Bin given limits

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Task
Bin given limits
You are encouraged to solve this task according to the task description, using any language you may know.

You are given a list of n ascending, unique numbers which are to form limits for n+1 bins which count how many of a large set of input numbers fall in the range of each bin.

(Assuming zero-based indexing)

   bin[0] counts how many inputs are < limit[0]
   bin[1] counts how many inputs are >= limit[0] and < limit[1]
   ..
   bin[n-1] counts how many inputs are >= limit[n-2] and < limit[n-1]
   bin[n] counts how many inputs are >= limit[n-1]
Task

The task is to create a function that given the ascending limits and a stream/ list of numbers, will return the bins; together with another function that given the same list of limits and the binning will print the limit of each bin together with the count of items that fell in the range.

Assume the numbers to bin are too large to practically sort.

Task examples

Part 1: Bin using the following limits the given input data

   limits  = [23, 37, 43, 53, 67, 83]
   data = [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
           16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]

Part 2: Bin using the following limits the given input data

   limits = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
   data = [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
           416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
           655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
           346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
           345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
           854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
           787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
           698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
           605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
           466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]

Show output here, on this page.

11l[edit]

Translation of: Python
F bisect_right(a, x)
   V lo = 0
   V hi = a.len
   L lo < hi
      V mid = (lo + hi) I/ 2
      I x < a[mid]
         hi = mid
      E
         lo = mid + 1
   R lo

F bin_it(limits, data)
   ‘Bin data according to (ascending) limits.’
   V bins = [0] * (limits.len + 1)
   L(d) data
      bins[bisect_right(limits, d)]++
   R bins

F bin_print(limits, bins)
   print(‘          < #3 := #3’.format(limits[0], bins[0]))
   L(lo, hi, count) zip(limits, limits[1..], bins[1..])
      print(‘>= #3 .. < #3 := #3’.format(lo, hi, count))
   print(‘>= #3          := #3’.format(limits.last, bins.last))

print("RC FIRST EXAMPLE\n")
V limits = [23, 37, 43, 53, 67, 83]
V data = [95, 21, 94, 12, 99, 4, 70, 75, 83, 93, 52, 80, 57, 5, 53, 86, 65, 17, 92, 83, 71, 61, 54, 58, 47,
          16,  8,  9, 32, 84, 7, 87, 46, 19, 30, 37, 96, 6, 98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55]
V bins = bin_it(limits, data)
bin_print(limits, bins)

print("\nRC SECOND EXAMPLE\n")
limits = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
data = [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
        416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
        655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
        346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
        345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
        854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
        787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
        698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
        605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
        466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]
bins = bin_it(limits, data)
bin_print(limits, bins)
Output:
RC FIRST EXAMPLE

          <  23 :=  11
>=  23 .. <  37 :=   4
>=  37 .. <  43 :=   2
>=  43 .. <  53 :=   6
>=  53 .. <  67 :=   9
>=  67 .. <  83 :=   5
>=  83          :=  13

RC SECOND EXAMPLE

          <  14 :=   3
>=  14 .. <  18 :=   0
>=  18 .. < 249 :=  44
>= 249 .. < 312 :=  10
>= 312 .. < 389 :=  16
>= 389 .. < 392 :=   2
>= 392 .. < 513 :=  28
>= 513 .. < 591 :=  16
>= 591 .. < 634 :=   6
>= 634 .. < 720 :=  16
>= 720          :=  59

Action![edit]

DEFINE MAX_BINS="20"

PROC Count(INT ARRAY limits INT nLimits INT ARRAY data INT nData INT ARRAY bins)
  INT i,j,v
  BYTE found

  FOR i=0 TO nLimits
  DO
    bins(i)=0
  OD
  FOR j=0 TO nData-1
  DO
    v=data(j) found=0
    FOR i=0 TO nLimits-1
    DO
      IF v<limits(i) THEN
        bins(i)==+1
        found=1
        EXIT
      FI
    OD
    IF found=0 THEN
      bins(nLimits)==+1
    FI
  OD
RETURN

PROC Test(INT ARRAY limits INT nLimits INT ARRAY data INT nData)
  INT ARRAY bins(MAX_BINS)
  INT i

  Count(limits,nLimits,data,nData,bins)
  FOR i=0 TO nLimits
  DO
    IF i=0 THEN
      PrintF("<%I",limits(i))
    ELSEIF i=nLimits THEN
      PrintF(">=%I",limits(i-1))
    ELSE
      PrintF("%I..%I",limits(i-1),limits(i)-1)
    FI
    PrintF(": %I%E",bins(i))
  OD
RETURN

PROC Main()
  INT ARRAY
    limits1(6)=[23 37 43 53 67 83],
    data1(50)=[
      95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71 61 54 58 47
      16  8  9 32 84 7 87 46 19 30 37 96 6 98 40 79 97 45 64 60 29 49 36 43 55],
    limits2(10)=[14 18 249 312 389 392 513 591 634 720],
    data2(200)=[
      445 814 519 697 700 130 255 889 481 122 932  77 323 525 570 219 367 523 442 933 
      416 589 930 373 202 253 775  47 731 685 293 126 133 450 545 100 741 583 763 306 
      655 267 248 477 549 238  62 678  98 534 622 907 406 714 184 391 913  42 560 247 
      346 860  56 138 546  38 985 948  58 213 799 319 390 634 458 945 733 507 916 123 
      345 110 720 917 313 845 426   9 457 628 410 723 354 895 881 953 677 137 397  97 
      854 740  83 216 421  94 517 479 292 963 376 981 480  39 257 272 157   5 316 395 
      787 942 456 242 759 898 576  67 298 425 894 435 831 241 989 614 987 770 384 692 
      698 765 331 487 251 600 879 342 982 527 736 795 585  40  54 901 408 359 577 237 
      605 847 353 968 832 205 838 427 876 959 686 646 835 127 621 892 443 198 988 791 
      466  23 707 467  33 670 921 180 991 396 160 436 717 918   8 374 101 684 727 749]
  
  Test(limits1,6,data1,50) PutE()
  Test(limits2,10,data2,200)
RETURN
Output:

Screenshot from Atari 8-bit computer

<23: 11
23..36: 4
37..42: 2
43..52: 6
53..66: 9
67..82: 5
>=83: 13

<14: 3
14..17: 0
18..248: 44
249..311: 10
312..388: 16
389..391: 2
392..512: 28
513..590: 16
591..633: 6
634..719: 16
>=720: 59

Ada[edit]

This example works with Ada 2012. The definition of the subtype Limits_Array employs a dynamic predicate to ensure that the limits array is sorted. The solution defines the binning types and operations within an Ada package, providing modularity and simplifying the code in the main procedure.

