Price fraction
You are encouraged to solve this task according to the task description, using any language you may know.
A friend of mine runs a Pharmacy. He has a specialised function in his Dispensary application which receives a decimal value of currency and replaces it to a standard value. This value is regulated by a government department.
Task: Given a floating point value between 0.00 and 1.00, rescale according to the following table:
>= 0.00 < 0.06 := 0.10 >= 0.06 < 0.11 := 0.18 >= 0.11 < 0.16 := 0.26 >= 0.16 < 0.21 := 0.32 >= 0.21 < 0.26 := 0.38 >= 0.26 < 0.31 := 0.44 >= 0.31 < 0.36 := 0.50 >= 0.36 < 0.41 := 0.54 >= 0.41 < 0.46 := 0.58 >= 0.46 < 0.51 := 0.62 >= 0.51 < 0.56 := 0.66 >= 0.56 < 0.61 := 0.70 >= 0.61 < 0.66 := 0.74 >= 0.66 < 0.71 := 0.78 >= 0.71 < 0.76 := 0.82 >= 0.76 < 0.81 := 0.86 >= 0.81 < 0.86 := 0.90 >= 0.86 < 0.91 := 0.94 >= 0.91 < 0.96 := 0.98 >= 0.96 < 1.01 := 1.00
Ada
<lang Ada> type Price is delta 0.01 digits 3 range 0.0..1.0; function Scale (Value : Price) return Price is
X : constant array (1..19) of Price :=
( 0.06, 0.11, 0.16, 0.21, 0.26, 0.31, 0.36, 0.41, 0.46, 0.51,
0.56, 0.61, 0.66, 0.71, 0.76, 0.81, 0.86, 0.91, 0.96
);
Y : constant array (1..20) of Price :=
( 0.10, 0.18, 0.26, 0.32, 0.38, 0.44, 0.50, 0.54, 0.58, 0.62,
0.66, 0.70, 0.74, 0.78, 0.82, 0.86, 0.90, 0.94, 0.98, 1.0
);
Low : Natural := X'First;
High : Natural := X'Last;
Middle : Natural;
begin
loop
Middle := (Low + High) / 2;
if Value = X (Middle) then
return Y (Middle + 1);
elsif Value < X (Middle) then
if Low = Middle then
return Y (Low);
end if;
High := Middle - 1;
else
if High = Middle then
return Y (High + 1);
end if;
Low := Middle + 1;
end if;
end loop;
end Scale; </lang> The solution uses fixed point type to prevent rounding and representation issues. With the above declarations a full coverage test: <lang Ada> with Ada.Text_IO; use Ada.Text_IO; procedure Test_Price_Fraction is
-- Put the declarations here Value : Price := Price'First;
begin
loop
Put_Line (Price'Image (Value) & "->" & Price'Image (Scale (Value)));
exit when Value = Price'Last;
Value := Price'Succ (Value);
end loop;
end Test_Price_Fraction; </lang> Sample output:
0.00-> 0.10 0.01-> 0.10 0.02-> 0.10 0.03-> 0.10 0.04-> 0.10 0.05-> 0.10 0.06-> 0.18 0.07-> 0.18 0.08-> 0.18 0.09-> 0.18 0.10-> 0.18 0.11-> 0.26 0.12-> 0.26 0.13-> 0.26 0.14-> 0.26 0.15-> 0.26 0.16-> 0.32 0.17-> 0.32 0.18-> 0.32 0.19-> 0.32 0.20-> 0.32 0.21-> 0.38 0.22-> 0.38 0.23-> 0.38 0.24-> 0.38 0.25-> 0.38 0.26-> 0.44 0.27-> 0.44 0.28-> 0.44 0.29-> 0.44 0.30-> 0.44 0.31-> 0.50 0.32-> 0.50 0.33-> 0.50 0.34-> 0.50 0.35-> 0.50 0.36-> 0.54 0.37-> 0.54 0.38-> 0.54 0.39-> 0.54 0.40-> 0.54 0.41-> 0.58 0.42-> 0.58 0.43-> 0.58 0.44-> 0.58 0.45-> 0.58 0.46-> 0.62 0.47-> 0.62 0.48-> 0.62 0.49-> 0.62 0.50-> 0.62 0.51-> 0.66 0.52-> 0.66 0.53-> 0.66 0.54-> 0.66 0.55-> 0.66 0.56-> 0.70 0.57-> 0.70 0.58-> 0.70 0.59-> 0.70 0.60-> 0.70 0.61-> 0.74 0.62-> 0.74 0.63-> 0.74 0.64-> 0.74 0.65-> 0.74 0.66-> 0.78 0.67-> 0.78 0.68-> 0.78 0.69-> 0.78 0.70-> 0.78 0.71-> 0.82 0.72-> 0.82 0.73-> 0.82 0.74-> 0.82 0.75-> 0.82 0.76-> 0.86 0.77-> 0.86 0.78-> 0.86 0.79-> 0.86 0.80-> 0.86 0.81-> 0.90 0.82-> 0.90 0.83-> 0.90 0.84-> 0.90 0.85-> 0.90 0.86-> 0.94 0.87-> 0.94 0.88-> 0.94 0.89-> 0.94 0.90-> 0.94 0.91-> 0.98 0.92-> 0.98 0.93-> 0.98 0.94-> 0.98 0.95-> 0.98 0.96-> 1.00 0.97-> 1.00 0.98-> 1.00 0.99-> 1.00 1.00-> 1.00
AutoHotkey
<lang AutoHotkey>; Submitted by MasterFocus --- http://tiny.cc/iTunis
Loop {
InputBox, OutputVar, Price Fraction Example, Insert the value to be rounded.`n* [ 0 < value < 1 ]`n* Press ESC or Cancel to exit, , 200, 150 If ErrorLevel Break MsgBox % "Input: " OutputVar "`nResult: " PriceFraction( OutputVar )
}
- -----------------------------------------
PriceFraction( p_Input ) {
If p_Input is not float ; returns 0 if input is not a float Return 0
If ( ( p_Input <= 0 ) OR ( p_Input >= 1 ) ) ; returns 0 is input is out of range Return 0
; declaring the table (arbitrary delimiters in use are '§' and '|') l_List := "0.06|0.10§0.11|0.18§0.16|0.26§0.21|0.32§0.26|0.38§0.31|0.44§0.36|0.50§0.41|0.54§0.46|0.58§0.51|0.62§0.56|0.66§0.61|0.70§0.66|0.74§0.71|0.78§0.76|0.82§0.81|0.86§0.86|0.90§0.91|0.94§0.96|0.98§1.01|1.00"
Loop, Parse, l_List, § ; retrieves each field (delimited by '§')
{
StringSplit, l_Array, A_LoopField, | ; splits current field (using delimiter '|')
If ( p_Input <= l_Array1 )
Return l_Array2 ; returns the second value if input <= first value
}
Return 0 ; returns 0, indicating failure (shouldn't be reached though)
}</lang>
ALGOL 68
- note: This specimen retains the original C coding style.
