpow = [] while true
n = n + 1
numb = 0
bin = binarydigits(n)
for nr = 1 to len(bin)
if bin[nr] = "1"
numb = numb + 1
ok
next
if numb % 2 = 0
neven = neven + 1
if neven < 31
add(bineven, n)
ok
else
nodd = nodd + 1
if nodd < 31
add(binodd, n)
ok
ok
if neven > 30 and nodd > 30
exit
ok
end
see "3^x:" + nl for n = 0 to 29
numb = 0
bin = binarydigits(pow(3,n))
for nr = 1 to len(bin)
if bin[nr] = "1"
numb = numb + 1
ok
next
add(binpow, numb)
next showarray(binpow) see nl
see "Evil numbers :" + nl showarray(bineven) see nl see "Odious numbers:" + nl showarray(binodd) see nl
func showarray(vect)
see "["
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
</lang> Output:
3^x: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] Evil numbers : [3, 4, 5, 6, 9, 10, 12, 15, 16, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57] Odious numbers: [1, 2, 7, 8, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62]
Ruby
Demonstrating lazy enumerators. <lang ruby>class Integer
def popcount
digits(2).count(1) #pre Ruby 2.4: self.to_s(2).count("1")
end
def evil?
self >= 0 && popcount.even?
end
end
puts "Powers of 3:", (0...30).map{|n| (3**n).popcount}.join(' ') puts "Evil:" , 0.step.lazy.select(&:evil?).first(30).join(' ') puts "Odious:", 0.step.lazy.reject(&:evil?).first(30).join(' ')</lang>
- Output:
Powers of 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Rust
<lang Rust> fn main() {
let mut num = 1u64;
let mut vec = Vec::new();
for _ in 0..30 {
vec.push(num.count_ones());
num *= 3;
}
println!("pop count of 3^0, 3^1 ... 3^29:\n{:?}",vec);
let mut even = Vec::new();
let mut odd = Vec::new();
num = 1;
while even.len() < 30 || odd.len() < 30 {
match 0 == num.count_ones()%2 {
true if even.len() < 30 => even.push(num),
false if odd.len() < 30 => odd.push(num),
_ => {}
}
num += 1;
}
println!("\nFirst 30 even pop count:\n{:?}",even);
println!("\nFirst 30 odd pop count:\n{:?}",odd);
} </lang>
- Output:
pop count of 3^0, 3^1 ... 3^29: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] First 30 even pop count: [3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60] First 30 odd pop count: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Seed7
The function popcount below converts
the integer into a bitset.
The function card
is used to compute the population count of the bitset.
<lang seed7>$ include "seed7_05.s7i";
const func integer: popcount (in integer: n) is
return card(bitset(n));
const proc: main is func
local
var integer: count is 0;
var integer: num is 0;
begin
for num range 0 to 29 do
write(popcount(3 ** num) <& " ");
end for;
writeln;
write("evil: ");
for num range 0 to integer.last until count >= 30 do
if not odd(popcount(num)) then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
write("odious: ");
count := 0;
for num range 0 to integer.last until count >= 30 do
if odd(popcount(num)) then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
end func;</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Sidef
<lang ruby>func population_count(n) { n.as_bin.count('1') } say "#{0..29 «**« 3 «call« population_count -> join(' ')}" var numbers = 60.of { |i|
[i, population_count(i)]
} say "Evil: #{numbers.grep{_[1] %% 2}.map{.first}.join(' ')}" say "Odious: #{numbers.grep{_[1] & 1}.map{.first}.join(' ')}"</lang>
- Output:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Swift
<lang swift>func populationCount(n: Int) -> Int {
guard n >= 0 else { fatalError() }
return String(n, radix: 2).filter({ $0 == "1" }).count
}
let pows = (0...)
.lazy
.map({ Int(pow(3, Double($0))) })
.map(populationCount)
.prefix(30)
let evils = (0...)
.lazy
.filter({ populationCount(n: $0) & 1 == 0 })
.prefix(30)
let odious = (0...)