package specification:

package binning is
   type Nums_Array is array (Natural range <>) of Integer;
   function Is_Sorted (Item : Nums_Array) return Boolean;
   subtype Limits_Array is Nums_Array with
        Dynamic_Predicate => Is_Sorted (Limits_Array);
   function Bins (Limits : Limits_Array; Data : Nums_Array) return Nums_Array;
   procedure Print (Limits : Limits_Array; Bin_Result : Nums_Array);
end binning;

package body:

pragma Ada_2012;
with Ada.Text_IO;         use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;

package body binning is

   ---------------
   -- Is_Sorted --
   ---------------

   function Is_Sorted (Item : Nums_Array) return Boolean is
   begin
      return
        (for all i in Item'First .. Item'Last - 1 => Item (i) < Item (i + 1));
   end Is_Sorted;

   ----------
   -- Bins --
   ----------

   function Bins (Limits : Limits_Array; Data : Nums_Array) return Nums_Array
   is
      Result : Nums_Array (Limits'First .. Limits'Last + 1) := (others => 0);
      Bin_Index : Natural;
   begin
      for value of Data loop
         Bin_Index := Result'First;
         for I in reverse Limits'Range loop
            if value >= Limits (I) then
               Bin_Index := I + 1;
               exit;
            end if;
         end loop;
         Result (Bin_Index) := Result (Bin_Index) + 1;
      end loop;
      return Result;
   end Bins;

   -----------
   -- Print --
   -----------

   procedure Print (Limits : Limits_Array; Bin_Result : Nums_Array) is
   begin
      if Limits'Length = 0 then
         return;
      end if;
      Put ("           < ");
      Put (Item => Limits (Limits'First), Width => 3);
      Put (": ");
      Put (Item => Bin_Result (Bin_Result'First), Width => 2);
      New_Line;
      for i in Limits'First + 1 .. Limits'Last loop
         Put (">= ");
         Put (Item => Limits (i - 1), Width => 3);
         Put (" and < ");
         Put (Item => Limits (i), Width => 3);
         Put (": ");
         Put (Item => Bin_Result (i), Width => 2);
         New_Line;
      end loop;
      Put (">= ");
      Put (Item => Limits (Limits'Last), Width => 3);
      Put ("          : ");
      Put (Item => Bin_Result (Bin_Result'Last), Width => 2);
      New_Line;
   end Print;

end binning;

main procedure:

with Ada.Text_IO;         use Ada.Text_IO;
with binning;             use binning;

procedure Main is
   Limits_1 : Limits_Array := (23, 37, 43, 53, 67, 83);
   Data_1   : Nums_Array   :=
     (95, 21, 94, 12, 99, 4, 70, 75, 83, 93, 52, 80, 57, 5, 53, 86, 65, 17, 92,
      83, 71, 61, 54, 58, 47, 16, 8, 9, 32, 84, 7, 87, 46, 19, 30, 37, 96, 6,
      98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55);
   Limits_2 : Limits_Array := (14, 18, 249, 312, 389, 392, 513, 591, 634, 720);
   Data_2   : Nums_Array   :=
     (445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77, 323, 525, 570,
      219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 253, 775, 47, 731, 685,
      293, 126, 133, 450, 545, 100, 741, 583, 763, 306, 655, 267, 248, 477,
      549, 238, 62, 678, 98, 534, 622, 907, 406, 714, 184, 391, 913, 42, 560,
      247, 346, 860, 56, 138, 546, 38, 985, 948, 58, 213, 799, 319, 390, 634,
      458, 945, 733, 507, 916, 123, 345, 110, 720, 917, 313, 845, 426, 9, 457,
      628, 410, 723, 354, 895, 881, 953, 677, 137, 397, 97, 854, 740, 83, 216,
      421, 94, 517, 479, 292, 963, 376, 981, 480, 39, 257, 272, 157, 5, 316,
      395, 787, 942, 456, 242, 759, 898, 576, 67, 298, 425, 894, 435, 831, 241,
      989, 614, 987, 770, 384, 692, 698, 765, 331, 487, 251, 600, 879, 342,
      982, 527, 736, 795, 585, 40, 54, 901, 408, 359, 577, 237, 605, 847, 353,
      968, 832, 205, 838, 427, 876, 959, 686, 646, 835, 127, 621, 892, 443,
      198, 988, 791, 466, 23, 707, 467, 33, 670, 921, 180, 991, 396, 160, 436,
      717, 918, 8, 374, 101, 684, 727, 749);
   Bin_1 : Nums_Array := Bins (Limits => Limits_1, Data => Data_1);
   Bin_2 : Nums_Array := Bins (Limits => Limits_2, Data => Data_2);
begin
   Put_Line ("Example 1:");
   Print (Limits => Limits_1, Bin_Result => Bin_1);
   New_Line;
   Put_Line ("Example 2:");
   Print (Limits => Limits_2, Bin_Result => Bin_2);
end Main;

{output}

Example 1:
           <  23: 11
>=  23 and <  37:  4
>=  37 and <  43:  2
>=  43 and <  53:  6
>=  53 and <  67:  9
>=  67 and <  83:  5
>=  83          : 13

Example 2:
           <  14:  3
>=  14 and <  18:  0
>=  18 and < 249: 44
>= 249 and < 312: 10
>= 312 and < 389: 16
>= 389 and < 392:  2
>= 392 and < 513: 28
>= 513 and < 591: 16
>= 591 and < 634:  6
>= 634 and < 720: 16
>= 720          : 59

ALGOL 68[edit]

BEGIN # count the number pf items that fall into "bins" given he limits #
    # returns an array of "bins" containing the counts of the data items #
    #         that fall into the bins given the limits                   #
    PRIO INTOBINS = 1;
    OP   INTOBINS = ( []INT data, []INT limits )[]INT:
         BEGIN
            [ LWB limits : UPB limits + 1 ]INT bins;
            FOR bin number FROM LWB bins TO UPB bins DO bins[ bin number ] := 0 OD;
            FOR d pos FROM LWB data TO UPB data DO
                INT bin number := LWB bins;
                INT item        = data[ d pos ];
                FOR b pos FROM LWB bins TO UPB bins - 1 WHILE item >= limits[ b pos ] DO
                    bin number +:= 1
                OD;
                bins[ bin number ] +:= 1
            OD;
            bins
         END # INTOBINS # ;
    # shows the limits of the bins and the number of items in each #
    PROC show bins = ( []INT limits, []INT bins )VOID:
         BEGIN
             print( ( "            < ", whole( limits[ LWB limits ], -4 )
                    , ": ", whole( bins[ LWB bins ], -4 )
                    , newline
                    )
                  );
             INT bin number := LWB bins + 1;
             FOR l pos FROM LWB limits + 1 TO UPB limits DO
                 print( ( ">= ",     whole( limits[ l pos - 1 ], -4 )
                        , " and < ", whole( limits[ l pos     ], -4 )
                        , ": ", whole( bins[ bin number ], -4 )
                        , newline
                        )
                      );
                 bin number +:= 1
             OD;
             print( ( "            > ", whole( limits[ UPB limits ], -4 )
                    , ": ", whole( bins[ UPB bins ], -4 )
                    , newline
                    )
                  )
         END # show bins # ;