<lang algol68>main: (
# Just get a random price between 0 and 1 # # srand(time(NIL)); # REAL price := random; REAL tops := 0.06; REAL std val := 0.10;
# Conditionals are a little odd here "(price-0.001 < tops AND
price+0.001 > tops)" is to check if they are equal. Stupid
C floats, right? :) #
WHILE ( price>tops OR (price-0.001 < tops AND price+0.001 > tops) ) AND tops<=1.01
DO
tops+:=0.05;
IF std val < 0.26 THEN
std val +:= 0.08
ELIF std val < 0.50 THEN
std val +:= 0.06
ELSE
std val +:= 0.04
FI;
IF std val > 0.98 THEN
std val := 1.0
FI
OD;
printf(($"Value : "z.2dl,"Converted to standard : "z.2dl$, price, std val))
)</lang> Sample Output:
Value : 0.38 Converted to standard : 0.54
BASIC
This could also be done by building an array, but I felt that this was simpler.
<lang qbasic>DECLARE FUNCTION PriceFraction! (price AS SINGLE)
RANDOMIZE TIMER DIM x AS SINGLE x = RND PRINT x, PriceFraction(x)
FUNCTION PriceFraction! (price AS SINGLE)
'returns price unchanged if invalid value
SELECT CASE price
CASE IS < 0!
PriceFraction! = price
CASE IS < .06
PriceFraction! = .1
CASE IS < .11
PriceFraction! = .18
CASE IS < .16
PriceFraction! = .26
CASE IS < .21
PriceFraction! = .32
CASE IS < .26
PriceFraction! = .38
CASE IS < .31
PriceFraction! = .44
CASE IS < .36
PriceFraction! = .5
CASE IS < .41
PriceFraction! = .54
CASE IS < .46
PriceFraction! = .58
CASE IS < .51
PriceFraction! = .62
CASE IS < .56
PriceFraction! = .66
CASE IS < .61
PriceFraction! = .7
CASE IS < .66
PriceFraction! = .74
CASE IS < .71
PriceFraction! = .78
CASE IS < .76
PriceFraction! = .82
CASE IS < .81
PriceFraction! = .86
CASE IS < .86
PriceFraction! = .9
CASE IS < .91
PriceFraction! = .94
CASE IS < .96
PriceFraction! = .98
CASE IS < 1.01
PriceFraction! = 1!
CASE ELSE
PriceFraction! = price
END SELECT
END FUNCTION</lang>
Sample outputs (run 5 times):
.7388727 .82 .8593103 .9 .826687 .9 .3444635 .5 .0491907 .1
C
<lang c>#include <stdlib.h>
- include <time.h>
- include <stdio.h>
int main() { //Just get a random price between 0 and 1 srand(time(NULL)); float price = (float)((int)rand()%101)/100; float tops=0.06; float std_val = 0.10;
//Conditionals are a little odd here
//"(price-0.001 < tops && price+0.001 > tops)" is to check if they are equal. Stupid C floats, right? :)
while((price>tops || (price-0.001 < tops && price+0.001 > tops)) && tops<=1.01)
{
tops+=0.05;
if(std_val < 0.26)
std_val += 0.08; else if(std_val<0.50) std_val +=0.06; else std_val +=0.04;
if(std_val > 0.98) std_val = 1.0;
}
printf("Value: %.2f\nConverted to standard: %.2f\n", price, std_val); }</lang>
C#
<lang csharp>namespace ConsoleApplication1 {
class Program
{
static void Main(string[] args)
{
for (int x = 0; x < 10; x++)
{
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", ((double)x) / 10, SpecialRound(((double)x) / 10));
}
Console.WriteLine();
for (int x = 0; x < 10; x++)
{
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", ((double)x) / 10 + 0.05, SpecialRound(((double)x) / 10 + 0.05));
}
Console.WriteLine();
Console.WriteLine("In: {0:0.00}, Out: {1:0.00}", 1.01, SpecialRound(1.01));
Console.Read();
}
private static double SpecialRound(double inValue)
{
if (inValue > 1) return 1;
double[] Splitters = new double[] {
0.00 , 0.06 , 0.11 , 0.16 , 0.21 ,
0.26 , 0.31 , 0.36 , 0.41 , 0.46 ,
0.51 , 0.56 , 0.61 , 0.66 , 0.71 ,
0.76 , 0.81 , 0.86 , 0.91 , 0.96 };
double[] replacements = new double[] {
0.10 , 0.18 , 0.26 , 0.32 , 0.38 ,
0.44 , 0.50 , 0.54 , 0.58 , 0.62 ,
0.66 , 0.70 , 0.74 , 0.78 , 0.82 ,
0.86 , 0.90 , 0.94 , 0.98 , 1.00 };
for (int x = 0; x < Splitters.Length - 1; x++)
{
if (inValue >= Splitters[x] &&
inValue < Splitters[x + 1])
{
return replacements[x];
}
}
return inValue;
}
}
}</lang>
C++
<lang cpp>#include <iostream>