.lazy
.filter({ populationCount(n: $0) & 1 == 1 })
.prefix(30)
print("Powers:", Array(pows)) print("Evils:", Array(evils)) print("Odious:", Array(odious))</lang>
- Output:
Powers: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25] Evils: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58] Odious: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Tcl
<lang tcl>package require Tcl 8.6
proc hammingWeight {n} {
tcl::mathop::+ {*}[split [format %llb $n] ""]
} for {set n 0;set l {}} {$n<30} {incr n} {
lappend l [hammingWeight [expr {3**$n}]]
} puts "p3: $l" for {set n 0;set e [set o {}]} {[llength $e]<30||[llength $o]<30} {incr n} {
lappend [expr {[hammingWeight $n]&1 ? "o" : "e"}] $n
} puts "evil: [lrange $e 0 29]" puts "odious: [lrange $o 0 29]"</lang>
- Output:
p3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
UNIX Shell
<lang bash>popcount() {
local -i n=$1
(( n < 0 )) && return 1
local ones=0
while (( n > 0 )); do
(( ones += n%2 ))
(( n /= 2 ))
done
echo $ones
}
popcount_3s=() n=1 for (( i=0; i<30; i++ )); do
popcount_3s+=( $(popcount $n) ) (( n *= 3 ))
done echo "powers of 3 popcounts: ${popcount_3s[*]}"
evil=() odious=() n=0 while (( ${#evil[@]} < 30 || ${#odious[@]} < 30 )); do
p=$( popcount $n )
if (( $p%2 == 0 )); then
evil+=( $n )
else
odious+=( $n )
fi
(( n++ ))
done echo "evil nums: ${evil[*]:0:30}" echo "odious nums: ${odious[*]:0:30}"</lang>
- Output:
powers of 3 popcounts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil nums: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious nums: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
VBA
The Decimal subtype of Variant does the job to expand 32-bit integers (Long) to 28-digit integers (Decimal). <lang vb>Sub Population_count()
nmax = 30
b = 3
n = 0: List = "": bb = 1
For i = 0 To nmax - 1
List = List & " " & popcount(bb)
bb = bb * b
Next 'i
Debug.Print "popcounts of the powers of " & b
Debug.Print List
For j = 0 To 1
If j = 0 Then c = "evil numbers" Else c = "odious numbers"
n = 0: List = "": i = 0
While n < nmax
If (popcount(i) Mod 2) = j Then
n = n + 1
List = List & " " & i
End If
i = i + 1
Wend
Debug.Print c
Debug.Print List
Next 'j
End Sub 'Population_count
Private Function popcount(x)
Dim y, xx, xq, xr
xx = x
While xx > 0
xq = Int(xx / 2)
xr = xx - xq * 2
If xr = 1 Then y = y + 1
xx = xq
Wend
popcount = y
End Function 'popcount </lang>
- Output:
popcounts of the powers of 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious numbers: ' 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
VBScript
Use of the variant currency subtype. Currency mode is a gray area where some operators do not work, for instance: ^ \ Mod <lang vb>' Population count - VBScript - 10/05/2019 nmax=30 b=3 n=0: list="": bb=1 For i=0 To nmax-1 list=list & " " & popcount(bb) bb=bb*b Next 'i Msgbox list,,"popcounts of the powers of " & b For j=0 to 1 If j=0 Then c="evil numbers": Else c="odious numbers" n=0: list="": i=0 While n<nmax If (popcount(i) Mod 2)=j Then n=n+1 list=list & " " & i End If i=i+1 Wend Msgbox list,,c Next 'j
Function popcount(x) Dim y,xx,xq,xr xx=x While xx>0 xq=Int(xx/2) xr=xx-xq*2 If xr=1 Then y=y+1 xx=xq Wend popcount=y End Function 'popcount </lang>
- Output:
popcounts of the powers of 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Visual Basic .NET
<lang vbnet>Module Module1
Function PopCnt(ByVal n As Long) As Integer
Return Convert.ToString(n, 2).ToCharArray().Where(Function(x) x = "1").Count()
End Function
Sub Aline(ByVal a As List(Of Integer), ByVal title As String)
Console.WriteLine("{0, -8}{1}", title, String.Join(" ", a.Take(30)))
End Sub
Sub Main(ByVal args As String())
Console.WriteLine("Population Counts:")
Dim t As New List(Of Integer), e As New List(Of Integer), o As New List(Of Integer)
For count As Integer = 0 To 99
If PopCnt(count) Mod 2 = 0 Then e.Add(count) Else o.Add(count)
If count < 30 Then t.Add(PopCnt(Math.Pow(3, count)))
Next
Aline(t, "3^n :") : Aline(e, "Evil:") : Aline(o, "Odious:")
Extra:
Dim eo As Boolean = e.Contains(0), res As String = "", i As Integer = 0
e.Add(0) : o.Add(0)
Do
If eo Then
If e(i + 1) = e(i) + 1 Then
res += "͞ " : i += 1
ElseIf o(i) = e(i) + 1 Then
res += "↓" : eo = Not eo
Else
res += "\" : eo = Not eo : i += 1
End If
Else
If o(i + 1) = o(i) + 1 Then
res += "͢ " : i += 1
ElseIf e(i) = o(i) + 1 Then
res += "↑" : eo = Not eo
Else
res += "/" : eo = Not eo : i += 1
End If
End If
Loop Until i >= e.Count - 1
Console.WriteLine(vbLf & "Pattern:{0}", res.Substring(0, res.Count() - 1))
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module </lang>
- Output:
Added a "Pattern" line. Not quite getting the arrows I wanted, but the "Pattern" line shows the sequence pattern of integers for the Evil and Odious output. The pattern goes to about 50, whereas only the first 30 Evil and Odious integers are shown.
Population Counts: 3^n : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59 Pattern:↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑\↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓/↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑\↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓/↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑͞ ↓͢ ↑
P.S., The underscore-right-arrows and overscore characters on the Pattern line may not appear properly on some browsers.
Yabasic
<lang Yabasic>print "Pop count (3^x): "
for i = 0 to 29
print population(3^i);
next print "\n"
print "Evil: " EvilOdious(30) print "\n"
print "Odious: " EvilOdious(30, 1) print "\n"
sub EvilOdious(limit, type)
local i, count, eo
repeat
eo = mod(population(i), 2)
if (type and eo) or (not type and not eo) count = count + 1 : print i;
i = i + 1
until(count = limit)
end sub
sub population(number)
local i, binary$, popul
binary$ = bin$(number)
for i = 1 to len(binary$)
popul = popul + val(mid$(binary$, i, 1))
next
return popul
end sub</lang>
zkl
Ints have the 1s count as a property. <lang zkl>n:=1; do(30){ print(n.num1s,","); n*=3 } println();
println("evil: ",[0..].filter(30,fcn(n){ n.num1s.isEven }).concat(","));
// now, as an iterator aka lazy: println("odious: ",(0).walker(*).tweak( // 0,1,2,3,4... iterator
fcn(n){ if(n.num1s.isEven) Void.Skip else n }).walk(30).concat(","));</lang>
- Output:
1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25, evil: 0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58 odious: 1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59
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