    # task test cases #
    BEGIN
        print( ( "data set 1", newline ) );
        []INT limits =
            ( 23, 37, 43, 53, 67, 83 );
        []INT data   =
            ( 95, 21, 94, 12, 99,  4, 70, 75, 83, 93, 52, 80, 57,  5, 53, 86, 65, 17, 92, 83, 71, 61, 54, 58, 47
            , 16,  8,  9, 32, 84,  7, 87, 46, 19, 30, 37, 96,  6, 98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55
            );
        show bins( limits, data INTOBINS limits )
    END;
    print( ( newline ) );
    BEGIN
        print( ( "data set 2", newline ) );
        []INT limits =
            (   14,  18, 249, 312, 389, 392, 513, 591, 634, 720 );
        []INT data   =
             ( 445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932,  77, 323, 525, 570, 219, 367, 523, 442, 933
             , 416, 589, 930, 373, 202, 253, 775,  47, 731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306
             , 655, 267, 248, 477, 549, 238,  62, 678,  98, 534, 622, 907, 406, 714, 184, 391, 913,  42, 560, 247
             , 346, 860,  56, 138, 546,  38, 985, 948,  58, 213, 799, 319, 390, 634, 458, 945, 733, 507, 916, 123
             , 345, 110, 720, 917, 313, 845, 426,   9, 457, 628, 410, 723, 354, 895, 881, 953, 677, 137, 397,  97
             , 854, 740,  83, 216, 421,  94, 517, 479, 292, 963, 376, 981, 480,  39, 257, 272, 157,   5, 316, 395
             , 787, 942, 456, 242, 759, 898, 576,  67, 298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692
             , 698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585,  40,  54, 901, 408, 359, 577, 237
             , 605, 847, 353, 968, 832, 205, 838, 427, 876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791
             , 466,  23, 707, 467,  33, 670, 921, 180, 991, 396, 160, 436, 717, 918,   8, 374, 101, 684, 727, 749
             );
        show bins( limits, data INTOBINS limits )
    END
END
Output:
data set 1
            <   23:   11
>=   23 and <   37:    4
>=   37 and <   43:    2
>=   43 and <   53:    6
>=   53 and <   67:    9
>=   67 and <   83:    5
            >   83:   13

data set 2
            <   14:    3
>=   14 and <   18:    0
>=   18 and <  249:   44
>=  249 and <  312:   10
>=  312 and <  389:   16
>=  389 and <  392:    2
>=  392 and <  513:   28
>=  513 and <  591:   16
>=  591 and <  634:    6
>=  634 and <  720:   16
            >  720:   59

AutoHotkey[edit]

Bin_given_limits(limits, data){
    bin := [], counter := 0
    for i, val in data	{
        if (limits[limits.count()] <= val)
            bin["∞", ++counter] := val
        
        else for j, limit in limits
            if (limits[j-1] <= val && val < limits[j])
                bin[limit, ++counter] := val
    }

    for j, limit in limits	{
        output .=  (prevlimit ? prevlimit : "-∞") ", " limit " : " ((x:=bin[limit].Count())?x:0) "`n"
        prevlimit := limit
    }
    return output .=  (prevlimit ? prevlimit : "-∞") ",  ∞ : " ((x:=bin["∞"].Count())?x:0) "`n"
}
Examples:
limits  := [23, 37, 43, 53, 67, 83]
data := [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,16
		, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]
MsgBox, 262144, , % Bin_given_limits(limits, data)

limits := [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
data := [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933
	   ,416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306
	   ,655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247
	   ,346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123
	   ,345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97
	   ,854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395
	   ,787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692
	   ,698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237
	   ,605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791
	   ,466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]
MsgBox, 262144, , % Bin_given_limits(limits, data)
return
Output:
-∞, 23 : 11
23, 37 : 4
37, 43 : 2
43, 53 : 6
53, 67 : 9
67, 83 : 5
83,  ∞ : 13
---------------------------
-∞, 14 : 3
14, 18 : 0
18, 249 : 44
249, 312 : 10
312, 389 : 16
389, 392 : 2
392, 513 : 28
513, 591 : 16
591, 634 : 6
634, 720 : 16
720,  ∞ : 59

C[edit]

#include <stdio.h>
#include <stdlib.h>

size_t upper_bound(const int* array, size_t n, int value) {
    size_t start = 0;
    while (n > 0) {
        size_t step = n / 2;
        size_t index = start + step;
        if (value >= array[index]) {
            start = index + 1;
            n -= step + 1;
        } else {
            n = step;
        }
    }
    return start;
}

int* bins(const int* limits, size_t nlimits, const int* data, size_t ndata) {
    int* result = calloc(nlimits + 1, sizeof(int));
    if (result == NULL)
        return NULL;
    for (size_t i = 0; i < ndata; ++i)
        ++result[upper_bound(limits, nlimits, data[i])];
    return result;
}

void print_bins(const int* limits, size_t n, const int* bins) {
    if (n == 0)
        return;
    printf("           < %3d: %2d\n", limits[0], bins[0]);
    for (size_t i = 1; i < n; ++i)
        printf(">= %3d and < %3d: %2d\n", limits[i - 1], limits[i], bins[i]);
    printf(">= %3d          : %2d\n", limits[n - 1], bins[n]);
}

int main() {
    const int limits1[] = {23, 37, 43, 53, 67, 83};
    const int data1[] = {95, 21, 94, 12, 99, 4,  70, 75, 83, 93, 52, 80, 57,
                         5,  53, 86, 65, 17, 92, 83, 71, 61, 54, 58, 47, 16,
                         8,  9,  32, 84, 7,  87, 46, 19, 30, 37, 96, 6,  98,
                         40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55};

    printf("Example 1:\n");
    size_t n = sizeof(limits1) / sizeof(int);
    int* b = bins(limits1, n, data1, sizeof(data1) / sizeof(int));
    if (b == NULL) {
        fprintf(stderr, "Out of memory\n");
        return EXIT_FAILURE;
    }
    print_bins(limits1, n, b);
    free(b);

    const int limits2[] = {14, 18, 249, 312, 389, 392, 513, 591, 634, 720};
    const int data2[] = {
        445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77,  323, 525,
        570, 219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 253, 775, 47,
        731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306, 655, 267,
        248, 477, 549, 238, 62,  678, 98,  534, 622, 907, 406, 714, 184, 391,
        913, 42,  560, 247, 346, 860, 56,  138, 546, 38,  985, 948, 58,  213,
        799, 319, 390, 634, 458, 945, 733, 507, 916, 123, 345, 110, 720, 917,
        313, 845, 426, 9,   457, 628, 410, 723, 354, 895, 881, 953, 677, 137,
        397, 97,  854, 740, 83,  216, 421, 94,  517, 479, 292, 963, 376, 981,
        480, 39,  257, 272, 157, 5,   316, 395, 787, 942, 456, 242, 759, 898,
        576, 67,  298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692,
        698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585, 40,
        54,  901, 408, 359, 577, 237, 605, 847, 353, 968, 832, 205, 838, 427,
        876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791, 466, 23,
        707, 467, 33,  670, 921, 180, 991, 396, 160, 436, 717, 918, 8,   374,
        101, 684, 727, 749};

    printf("\nExample 2:\n");
    n = sizeof(limits2) / sizeof(int);
    b = bins(limits2, n, data2, sizeof(data2) / sizeof(int));
    if (b == NULL) {
        fprintf(stderr, "Out of memory\n");
        return EXIT_FAILURE;
    }
    print_bins(limits2, n, b);
    free(b);

    return EXIT_SUCCESS;
}
Output:
Example 1:
           <  23: 11
>=  23 and <  37:  4
>=  37 and <  43:  2
>=  43 and <  53:  6
>=  53 and <  67:  9
>=  67 and <  83:  5
>=  83          : 13