- include <cmath>
int main( ) {
double froms[ ] = { 0.00 , 0.06 , 0.11 , 0.16 , 0.21 , 0.26 ,
0.31 , 0.36 , 0.41 , 0.46 , 0.51 , 0.56 , 0.61 , 0.66 ,
0.71 , 0.76 , 0.81 , 0.86 , 0.91 , 0.96 } ;
double tos[ ] = { 0.06 , 0.11 , 0.16 , 0.21 , 0.26 , 0.31 ,
0.36 , 0.41 , 0.46 , 0.51 , 0.56 , 0.61 , 0.66 , 0.71 ,
0.76 , 0.81 , 0.86 , 0.91 , 0.96 , 1.01 } ;
double replacements [] = { 0.10 , 0.18 , 0.26 , 0.32 , 0.38 ,
0.44 , 0.50 , 0.54 , 0.58 , 0.62 , 0.66 , 0.70 , 0.74 ,
0.78 , 0.82 , 0.86 , 0.90 , 0.94 , 0.98 , 1.00 } ;
double number = 0.1 ;
std::cout << "Enter a fractional number between 0 and 1 ( 0 to end )!\n" ;
std::cin >> number ;
while ( number != 0 ) {
if ( number < 0 || number > 1 ) {
std::cerr << "Error! Only positive values between 0 and 1 are allowed!\n" ; return 1 ;
}
int n = 0 ;
while ( ! ( number >= froms[ n ] && number < tos[ n ] ) )
n++ ;
std::cout << "-->" << replacements[ n ] << '\n' ;
std::cout << "Enter a fractional number ( 0 to end )!\n" ;
std::cin >> number ;
}
return 0 ;
} </lang>
Sample output: Enter a fractional number between 0 and 1 ( 0 to end )! 0.7 -->0.78 Enter a fractional number ( 0 to end )! 0.32 -->0.5 Enter a fractional number ( 0 to end )! 0.12 -->0.26 Enter a fractional number ( 0 to end )! 0
Clipper
<lang dbase>FUNCTION PriceFraction( npQuantDispensed )
LOCAL aPriceFraction := { {0,.06,.1},;
{.06,.11,.18}, ;
{.11,.16,.26}, ;
{.16,.21,.32}, ;
{.21,.26,.38}, ;
{.26,.31,.44}, ;
{.31,.36,.5}, ;
{.36,.41,.54}, ;
{.41,.46,.58}, ;
{.46,.51,.62}, ;
{.51,.56,.66}, ;
{.56,.61,.7}, ;
{.61,.66,.74}, ;
{.66,.71,.78}, ;
{.71,.76,.82}, ;
{.76,.81,.86}, ;
{.81,.86,.9}, ;
{.86,.91,.94}, ;
{.91,.96,.98} }
LOCAL nResult
LOCAL nScan
IF npQuantDispensed = 0
nResult = 0
ELSEIF npQuantDispensed >= .96
nResult = 1
ELSE
nScan := ASCAN( aPriceFraction, ;
{ |aItem| npQuantDispensed >= aItem[ 1 ] .AND.;
npQuantDispensed < aItem[ 2 ] } )
nResult := aPriceFraction[ nScan ][ 3 ]
END IF
RETURN nResult</lang>
D
<lang d>import std.stdio: writeln;
double priceRounder(double price)
in { assert(price >= 0 && price <= 1.0); }
body {
enum cin = [.06, .11, .16, .21, .26, .31, .36, .41, .46, .51,
.56, .61, .66, .71, .76, .81, .86, .91, .96, 1.01];
enum cout = [.10, .18, .26, .32, .38, .44, .50, .54, .58, .62,
.66, .70, .74, .78, .82, .86, .90, .94, .98, 1.00];
foreach (i, p; cin)
if (p >= price)
return cout[i];
assert(0);
}
void main() {
foreach (price; [0.7388727, 0.8593103, 0.826687, 0.3444635])
writeln(priceRounder(price));
}</lang> Output:
0.82 0.9 0.9 0.5
Erlang
<lang erlang>priceFraction(N) when N < 0 orelse N > 1 ->
erlang:error('Values must be between 0 and 1.');
priceFraction(N) when N < 0.06 -> 0.10; priceFraction(N) when N < 0.11 -> 0.18; priceFraction(N) when N < 0.16 -> 0.26; priceFraction(N) when N < 0.21 -> 0.32; priceFraction(N) when N < 0.26 -> 0.38; priceFraction(N) when N < 0.31 -> 0.44; priceFraction(N) when N < 0.36 -> 0.50; priceFraction(N) when N < 0.41 -> 0.54; priceFraction(N) when N < 0.46 -> 0.58; priceFraction(N) when N < 0.51 -> 0.62; priceFraction(N) when N < 0.56 -> 0.66; priceFraction(N) when N < 0.61 -> 0.70; priceFraction(N) when N < 0.66 -> 0.74; priceFraction(N) when N < 0.71 -> 0.78; priceFraction(N) when N < 0.76 -> 0.82; priceFraction(N) when N < 0.81 -> 0.86; priceFraction(N) when N < 0.86 -> 0.90; priceFraction(N) when N < 0.91 -> 0.94; priceFraction(N) when N < 0.96 -> 0.98; priceFraction(N) -> 1.00.</lang>
Forth
A floating-point version wouldn't be hard -- four words would change ( , @ @ cell+ -to- f, f@ f@ float+ ), EVALUATE would be replaced with a small word that forced a floating-point interpretation, and the return stack would not be used in ROUND -- but it would be strikingly unusual. See this page's discussion.