Example 2:
           <  14:  3
>=  14 and <  18:  0
>=  18 and < 249: 44
>= 249 and < 312: 10
>= 312 and < 389: 16
>= 389 and < 392:  2
>= 392 and < 513: 28
>= 513 and < 591: 16
>= 591 and < 634:  6
>= 634 and < 720: 16
>= 720          : 59

C#[edit]

using System;

public class Program
{
    static void Main()
    {
        PrintBins(new [] { 23, 37, 43, 53, 67, 83 },
            95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
            16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55
        );
        Console.WriteLine();

        PrintBins(new [] { 14, 18, 249, 312, 389, 392, 513, 591, 634, 720 },
            445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,416,589,930,373,202,
            253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,655,267,248,477,549,238, 62,678, 98,534,
            622,907,406,714,184,391,913, 42,560,247,346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,
            945,733,507,916,123,345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
            854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,787,942,456,242,759,
            898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,698,765,331,487,251,600,879,342,982,527,
            736,795,585, 40, 54,901,408,359,577,237,605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,
            892,443,198,988,791,466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749);
    }

    static void PrintBins(int[] limits, params int[] data)
    {
        int[] bins = Bins(limits, data);
        Console.WriteLine($"-∞ .. {limits[0]} => {bins[0]}");
        for (int i = 0; i < limits.Length-1; i++) {
            Console.WriteLine($"{limits[i]} .. {limits[i+1]} => {bins[i+1]}");
        }
        Console.WriteLine($"{limits[^1]} .. ∞ => {bins[^1]}");
    }

    static int[] Bins(int[] limits, params int[] data)
    {
        Array.Sort(limits);
        int[] bins = new int[limits.Length + 1];
        foreach (int n in data) {
            int i = Array.BinarySearch(limits, n);
            i = i < 0 ? ~i : i+1;
            bins[i]++;
        }
        return bins;
    }
}
Output:
-∞ .. 23 => 11
23 .. 37 => 4
37 .. 43 => 2
43 .. 53 => 6
53 .. 67 => 9
67 .. 83 => 5
83 .. ∞ => 13

-∞ .. 14 => 3
14 .. 18 => 0
18 .. 249 => 44
249 .. 312 => 10
312 .. 389 => 16
389 .. 392 => 2
392 .. 513 => 28
513 .. 591 => 16
591 .. 634 => 6
634 .. 720 => 16
720 .. ∞ => 59

C++[edit]

#include <algorithm>
#include <cassert>
#include <iomanip>
#include <iostream>
#include <vector>

std::vector<int> bins(const std::vector<int>& limits,
                      const std::vector<int>& data) {
    std::vector<int> result(limits.size() + 1, 0);
    for (int n : data) {
        auto i = std::upper_bound(limits.begin(), limits.end(), n);
        ++result[i - limits.begin()];
    }
    return result;
}

void print_bins(const std::vector<int>& limits, const std::vector<int>& bins) {
    size_t n = limits.size();
    if (n == 0)
        return;
    assert(n + 1 == bins.size());
    std::cout << "           < " << std::setw(3) << limits[0] << ": "
              << std::setw(2) << bins[0] << '\n';
    for (size_t i = 1; i < n; ++i)
        std::cout << ">= " << std::setw(3) << limits[i - 1] << " and < "
                  << std::setw(3) << limits[i] << ": " << std::setw(2)
                  << bins[i] << '\n';
    std::cout << ">= " << std::setw(3) << limits[n - 1] << "          : "
              << std::setw(2) << bins[n] << '\n';
}

int main() {
    const std::vector<int> limits1{23, 37, 43, 53, 67, 83};
    const std::vector<int> data1{
        95, 21, 94, 12, 99, 4,  70, 75, 83, 93, 52, 80, 57, 5,  53, 86, 65,
        17, 92, 83, 71, 61, 54, 58, 47, 16, 8,  9,  32, 84, 7,  87, 46, 19,
        30, 37, 96, 6,  98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55};

    std::cout << "Example 1:\n";
    print_bins(limits1, bins(limits1, data1));

    const std::vector<int> limits2{14,  18,  249, 312, 389,
                                   392, 513, 591, 634, 720};
    const std::vector<int> data2{
        445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77,  323, 525,
        570, 219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 253, 775, 47,
        731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306, 655, 267,
        248, 477, 549, 238, 62,  678, 98,  534, 622, 907, 406, 714, 184, 391,
        913, 42,  560, 247, 346, 860, 56,  138, 546, 38,  985, 948, 58,  213,
        799, 319, 390, 634, 458, 945, 733, 507, 916, 123, 345, 110, 720, 917,
        313, 845, 426, 9,   457, 628, 410, 723, 354, 895, 881, 953, 677, 137,
        397, 97,  854, 740, 83,  216, 421, 94,  517, 479, 292, 963, 376, 981,
        480, 39,  257, 272, 157, 5,   316, 395, 787, 942, 456, 242, 759, 898,
        576, 67,  298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692,
        698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585, 40,
        54,  901, 408, 359, 577, 237, 605, 847, 353, 968, 832, 205, 838, 427,
        876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791, 466, 23,
        707, 467, 33,  670, 921, 180, 991, 396, 160, 436, 717, 918, 8,   374,
        101, 684, 727, 749};

    std::cout << "\nExample 2:\n";
    print_bins(limits2, bins(limits2, data2));
}
Output:
Example 1:
           <  23: 11
>=  23 and <  37:  4
>=  37 and <  43:  2
>=  43 and <  53:  6
>=  53 and <  67:  9
>=  67 and <  83:  5
>=  83          : 13

Example 2:
           <  14:  3
>=  14 and <  18:  0
>=  18 and < 249: 44
>= 249 and < 312: 10
>= 312 and < 389: 16
>= 389 and < 392:  2
>= 392 and < 513: 28
>= 513 and < 591: 16
>= 591 and < 634:  6
>= 634 and < 720: 16
>= 720          : 59

CLU[edit]

% Bin the given data, return an array of counts.
% CLU allows arrays to start at any index; the result array
% will have the same lower bound as the limit array.

% The datatype for the limits and data may be any type
% that allows the < comparator.
bin_count = proc [T: type] (limits, data: array[T]) returns (array[int])
            where T has lt: proctype (T,T) returns (bool)
    ad = array[T]       % abbreviations for array types
    ai = array[int] 
    
    lowbin: int := ad$low(limits)
    bins: ai := ai$fill(lowbin, ad$size(limits)+1, 0)
    
    for item: T in ad$elements(data) do
        bin: int := lowbin
        while bin <= ad$high(limits) do
            if item < limits[bin] then break end
            bin := bin + 1
        end
        bins[bin] := bins[bin] + 1
    end
    
    return(bins)
end bin_count

% Display the bins and the amount of items in each bin.
% This imposes the further restriction on the datatype
% that it allows `unparse' (may be turned into a string).
display_bins = proc [T: type] (limits, data: array[T])
               where T has unparse: proctype (T) returns (string),
                     T has lt: proctype (T,T) returns (bool)
    ad = array[T]
    ai = array[int]
    
    po: stream := stream$primary_output()
    bins: ai := bin_count[T](limits, data)
    
    for i: int in int$from_to(ad$low(limits), ad$high(limits)+1) do
        lo, hi: string
        if i-1 < ad$low(limits) 
            then lo := "-inf"
            else lo := T$unparse(limits[i-1])
        end 
        if i > ad$high(limits)
            then hi := "inf"
            else hi := T$unparse(limits[i])
        end
        
        stream$putright(po, lo, 5)
        stream$puts(po, " - ")
        stream$putright(po, hi, 5)
        stream$puts(po, " : ")
        stream$putright(po, int$unparse(bins[i]), 5)
        stream$putl(po, "")
    end
    
    stream$putl(po, "------------------------------------------\n")
end display_bins

% Try both example inputs
start_up = proc () 
    ai = array[int]
    
    limits1: ai := ai$[23, 37, 43, 53, 67, 83]
    data1: ai := ai$
     [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
      16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]
    
    limits2: ai := ai$[14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
    data2: ai := ai$
     [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
      416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
      655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
      346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
      345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
      854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
      787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
      698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
      605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
      466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]   

    display_bins[int](limits1, data1)
    display_bins[int](limits2, data2)
end start_up
Output:
 -inf -    23 :    11
   23 -    37 :     4
   37 -    43 :     2
   43 -    53 :     6
   53 -    67 :     9
   67 -    83 :     5
   83 -   inf :    13
------------------------------------------

 -inf -    14 :     3
   14 -    18 :     0
   18 -   249 :    44
  249 -   312 :    10
  312 -   389 :    16
  389 -   392 :     2
  392 -   513 :    28
  513 -   591 :    16
  591 -   634 :     6
  634 -   720 :    16
  720 -   inf :    59
------------------------------------------

Factor[edit]

Factor provides the bisect-right word in the sorting.extras vocabulary. See the implementation here.

USING: assocs formatting grouping io kernel math math.parser
math.statistics sequences sequences.extras sorting.extras ;

: bin ( data limits -- seq )
    dup length 1 + [ 0 ] replicate -rot
    [ bisect-right over [ 1 + ] change-nth ] curry each ;

: .bin ( {lo,hi} n i -- )
    swap "%3d members in " printf zero? "(" "[" ? write
    "%s, %s)\n" vprintf ;

: .bins ( data limits -- )
    dup [ number>string ] map "-∞" prefix "∞" suffix 2 clump
    -rot bin [ .bin ] 2each-index ;


"First example:" print
{
    95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71
    61 54 58 47 16 8 9 32 84 7 87 46 19 30 37 96 6 98 40 79 97
    45 64 60 29 49 36 43 55
}
{ 23 37 43 53 67 83 } .bins nl

"Second example:" print
{
    445 814 519 697 700 130 255 889 481 122 
    932  77 323 525 570 219 367 523 442 933 
    416 589 930 373 202 253 775  47 731 685 
    293 126 133 450 545 100 741 583 763 306 
    655 267 248 477 549 238  62 678  98 534 
    622 907 406 714 184 391 913  42 560 247 
    346 860  56 138 546  38 985 948  58 213 
    799 319 390 634 458 945 733 507 916 123 
    345 110 720 917 313 845 426   9 457 628 
    410 723 354 895 881 953 677 137 397  97 
    854 740  83 216 421  94 517 479 292 963 
    376 981 480  39 257 272 157   5 316 395 
    787 942 456 242 759 898 576  67 298 425 
    894 435 831 241 989 614 987 770 384 692 
    698 765 331 487 251 600 879 342 982 527 
    736 795 585  40  54 901 408 359 577 237 
    605 847 353 968 832 205 838 427 876 959 
    686 646 835 127 621 892 443 198 988 791 
    466  23 707 467  33 670 921 180 991 396 
    160 436 717 918   8 374 101 684 727 749
}
{ 14 18 249 312 389 392 513 591 634 720 } .bins
Output:
First example:
 11 members in (-∞, 23)
  4 members in [23, 37)
  2 members in [37, 43)
  6 members in [43, 53)
  9 members in [53, 67)
  5 members in [67, 83)
 13 members in [83, ∞)

Second example:
  3 members in (-∞, 14)
  0 members in [14, 18)
 44 members in [18, 249)
 10 members in [249, 312)
 16 members in [312, 389)
  2 members in [389, 392)
 28 members in [392, 513)
 16 members in [513, 591)
  6 members in [591, 634)
 16 members in [634, 720)
 59 members in [720, ∞)

FreeBASIC[edit]

sub binlims( dat() as integer, limits() as integer, bins() as uinteger )
    dim as uinteger n = ubound(limits), j, i
    for i = 0 to ubound(dat)
        if dat(i)<limits(0) then
            bins(0) += 1
        elseif dat(i) >= limits(n) then
            bins(n+1) += 1
        else
            for j = 1 to n 
                if dat(i)<limits(j) then
                    bins(j) += 1
                    exit for
                end if
            next j
        end if
    next i
end sub
'example 1
dim as integer limits1(0 to ...) = {23, 37, 43, 53, 67, 83}
dim as integer dat1(0 to ...) = {95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,_
           16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55}
dim as uinteger bins1(0 to ubound(limits1)+1)
binlims( dat1(), limits1(), bins1() )
print "=====EXAMPLE ONE====="
print "< ";limits1(0);": ";bins1(0)
for i as uinteger = 1 to ubound(limits1)
    print ">= ";limits1(i-1);" and < ";limits1(i);": ";bins1(i)
next i
print ">= ";limits1(ubound(limits1));": ";bins1(ubound(bins1))
print

'example 2
dim as integer limits2(0 to ...) = {14, 18, 249, 312, 389, 392, 513, 591, 634, 720}
dim as integer dat2(0 to ...) = {445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,_
           416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,_
           655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,_
           346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,_
           345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,_
           854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,_
           787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,_
           698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,_
           605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,_
           466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749}
redim as uinteger bins2(0 to ubound(limits2)+1)

binlims( dat2(), limits2(), bins2() )
print "=====EXAMPLE TWO====="
print "< ";limits2(0);": ";bins2(0)
for i as uinteger = 1 to ubound(limits2)
    print ">= ";limits2(i-1);" and < ";limits2(i);": ";bins2(i)
next i
print ">= ";limits2(ubound(limits2));": ";bins2(ubound(bins2))
Output:
=====EXAMPLE ONE=====
<  23: 11
>=  23 and <  37: 4
>=  37 and <  43: 2
>=  43 and <  53: 6
>=  53 and <  67: 9
>=  67 and <  83: 5
>=  83: 13