<lang>: as begin parse-word dup while evaluate , repeat 2drop ;
create bounds as 96 91 86 81 76 71 66 61 56 51 46 41 36 31 26 21 16 11 6 0 create official as 100 98 94 90 86 82 78 74 70 66 62 58 54 50 44 38 32 26 18 10
- official@ ( a-bounds -- +n )
\ (a+n) - a + b = (a+n) + (b - a) = (b+n) [ official bounds - ] literal + @ ;
- round ( n-cents -- n-cents' )
>r bounds begin dup @ r@ > while cell+ repeat r> drop official@ ;</lang>
Fortran
<lang fortran>program price_fraction
implicit none integer, parameter :: i_max = 10 integer :: i real, dimension (20), parameter :: in = & & (/0.00, 0.06, 0.11, 0.16, 0.21, 0.26, 0.31, 0.36, 0.41, 0.46, & & 0.51, 0.56, 0.61, 0.66, 0.71, 0.76, 0.81, 0.86, 0.91, 0.96/) real, dimension (20), parameter :: out = & & (/0.10, 0.18, 0.26, 0.32, 0.38, 0.44, 0.50, 0.54, 0.58, 0.62, & & 0.66, 0.70, 0.74, 0.78, 0.82, 0.86, 0.90, 0.94, 0.98, 1.00/) real :: r
do i = 1, i_max call random_number (r) write (*, '(f8.6, 1x, f4.2)') r, out (maxloc (in, r >= in)) end do
end program price_fraction</lang> Sample output: <lang>0.997560 1.00 0.566825 0.70 0.965915 1.00 0.747928 0.82 0.367391 0.54 0.480637 0.62 0.073754 0.18 0.005355 0.10 0.347081 0.50 0.342244 0.50</lang>
Haskell
<lang haskell>price_fraction n
| n < 0 || n > 1 = error "Values must be between 0 and 1." | n < 0.06 = 0.10 | n < 0.11 = 0.18 | n < 0.16 = 0.26 | n < 0.21 = 0.32 | n < 0.26 = 0.38 | n < 0.31 = 0.44 | n < 0.36 = 0.50 | n < 0.41 = 0.54 | n < 0.46 = 0.58 | n < 0.51 = 0.62 | n < 0.56 = 0.66 | n < 0.61 = 0.70 | n < 0.66 = 0.74 | n < 0.71 = 0.78 | n < 0.76 = 0.82 | n < 0.81 = 0.86 | n < 0.86 = 0.90 | n < 0.91 = 0.94 | n < 0.96 = 0.98 | otherwise = 1.00</lang>
Alternative
:
<lang haskell>table = [
(0.06, 0.10), (0.11, 0.18), (0.16, 0.26), (0.21, 0.32), (0.26, 0.38), (0.31, 0.44), (0.36, 0.50), (0.41, 0.54), (0.46, 0.58), (0.51, 0.62), (0.56, 0.66), (0.61, 0.70), (0.66, 0.74), (0.71, 0.78), (0.76, 0.82), (0.81, 0.86), (0.86, 0.90), (0.91, 0.94), (0.96, 0.98), (1.01, 1.00), ]
price_fraction n
| n < 0 || n > 1 = error "Values must be between 0 and 1." | otherwise = snd $ head $ dropWhile ((<= n) . fst) table</lang>
J
Solution: <lang j>le =: -0.96 0.91 0.86 0.81 0.76 0.71 0.66 0.61 0.56 0.51 0.46 0.41 0.36 0.31 0.26 0.21 0.16 0.11 0.06 0.0 out =: 1.00 0.98 0.94 0.90 0.86 0.82 0.78 0.74 0.70 0.66 0.62 0.58 0.54 0.50 0.44 0.38 0.32 0.26 0.18 0.1
priceFraction =: out {~ le I. -</lang>
Example: <lang j> priceFraction 0.34 0.070145 0.06 0.05 0.50214 0.56 1 0.99 0 0.5 0.18 0.18 0.1 0.62 0.7 1 1 0.1</lang>
This implementation performs a binary search on the boundary values, and then uses the resulting index to select from the result values.
To prevent J's binary search from doing the wrong thing for values equal to a boundary, both the boundary values and the search value are negated.
Java
<lang java>import java.util.Random;
public class Main { private static float priceFraction(float f) { if (0.00f <= f && f < 0.06f) return 0.10f; else if (f < 0.11f) return 0.18f; else if (f < 0.16f) return 0.26f; else if (f < 0.21f) return 0.32f; else if (f < 0.26f) return 0.38f; else if (f < 0.31f) return 0.44f; else if (f < 0.36f) return 0.50f; else if (f < 0.41f) return 0.54f; else if (f < 0.46f) return 0.58f; else if (f < 0.51f) return 0.62f; else if (f < 0.56f) return 0.66f; else if (f < 0.61f) return 0.70f; else if (f < 0.66f) return 0.74f; else if (f < 0.71f) return 0.78f; else if (f < 0.76f) return 0.82f; else if (f < 0.81f) return 0.86f; else if (f < 0.86f) return 0.90f; else if (f < 0.91f) return 0.94f; else if (f < 0.96f) return 0.98f; else if (f < 1.01f) return 1.00f; else throw new IllegalArgumentException(); }