=====EXAMPLE TWO=====
<  14: 3
>=  14 and <  18: 0
>=  18 and <  249: 44
>=  249 and <  312: 10
>=  312 and <  389: 16
>=  389 and <  392: 2
>=  392 and <  513: 28
>=  513 and <  591: 16
>=  591 and <  634: 6
>=  634 and <  720: 16
>=  720: 59

Go[edit]

package main

import (
    "fmt"
    "sort"
)

func getBins(limits, data []int) []int {
    n := len(limits)
    bins := make([]int, n+1)
    for _, d := range data {
        index := sort.SearchInts(limits, d) // uses binary search
        if index < len(limits) && d == limits[index] {
            index++
        }
        bins[index]++
    }
    return bins
}

func printBins(limits, bins []int) {
    n := len(limits)
    fmt.Printf("           < %3d = %2d\n", limits[0], bins[0])
    for i := 1; i < n; i++ {
        fmt.Printf(">= %3d and < %3d = %2d\n", limits[i-1], limits[i], bins[i])
    }
    fmt.Printf(">= %3d           = %2d\n", limits[n-1], bins[n])
    fmt.Println()
}

func main() {
    limitsList := [][]int{
        {23, 37, 43, 53, 67, 83},
        {14, 18, 249, 312, 389, 392, 513, 591, 634, 720},
    }

    dataList := [][]int{
        {
            95, 21, 94, 12, 99, 4, 70, 75, 83, 93, 52, 80, 57, 5, 53, 86, 65, 17, 92, 83, 71, 61, 54, 58, 47,
            16,  8,  9, 32, 84, 7, 87, 46, 19, 30, 37, 96, 6, 98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55,
        },
        {
            445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932,  77, 323, 525, 570, 219, 367, 523, 442, 933,
            416, 589, 930, 373, 202, 253, 775,  47, 731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306,
            655, 267, 248, 477, 549, 238,  62, 678,  98, 534, 622, 907, 406, 714, 184, 391, 913,  42, 560, 247,
            346, 860,  56, 138, 546,  38, 985, 948,  58, 213, 799, 319, 390, 634, 458, 945, 733, 507, 916, 123,
            345, 110, 720, 917, 313, 845, 426,   9, 457, 628, 410, 723, 354, 895, 881, 953, 677, 137, 397,  97,
            854, 740,  83, 216, 421,  94, 517, 479, 292, 963, 376, 981, 480,  39, 257, 272, 157,   5, 316, 395,
            787, 942, 456, 242, 759, 898, 576,  67, 298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692,
            698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585,  40,  54, 901, 408, 359, 577, 237,
            605, 847, 353, 968, 832, 205, 838, 427, 876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791,
            466,  23, 707, 467,  33, 670, 921, 180, 991, 396, 160, 436, 717, 918,   8, 374, 101, 684, 727, 749,
        },
    }

    for i := 0; i < len(limitsList); i++ {
        fmt.Println("Example", i+1, "\b\n")
        bins := getBins(limitsList[i], dataList[i])
        printBins(limitsList[i], bins)
    }
}
Output:
Example 1 

           <  23 = 11
>=  23 and <  37 =  4
>=  37 and <  43 =  2
>=  43 and <  53 =  6
>=  53 and <  67 =  9
>=  67 and <  83 =  5
>=  83           = 13

Example 2 

           <  14 =  3
>=  14 and <  18 =  0
>=  18 and < 249 = 44
>= 249 and < 312 = 10
>= 312 and < 389 = 16
>= 389 and < 392 =  2
>= 392 and < 513 = 28
>= 513 and < 591 = 16
>= 591 and < 634 =  6
>= 634 and < 720 = 16
>= 720           = 59

Haskell[edit]

Splitting the data into bins may be done using the monadic nature of a tuple. Here tuple plays role of the Writer monad, so that sequential partitioning by each bin boundary adds new bin contents.

import Control.Monad (foldM)
import Data.List (partition)

binSplit :: Ord a => [a] -> [a] -> [[a]]
binSplit lims ns = counts ++ [rest] 
  where
    (counts, rest) = foldM split ns lims
    split l i = let (a, b) = partition (< i) l in ([a], b)

binCounts :: Ord a => [a] -> [a] -> [Int]
binCounts b = fmap length . binSplit b
λ> binSplit [2,4,7] [1,4,2,6,3,8,9,4,1,2,7,4,1,5,1]
[[1,1,1,1],[2,3,2],[4,6,4,4,5],[8,9,7]]

λ> binCounts [2,4,7] [1,4,2,6,3,8,9,4,1,2,7,4,1,5,1]
[4,3,5,3]

More efficient binning procedure exploits the binary search tree.

{-# language DeriveFoldable #-}

import Data.Foldable (toList)

data BTree a b = Node a (BTree a b) (BTree a b)
               | Val b
  deriving Foldable

-- assuming list is sorted.
mkTree :: [a] -> BTree a [a]
mkTree [] = Val []
mkTree [x] = Node x (Val []) (Val [])
mkTree lst = Node x (mkTree l) (mkTree r)
  where (l, x:r) = splitAt (length lst `div` 2) lst

binSplit :: Ord a => [a] -> [a] -> [[a]]
binSplit lims = toList . foldr add (mkTree lims)
  where
    add x (Val v) = Val (x:v)
    add x (Node y l r) = if x < y
                         then Node y (add x l) r
                         else Node y l (add x r)

Tasks examples

import Text.Printf

task bs ns = mapM_ putStrLn
           $ zipWith mkLine (binCounts bs ns) bins
  where
    bins :: [String]
    bins = [printf "(-∞, %v)" $ head bs] <>
           zipWith mkInterval bs (tail bs) <>
           [printf "[%v, ∞)" $ last bs]

    mkLine = printf "%v\t in %s"
    mkInterval = printf "[%v, %v)"

bins1 = [23, 37, 43, 53, 67, 83]
data1 = [ 95, 21, 94, 12, 99, 4,  70, 75, 83, 93, 52, 80, 57
        , 5,  53, 86, 65, 17, 92, 83, 71, 61, 54, 58, 47, 16
        , 8,  9,  32, 84, 7,  87, 46, 19, 30, 37, 96, 6,  98
        , 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55]

bins2 = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
data2 = [ 445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77,  323, 525
        , 570, 219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 253, 775, 47
        , 731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306, 655, 267
        , 248, 477, 549, 238, 62,  678, 98,  534, 622, 907, 406, 714, 184, 391
        , 913, 42,  560, 247, 346, 860, 56,  138, 546, 38,  985, 948, 58,  213
        , 799, 319, 390, 634, 458, 945, 733, 507, 916, 123, 345, 110, 720, 917
        , 313, 845, 426, 9,   457, 628, 410, 723, 354, 895, 881, 953, 677, 137
        , 397, 97,  854, 740, 83,  216, 421, 94,  517, 479, 292, 963, 376, 981
        , 480, 39,  257, 272, 157, 5,   316, 395, 787, 942, 456, 242, 759, 898
        , 576, 67,  298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692
        , 698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585, 40
        , 54,  901, 408, 359, 577, 237, 605, 847, 353, 968, 832, 205, 838, 427
        , 876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791, 466, 23
        , 707, 467, 33,  670, 921, 180, 991, 396, 160, 436, 717, 918, 8,   374
        , 101, 684, 727, 749]
λ> task bins1 data1
11	 in (-∞, 23)
4	 in [23, 37)
2	 in [37, 43)
6	 in [43, 53)
9	 in [53, 67)
5	 in [67, 83)
13	 in [83, ∞)