public static void main(String[] args) { Random rnd = new Random(); for (int i = 0; i < 5; i++) { float f = rnd.nextFloat(); System.out.format("%8.6f -> %4.2f%n", f, priceFraction(f)); } } }</lang> Output:
0.149969 -> 0.26 0.310605 -> 0.50 0.616683 -> 0.74 0.194047 -> 0.32 0.724852 -> 0.82
MUMPS
<lang MUMPS>PRICFRAC(X)
;Outputs a specified value dependent upon the input value ;The non-inclusive upper limits are encoded in the PFMAX string, and the values ;to convert to are encoded in the PFRES string. NEW PFMAX,PFRES,I,RESULT SET PFMAX=".06^.11^.16^.21^.26^.31^.36^.41^.46^.51^.56^.61^.66^.71^.76^.81^.86^.91^.96^1.01" SET PFRES=".10^.18^.26^.32^.38^.44^.50^.54^.58^.62^.66^.70^.74^.78^.82^.86^.90^.94^.98^1.00" Q:(X<0)!(X>1.01) "" FOR I=1:1:$LENGTH(PFMAX,"^") Q:($DATA(RESULT)'=0) SET:X<$P(PFMAX,"^",I) RESULT=$P(PFRES,"^",I) KILL PFMAX,PFRES,I QUIT RESULT</lang>
Output:
USER>W $$PRICFRAC^ROSETTA(.04) .10 USER>W $$PRICFRAC^ROSETTA(.06) .18 USER>W $$PRICFRAC^ROSETTA(.40) .54 USER>W $$PRICFRAC^ROSETTA(1.40) USER>W $$PRICFRAC^ROSETTA(.81) .90
OCaml
<lang ocaml>let price_fraction v =
if v < 0.0 || v >= 1.01 then
invalid_arg "price_fraction";
let rec aux = function
| (x,r)::tl ->
if v < x then r
else aux tl
| [] -> assert false
in
aux [
0.06, 0.10; 0.11, 0.18; 0.16, 0.26; 0.21, 0.32; 0.26, 0.38;
0.31, 0.44; 0.36, 0.50; 0.41, 0.54; 0.46, 0.58; 0.51, 0.62;
0.56, 0.66; 0.61, 0.70; 0.66, 0.74; 0.71, 0.78; 0.76, 0.82;
0.81, 0.86; 0.86, 0.90; 0.91, 0.94; 0.96, 0.98; 1.01, 1.00;
]</lang>
<lang ocaml>let () =
let ok_tests = [ (0.3793, 0.54); (0.4425, 0.58); (0.0746, 0.18); (0.6918, 0.78); (0.2993, 0.44); (0.5486, 0.66); (0.7848, 0.86); (0.9383, 0.98); (0.2292, 0.38); ] in Printf.printf " input res ok\n"; List.iter (fun (v,ok) -> let r = price_fraction v in Printf.printf " %6g %g %b\n" v r (r = ok); ) ok_tests;
- </lang>
Oz
Using a for-loop with return and a default value for values >= 1.01. For out-of-range input, a "failed value" is returned, i.e. a value that throws an exception when it is accessed.
<lang oz>fun {PriceFraction X}
OutOfRange = {Value.failed outOfRange(X)}
in
for Limit#Result in
[0.00#OutOfRange
0.06#0.10 0.11#0.18 0.16#0.26 0.21#0.32 0.26#0.38 0.31#0.44 0.36#0.5
0.41#0.54 0.46#0.58 0.51#0.62 0.56#0.66 0.61#0.70 0.66#0.74 0.71#0.78
0.76#0.82 0.81#0.86 0.86#0.90 0.91#0.94 0.96#0.98 1.01#1.00
]
return:Return
default:OutOfRange
do
if X < Limit then {Return Result} end
end
end</lang>
Perl 6
<lang perl6>my $table = " >= 0.00 < 0.06 := 0.10 >= 0.06 < 0.11 := 0.18 >= 0.11 < 0.16 := 0.26 >= 0.16 < 0.21 := 0.32 >= 0.21 < 0.26 := 0.38 >= 0.26 < 0.31 := 0.44 >= 0.31 < 0.36 := 0.50 >= 0.36 < 0.41 := 0.54 >= 0.41 < 0.46 := 0.58 >= 0.46 < 0.51 := 0.62 >= 0.51 < 0.56 := 0.66 >= 0.56 < 0.61 := 0.70 >= 0.61 < 0.66 := 0.74 >= 0.66 < 0.71 := 0.78 >= 0.71 < 0.76 := 0.82 >= 0.76 < 0.81 := 0.86 >= 0.81 < 0.86 := 0.90 >= 0.86 < 0.91 := 0.94 >= 0.91 < 0.96 := 0.98 >= 0.96 < 1.01 := 1.00 ";
my $value = 0.44;
say price($value);
sub price($value) { for $table.lines -> $line { $line ~~ / '>=' \s+ (\S+) \s+ '<' \s+ (\S+) \s+ ':=' \s+ (\S+)/; return $2 if $0 <= $value < $1; } fail "Out of range"; }</lang> Perhaps a better approach is just to build an array of 101 entries. Memory is cheap, and array lookup is blazing fast, especially important if used in a loop as below. Moreover, in Perl 6 we don't have to worry about floating point misrepresentations of decimals because decimal fractions are stored as rationals.