λ> task bins2 data2
3	 in (-∞, 14)
0	 in [14, 18)
44	 in [18, 249)
10	 in [249, 312)
16	 in [312, 389)
2	 in [389, 392)
28	 in [392, 513)
16	 in [513, 591)
6	 in [591, 634)
16	 in [634, 720)
59	 in [720, ∞)

J[edit]

Solution: Using Idotr from this JWiki page

Idotr=: |.@[ (#@[ - I.) ]             NB. reverses order of limits to obtain intervals closed on left, open on right (>= y <)
binnedData=: adverb define
  bidx=. i.@>:@# x                    NB. indicies of bins
  x (Idotr (u@}./.)&(bidx&,) ]) y     NB. apply u to data in each bin after dropping first value
)

require 'format/printf'
printBinCounts=: dyad define
  counts =. y
  '%2d   in [ -∞, %3d)' printf ({. counts) , {. x
  '%2d   in [%3d, %3d)' printf (}.}: counts) ,. 2 ]\ x
  '%2d   in [%3d, ∞]' printf ({: counts) , {: x
)

Required Examples:

limits1=: 23 37 43 53 67 83
data1=: , 0&".;._2 noun define
95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71 61 54 58 47
16  8  9 32 84 7 87 46 19 30 37 96 6 98 40 79 97 45 64 60 29 49 36 43 55
)

limits2=: 14 18 249 312 389 392 513 591 634 720
data2=: , 0&".;._2 noun define
445 814 519 697 700 130 255 889 481 122 932  77 323 525 570 219 367 523 442 933
416 589 930 373 202 253 775  47 731 685 293 126 133 450 545 100 741 583 763 306
655 267 248 477 549 238  62 678  98 534 622 907 406 714 184 391 913  42 560 247
346 860  56 138 546  38 985 948  58 213 799 319 390 634 458 945 733 507 916 123
345 110 720 917 313 845 426   9 457 628 410 723 354 895 881 953 677 137 397  97
854 740  83 216 421  94 517 479 292 963 376 981 480  39 257 272 157   5 316 395
787 942 456 242 759 898 576  67 298 425 894 435 831 241 989 614 987 770 384 692
698 765 331 487 251 600 879 342 982 527 736 795 585  40  54 901 408 359 577 237
605 847 353 968 832 205 838 427 876 959 686 646 835 127 621 892 443 198 988 791
466  23 707 467  33 670 921 180 991 396 160 436 717 918   8 374 101 684 727 749
)
   limits1 < binnedData data1   NB. box/group binned data
┌──────────────────────────┬───────────┬─────┬─────────────────┬──────────────────────────┬──────────────┬──────────────────────────────────────┐
21 12 4 5 17 16 8 9 7 19 632 30 29 3637 4052 47 46 45 49 4357 53 65 61 54 58 64 60 5570 75 80 71 7995 94 99 83 93 86 92 83 84 87 96 98 97
└──────────────────────────┴───────────┴─────┴─────────────────┴──────────────────────────┴──────────────┴──────────────────────────────────────┘
   limits1 # binnedData data1   NB. tally binned data
11 4 2 6 9 5 13
   limits2 printBinCounts limits2 # binnedData data2
 3   in [ -,  14)
 0   in [ 14,  18)
44   in [ 18, 249)
10   in [249, 312)
16   in [312, 389)
 2   in [389, 392)
28   in [392, 513)
16   in [513, 591)
 6   in [591, 634)
16   in [634, 720)
59   in [720, ]

Java[edit]

import java.util.Arrays;
import java.util.Collections;
import java.util.List;

public class Bins {
    public static <T extends Comparable<? super T>> int[] bins(
            List<? extends T> limits, Iterable<? extends T> data) {
        int[] result = new int[limits.size() + 1];
        for (T n : data) {
            int i = Collections.binarySearch(limits, n);
            if (i >= 0) {
                // n == limits[i]; we put it in right-side bin (i+1)
                i = i+1;
            } else {
                // n is not in limits and i is ~(insertion point)
                i = ~i;
            }
            result[i]++;
        }
        return result;
    }

    public static void printBins(List<?> limits, int[] bins) {
        int n = limits.size();
        if (n == 0) {
            return;
        }
        assert n+1 == bins.length;
        System.out.printf("           < %3s: %2d\n", limits.get(0), bins[0]);
        for (int i = 1; i < n; i++) {
            System.out.printf(">= %3s and < %3s: %2d\n", limits.get(i-1), limits.get(i), bins[i]);
        }
        System.out.printf(">= %3s          : %2d\n", limits.get(n-1), bins[n]);
    }

    public static void main(String[] args) {
        List<Integer> limits = Arrays.asList(23, 37, 43, 53, 67, 83);
        List<Integer> data = Arrays.asList(
            95, 21, 94, 12, 99, 4,  70, 75, 83, 93, 52, 80, 57, 5,  53, 86, 65,
            17, 92, 83, 71, 61, 54, 58, 47, 16, 8,  9,  32, 84, 7,  87, 46, 19,
            30, 37, 96, 6,  98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 55);

        System.out.println("Example 1:");
        printBins(limits, bins(limits, data));

        limits = Arrays.asList(14,  18,  249, 312, 389,
                               392, 513, 591, 634, 720);
        data = Arrays.asList(
            445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77,  323, 525,
            570, 219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 253, 775, 47,
            731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 763, 306, 655, 267,
            248, 477, 549, 238, 62,  678, 98,  534, 622, 907, 406, 714, 184, 391,
            913, 42,  560, 247, 346, 860, 56,  138, 546, 38,  985, 948, 58,  213,
            799, 319, 390, 634, 458, 945, 733, 507, 916, 123, 345, 110, 720, 917,
            313, 845, 426, 9,   457, 628, 410, 723, 354, 895, 881, 953, 677, 137,
            397, 97,  854, 740, 83,  216, 421, 94,  517, 479, 292, 963, 376, 981,
            480, 39,  257, 272, 157, 5,   316, 395, 787, 942, 456, 242, 759, 898,
            576, 67,  298, 425, 894, 435, 831, 241, 989, 614, 987, 770, 384, 692,
            698, 765, 331, 487, 251, 600, 879, 342, 982, 527, 736, 795, 585, 40,
            54,  901, 408, 359, 577, 237, 605, 847, 353, 968, 832, 205, 838, 427,
            876, 959, 686, 646, 835, 127, 621, 892, 443, 198, 988, 791, 466, 23,
            707, 467, 33,  670, 921, 180, 991, 396, 160, 436, 717, 918, 8,   374,
            101, 684, 727, 749);