<lang perl6>my @price = map *.value,
( 0 ..^ 6 X=> 0.10), ( 6 ..^ 11 X=> 0.18), (11 ..^ 16 X=> 0.26), (16 ..^ 21 X=> 0.32), (21 ..^ 26 X=> 0.38), (26 ..^ 31 X=> 0.44), (31 ..^ 36 X=> 0.50), (36 ..^ 41 X=> 0.54), (41 ..^ 46 X=> 0.58), (46 ..^ 51 X=> 0.62), (51 ..^ 56 X=> 0.66), (56 ..^ 61 X=> 0.70), (61 ..^ 66 X=> 0.74), (66 ..^ 71 X=> 0.78), (71 ..^ 76 X=> 0.82), (76 ..^ 81 X=> 0.86), (81 ..^ 86 X=> 0.90), (86 ..^ 91 X=> 0.94), (91 ..^ 96 X=> 0.98), (96 ..^101 X=> 1.00),
while prompt("value: ") -> $value {
say @price[ $value * 100 ] // note "Out of range";
}</lang>
Yet another approach is to use the conditional operator to encode the table. This allows each endpoint to be written once, avoiding duplication. <lang perl6>sub price_fraction ( Num $n where { $^n >= 0 and $^n <= 1 } ) {
( $n < 0.06 ) ?? 0.10 !! ( $n < 0.11 ) ?? 0.18 !! ( $n < 0.16 ) ?? 0.26 !! ( $n < 0.21 ) ?? 0.32 !! ( $n < 0.26 ) ?? 0.38 !! ( $n < 0.31 ) ?? 0.44 !! ( $n < 0.36 ) ?? 0.50 !! ( $n < 0.41 ) ?? 0.54 !! ( $n < 0.46 ) ?? 0.58 !! ( $n < 0.51 ) ?? 0.62 !! ( $n < 0.56 ) ?? 0.66 !! ( $n < 0.61 ) ?? 0.70 !! ( $n < 0.66 ) ?? 0.74 !! ( $n < 0.71 ) ?? 0.78 !! ( $n < 0.76 ) ?? 0.82 !! ( $n < 0.81 ) ?? 0.86 !! ( $n < 0.86 ) ?? 0.90 !! ( $n < 0.91 ) ?? 0.94 !! ( $n < 0.96 ) ?? 0.98 !! 1.00 ;
}
while prompt("value: ") -> $value {
last if $value ~~ /exit|quit/; say price_fraction(+$value);
}</lang>
PL/I
<lang PL/I> declare t(20) fixed decimal (3,2) static initial (
.06, .11, .16, .21, .26, .31, .36, .41, .46, .51, .56, .61, .66, .71, .76, .81, .86, .91, .96, 1.01);
declare r(20) fixed decimal (3,2) static initial (
.10, .18, .26, .32, .38, .44, .50, .54, .58, .62, .66, .70, .74, .78, .82, .86, .90, .94, .98, 1);
declare x float, d fixed decimal (3,2); declare i fixed binary;
loop:
do i = 1 to 20;
if x < t(i) then
do; d = r(i); leave loop; end;
end;
</lang>
PicoLisp
<lang PicoLisp>(scl 2)
(de price (Pr)
(format
(cdr
(rank Pr
(quote
(0.00 . 0.10)
(0.06 . 0.18)
(0.11 . 0.26)
(0.16 . 0.32)
(0.21 . 0.38)
(0.26 . 0.44)
(0.31 . 0.50)
(0.36 . 0.54)
(0.41 . 0.58)
(0.46 . 0.62)
(0.51 . 0.66)
(0.56 . 0.70)
(0.61 . 0.74)
(0.66 . 0.78)
(0.71 . 0.82)
(0.76 . 0.86)
(0.81 . 0.90)
(0.86 . 0.94)
(0.91 . 0.98)
(0.96 . 1.00) ) ) )
*Scl ) )
(for N (0.3793 0.4425 0.0746 0.6918 0.2993 0.5486 0.7848 0.9383 0.2292)
(prinl (price N)) )</lang>
Output:
0.54 0.58 0.18 0.78 0.44 0.66 0.86 0.98 0.38
PureBasic
<lang PureBasic>Procedure.f PriceFraction(price.f)
;returns price unchanged if value is invalid
Protected fraction
Select price * 100
Case 0 To 5
fraction = 10
Case 06 To 10
fraction = 18
Case 11 To 15
fraction = 26
Case 16 To 20
fraction = 32
Case 21 To 25
fraction = 38
Case 26 To 30
fraction = 44
Case 31 To 35
fraction = 5
Case 36 To 40
fraction = 54
Case 41 To 45
fraction = 58
Case 46 To 50
fraction = 62
Case 51 To 55
fraction = 66
Case 56 To 60
fraction = 7
Case 61 To 65
fraction = 74
Case 66 To 70
fraction = 78
Case 71 To 75
fraction = 82
Case 76 To 80
fraction = 86
Case 81 To 85
fraction = 9
Case 86 To 90
fraction = 94
Case 91 To 95
fraction = 98
Case 96 To 100
fraction = 100
Default
ProcedureReturn price
EndSelect
ProcedureReturn fraction / 100
EndProcedure
If OpenConsole()
Define x.f, i For i = 1 To 10 x = Random(10000)/10000 PrintN(StrF(x, 4) + " -> " + StrF(PriceFraction(x), 2)) Next Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang> Sample output:
0.3793 -> 0.54 0.4425 -> 0.58 0.0746 -> 0.18 0.6918 -> 0.78 0.2993 -> 0.44 0.5486 -> 0.66 0.7848 -> 0.86 0.9383 -> 0.98 0.2292 -> 0.38 0.9560 -> 1.00
Python
Using the bisect standard module to reduce the comparisons with members of the cin array.
<lang python>>>> import bisect >>> _cin = [.06, .11, .16, .21, .26, .31, .36, .41, .46, .51, .56, .61, .66, .71, .76, .81, .86, .91, .96, 1.01] >>> _cout = [.10, .18, .26, .32, .38, .44, .50, .54, .58, .62, .66, .70, .74, .78, .82, .86, .90, .94, .98, 1.00] >>> def pricerounder(pricein): return _cout[ bisect.bisect_right(_cin, pricein) ]</lang>
When dealing with money it is good to think about possible loss of precision. If we change the units to be integer cents we could use the following exact routine: <lang python>>>> import bisect >>> _cin = [ 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101] >>> _cout = [10, 18, 26, 32, 38, 44, 50, 54, 57, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 100] >>> def centsrounder(centsin): return _cout[ bisect.bisect_right(_cin, centsin) ]</lang> Other options are to use the fractions or decimals modules for calculating money to a known precision.
Bisection library code
- The
bisectPython standard library function uses the following code that improves on a simple linear scan through a sorted list: - <lang python>def bisect_right(a, x, lo=0, hi=None):
"""Return the index where to insert item x in list a, assuming a is sorted.
The return value i is such that all e in a[:i] have e <= x, and all e in a[i:] have e > x. So if x already appears in the list, a.insert(x) will insert just after the rightmost x already there.
Optional args lo (default 0) and hi (default len(a)) bound the slice of a to be searched. """
if lo < 0:
raise ValueError('lo must be non-negative')
if hi is None:
hi = len(a)
while lo < hi:
mid = (lo+hi)//2
if x < a[mid]: hi = mid
else: lo = mid+1
return lo</lang>
R
<lang r> price_fraction <- function(x) {
stopifnot(all(x >= 0 & x <= 1)) breaks <- seq(0.06, 1.01, 0.05) values <- c(.1, .18, .26, .32, .38, .44, .5, .54, .58, .62, .66, .7, .74, .78, .82, .86, .9, .94, .98, 1) indices <- sapply(x, function(x) which(x < breaks)[1]) values[indices]
}
- Example usage:
price_fraction(c(0, .01, 0.06, 0.25, 1)) # 0.10 0.10 0.18 0.38 1.00 </lang>
You can extract the contents of the table as follows:
<lang r> dfr <- read.table(tc <- textConnection( ">= 0.00 < 0.06 := 0.10 >= 0.06 < 0.11 := 0.18 >= 0.11 < 0.16 := 0.26 >= 0.16 < 0.21 := 0.32 >= 0.21 < 0.26 := 0.38 >= 0.26 < 0.31 := 0.44 >= 0.31 < 0.36 := 0.50 >= 0.36 < 0.41 := 0.54 >= 0.41 < 0.46 := 0.58 >= 0.46 < 0.51 := 0.62 >= 0.51 < 0.56 := 0.66 >= 0.56 < 0.61 := 0.70 >= 0.61 < 0.66 := 0.74 >= 0.66 < 0.71 := 0.78 >= 0.71 < 0.76 := 0.82 >= 0.76 < 0.81 := 0.86 >= 0.81 < 0.86 := 0.90 >= 0.86 < 0.91 := 0.94 >= 0.91 < 0.96 := 0.98 >= 0.96 < 1.01 := 1.00")); close(tc) breaks <- dfr$V4 values <- dfr$V6 </lang>
Ruby
A simple function with hardcoded values. <lang ruby>def rescale_price_fraction(value)
raise ArgumentError, "value=#{value}, must have: 0 <= value < 1.01" if value < 0 || value >= 1.01
if value < 0.06 then 0.10
elsif value < 0.11 then 0.18
elsif value < 0.16 then 0.26
elsif value < 0.21 then 0.32
elsif value < 0.26 then 0.38
elsif value < 0.31 then 0.44
elsif value < 0.36 then 0.50
elsif value < 0.41 then 0.54
elsif value < 0.46 then 0.58
elsif value < 0.51 then 0.62
elsif value < 0.56 then 0.66
elsif value < 0.61 then 0.70
elsif value < 0.66 then 0.74
elsif value < 0.71 then 0.78
elsif value < 0.76 then 0.82
elsif value < 0.81 then 0.86
elsif value < 0.86 then 0.90
elsif value < 0.91 then 0.94
elsif value < 0.96 then 0.98
elsif value < 1.01 then 1.00
end
end</lang>
Or, where we can cut and paste the textual table in one place
for the String#lines method.
For Ruby 1.8.6, use String#each_line
<lang ruby>class Price
ConversionTable = <<-END_OF_TABLE >= 0.00 < 0.06 := 0.10 >= 0.06 < 0.11 := 0.18 >= 0.11 < 0.16 := 0.26 >= 0.16 < 0.21 := 0.32 >= 0.21 < 0.26 := 0.38 >= 0.26 < 0.31 := 0.44 >= 0.31 < 0.36 := 0.50 >= 0.36 < 0.41 := 0.54 >= 0.41 < 0.46 := 0.58 >= 0.46 < 0.51 := 0.62 >= 0.51 < 0.56 := 0.66 >= 0.56 < 0.61 := 0.70 >= 0.61 < 0.66 := 0.74 >= 0.66 < 0.71 := 0.78 >= 0.71 < 0.76 := 0.82 >= 0.76 < 0.81 := 0.86 >= 0.81 < 0.86 := 0.90 >= 0.86 < 0.91 := 0.94 >= 0.91 < 0.96 := 0.98 >= 0.96 < 1.01 := 1.00 END_OF_TABLE
RE = %r{ ([<>=]+) \s* (\d\.\d\d) \s* ([<>=]+) \s* (\d\.\d\d) \D+ (\d\.\d\d) }x
# extract the comparison operators and numbers from the table
CONVERSION_TABLE = ConversionTable.lines.inject([]) do |table, line|
m = line.match(RE)
if not m.nil? and m.length == 6
table << [m[1], m[2].to_f, m[3], m[4].to_f, m[5].to_f]
end
table
end
MIN_COMP, MIN = CONVERSION_TABLE[0][0..1] MAX_COMP, MAX = CONVERSION_TABLE[-1][2..3]
def initialize(value)
if (not value.send(MIN_COMP, MIN)) or (not value.send(MAX_COMP, MAX))
raise ArgumentError, "value=#{value}, must have: #{MIN} #{MIN_COMP} value #{MAX_COMP} #{MAX}"
end
@standard_value = CONVERSION_TABLE.find do |comp1, lower, comp2, upper, standard|
value.send(comp1, lower) and value.send(comp2, upper)
end.last
end
attr_reader :standard_value
end</lang>
And a test suite <lang ruby>require 'test/unit'
class PriceFractionTests < Test::Unit::TestCase
@@ok_tests = [ [0.3793, 0.54], [0.4425, 0.58], [0.0746, 0.18], [0.6918, 0.78], [0.2993, 0.44], [0.5486, 0.66], [0.7848, 0.86], [0.9383, 0.98], [0.2292, 0.38], ] @@bad_tests = [1.02, -3]
def test_ok
@@ok_tests.each do |val, exp|
assert_equal(exp, rescale_price_fraction(val))
assert_equal(exp, Price.new(val).standard_value)
end
@@bad_tests.each do |val|
assert_raise(ArgumentError) {rescale_price_fraction(val)}
assert_raise(ArgumentError) {Price.new(val).standard_value}
end
end
end</lang>
output
Loaded suite price_fraction Started . Finished in 0.001000 seconds. 1 tests, 22 assertions, 0 failures, 0 errors, 0 skips
Scala
<lang scala>def priceFraction(x:Double)=x match {
case n if n>=0 && n<0.06 => 0.10 case n if n<0.11 => 0.18 case n if n<0.36 => ((((n*100).toInt-11)/5)*6+26)/100.toDouble case n if n<0.96 => ((((n*100).toInt-31)/5)*4+50)/100.toDouble case _ => 1.00
}
def testPriceFraction()=
for(n <- 0.00 to (1.00, 0.01)) println("%.2f %.2f".format(n, priceFraction(n)))</lang>
Output
0,00 0,10 0,01 0,10 0,02 0,10 0,03 0,10 0,04 0,10 0,05 0,10 0,06 0,18 ... 0,25 0,38 0,26 0,44 0,27 0,44 0,28 0,44 0,29 0,44 0,30 0,44 0,31 0,50 0,32 0,50 0,33 0,50 0,34 0,50 0,35 0,50 0,36 0,54 0,37 0,54 ... 0,88 0,94 0,89 0,94 0,90 0,94 0,91 0,98 0,92 0,98 0,93 0,98 0,94 0,98 0,95 0,98 0,96 1,00 0,97 1,00 0,98 1,00 0,99 1,00 1,00 1,00
Smalltalk
<lang smalltalk>"Table driven rescale" Object subclass: PriceRescale [
|table|
PriceRescale class >> new: theTable [
^ self basicNew initialize: theTable
]
initialize: theTable [
table := theTable asOrderedCollection.
^self
]
rescale: aPrice [ |v1 v2|
1 to: (table size - 1) do: [:i|
v1 := table at: i.
v2 := table at: (i+1).
((aPrice >= (v1 x)) & (aPrice < (v2 x)))
ifTrue: [ ^ v1 y ]
].
(aPrice < ((v1:=(table first)) x)) ifTrue: [ ^ v1 y ].
(aPrice >= ((v1:=(table last)) x)) ifTrue: [ ^ v1 y ]
]
].
|pr| pr := PriceRescale
new: { 0.00@0.10 .
0.06@0.18 .
0.11@0.26 .
0.16@0.32 .
0.21@0.38 .
0.26@0.44 .
0.31@0.50 .
0.36@0.54 .
0.41@0.58 .
0.46@0.62 .
0.51@0.66 .
0.56@0.70 .
0.61@0.74 .
0.66@0.78 .
0.71@0.82 .
0.76@0.86 .
0.81@0.90 .
0.86@0.94 .
0.91@0.98 .
0.96@1.00 .
1.01@1.00
}.
"get a price" (pr rescale: ( (Random between: 0 and: 100)/100 )) displayNl.</lang>
Tcl
Structured as two functions, one to parse the input data as described in the problem into a form which Tcl can work with easily, and the other to perform the mapping. <lang tcl># Used once to turn the table into a "nice" form proc parseTable table {
set map {}
set LINE_RE {^ *>= *([0-9.]+) *< *([0-9.]+) *:= *([0-9.]+) *$}
foreach line [split $table \n] {
if {[string trim $line] eq ""} continue if {[regexp $LINE_RE $line -> min max target]} { lappend map $min $max $target } else { error "invalid table format: $line" }
} return $map
}
- How to apply the "nice" table to a particular value
proc priceFraction {map value} {
foreach {minimum maximum target} $map {
if {$value >= $minimum && $value < $maximum} {return $target}
} # Failed to map; return the input return $value
}</lang> How it is used: <lang tcl># Make the mapping set inputTable {
>= 0.00 < 0.06 := 0.10 >= 0.06 < 0.11 := 0.18 >= 0.11 < 0.16 := 0.26 >= 0.16 < 0.21 := 0.32 >= 0.21 < 0.26 := 0.38 >= 0.26 < 0.31 := 0.44 >= 0.31 < 0.36 := 0.50 >= 0.36 < 0.41 := 0.54 >= 0.41 < 0.46 := 0.58 >= 0.46 < 0.51 := 0.62 >= 0.51 < 0.56 := 0.66 >= 0.56 < 0.61 := 0.70 >= 0.61 < 0.66 := 0.74 >= 0.66 < 0.71 := 0.78 >= 0.71 < 0.76 := 0.82 >= 0.76 < 0.81 := 0.86 >= 0.81 < 0.86 := 0.90 >= 0.86 < 0.91 := 0.94 >= 0.91 < 0.96 := 0.98 >= 0.96 < 1.01 := 1.00
} set map [parseTable $inputTable]
- Apply the mapping to some inputs (from the Oz example)
foreach example {.7388727 .8593103 .826687 .3444635 .0491907} {
puts "$example -> [priceFraction $map $example]"
}</lang> Output:
.7388727 -> 0.82 .8593103 -> 0.90 .826687 -> 0.90 .3444635 -> 0.50 .0491907 -> 0.10
Ursala
<lang Ursala>#import flo
le = <0.06,.11,.16,.21,.26,.31,.36,.41,.46,.51,.56,.61,.66,.71,.76,.81,.86,.91,.96,1.01> out = <0.10,.18,.26,.32,.38,.44,.50,.54,.58,.62,.66,.70,.74,.78,.82,.86,.90,.94,.98,1.>
price_fraction = fleq@rlPlX*|rhr\~&p(le,out)</lang> main points:
~&p(le,out)zips the pair of listsleandoutinto a list of pairs- A function of the form
f\yapplied to an argumentxevaluates tof(x,y) - A function of the form
f*|applied to a pair(x,y)whereyis a list, makes a list of pairs withxon the left of each item and an item ofyon the right. Then it appliesfto each pair, makes a list of the right sides of those for whichfreturned true, and makes a separate list of the right sides of those for whichfreturned false. - The suffix
rhrafter the*|operator extracts the right side of the head of the right list from the result. - The operand to the
*|operator,fleq@rlPlXis the less-or-equal predicate on floating point numbers, composed with the function~&rlPlXwhich transforms a triple(u,(v,w))to(v,u)
test program: <lang Ursala>#cast %eL
test = price_fraction* <0.34,0.070145,0.06,0.05,0.50214,0.56,1.,0.99,0.> </lang> output:
< 5.000000e-01, 1.800000e-01, 1.800000e-01, 1.000000e-01, 6.200000e-01, 7.000000e-01, 1.000000e+00, 1.000000e+00, 1.000000e-01>