        System.out.println();
        System.out.println("Example 2:");
        printBins(limits, bins(limits, data));
    }
}
Output:
Example 1:
           <  23: 11
>=  23 and <  37:  4
>=  37 and <  43:  2
>=  43 and <  53:  6
>=  53 and <  67:  9
>=  67 and <  83:  5
>=  83          : 13

Example 2:
           <  14:  3
>=  14 and <  18:  0
>=  18 and < 249: 44
>= 249 and < 312: 10
>= 312 and < 389: 16
>= 389 and < 392:  2
>= 392 and < 513: 28
>= 513 and < 591: 16
>= 591 and < 634:  6
>= 634 and < 720: 16
>= 720          : 59

jq[edit]

The following takes advantage of jq's built-in filter for conducting a binary search, `bsearch/1`, which returns a negative value giving the insertion point if the item is not already in the input array.

The "data" is assumed to be a stream of values (rather than an array), thus allowing an indefinitely large number of items to be processed. These items could, but need not, be presented one line at a time.

# input and output: {limits, count} where
#   .limits holds an array defining the limits, and
#   .count[$i] holds the count of bin $i, where bin[0] is the left-most bin
def bin($x):  
  (.limits | bsearch($x)) as $ix
  | (if $ix > -1 then $ix + 1 else -1 - $ix end) as $i
  | .count[$i] += 1;

# pretty-print for the structure defined at bin/1
def pp:
   (.limits|length) as $length
   | (range(0;$length) as $i
      | "< \(.limits[$i]) => \(.count[$i] // 0)" ),
     ">= \(.limits[$length-1] ) => \(.count[$length] // 0)"  ;

# Main program
reduce inputs as $x ({$limits, count: []}; bin($x)) 
| pp
Output:

Invocation:

< data.json jq -rn --argfile limits limits.json -f program.jq

Example 1:

< 23 => 11
< 37 => 4
< 43 => 2
< 53 => 6
< 67 => 9
< 83 => 5
>= 83 => 13

Example 2:

< 14 => 3
< 18 => 0
< 249 => 44
< 312 => 10
< 389 => 16
< 392 => 2
< 513 => 28
< 591 => 16
< 634 => 6
< 720 => 16
>= 720 => 59

Julia[edit]

Translation of: Python
"""Add the function Python has in its bisect library"""
function bisect_right(array, x, low = 1, high = length(array) + 1)
    while low < high
        middle = (low + high) ÷ 2
        x < array[middle] ? (high = middle) : (low = middle + 1)
    end
    return low
end

""" Bin data according to (ascending) limits """
function bin_it(limits, data)
    bins = zeros(Int, length(limits) + 1)    # adds under/over range bins too
    for d in data
        bins[bisect_right(limits, d)] += 1
    end
    return bins
end

""" Pretty print the resulting bins and counts """
function bin_print(limits, bins)
    println("          < $(lpad(limits[1], 3)) := $(lpad(bins[1], 3))")
    for (lo, hi, count) in zip(limits, limits[2:end], bins[2:end])
        println(">= $(lpad(lo, 3)) .. < $(lpad(hi, 3)) := $(lpad(count, 3))")
    end
    println(">= $(lpad(limits[end], 3))          := $(lpad(bins[end], 3))")
end

""" Test on data provided """
function testbins()
    println("RC FIRST EXAMPLE:")
    limits  = [23, 37, 43, 53, 67, 83]
    data = [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
            16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]
    bins = bin_it(limits, data)
    bin_print(limits, bins)

    println("\nRC SECOND EXAMPLE:")
    limits = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
    data = [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
            416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
            655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
            346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
            345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
            854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
            787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
            698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
            605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
            466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]
    bins = bin_it(limits, data)
    bin_print(limits, bins)
end

testbins()
Output:
RC FIRST EXAMPLE:
          <  23 :=  11
>=  23 .. <  37 :=   4
>=  37 .. <  43 :=   2
>=  43 .. <  53 :=   6
>=  53 .. <  67 :=   9
>=  67 .. <  83 :=   5
>=  83          :=  13

RC SECOND EXAMPLE:
          <  14 :=   3
>=  14 .. <  18 :=   0
>=  18 .. < 249 :=  44
>= 249 .. < 312 :=  10
>= 312 .. < 389 :=  16
>= 389 .. < 392 :=   2
>= 392 .. < 513 :=  28
>= 513 .. < 591 :=  16
>= 591 .. < 634 :=   6
>= 634 .. < 720 :=  16
>= 720          :=  59

Lua[edit]

Array indexing is 1-based, as is customary for Lua:

function binner(limits, data)
  local bins = setmetatable({}, {__index=function() return 0 end})
  local n, flr = #limits+1, math.floor
  for _, x in ipairs(data) do
    local lo, hi = 1, n
    while lo < hi do 
      local mid = flr((lo + hi) / 2)
      if not limits[mid] or x < limits[mid] then hi=mid else lo=mid+1 end
    end
    bins[lo] = bins[lo] + 1
  end
  return bins
end

function printer(limits, bins)
  for i = 1, #limits+1 do
    print(string.format("[%3s,%3s) : %d", limits[i-1] or " -∞", limits[i] or " +∞", bins[i]))
  end
end

print("PART 1:")
limits = {23, 37, 43, 53, 67, 83}
data = {95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
        16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55}
bins = binner(limits, data)
printer(limits, bins)

print("\nPART 2:")          
limits = {14, 18, 249, 312, 389, 392, 513, 591, 634, 720}
data = {445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
        416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
        655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
        346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
        345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
        854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
        787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
        698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
        605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
        466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749}
bins = binner(limits, data)
printer(limits, bins)
Output:
PART 1:
[ -∞, 23) : 11
[ 23, 37) : 4
[ 37, 43) : 2
[ 43, 53) : 6
[ 53, 67) : 9
[ 67, 83) : 5
[ 83, +∞) : 13

PART 2:
[ -∞, 14) : 3
[ 14, 18) : 0
[ 18,249) : 44
[249,312) : 10
[312,389) : 16
[389,392) : 2
[392,513) : 28
[513,591) : 16
[591,634) : 6
[634,720) : 16
[720, +∞) : 59

Mathematica/Wolfram Language[edit]

limits = {23, 37, 43, 53, 67, 83};
data = {95, 21, 94, 12, 99, 4, 70, 75, 83, 93, 52, 80, 57, 5, 53, 86, 
   65, 17, 92, 83, 71, 61, 54, 58, 47, 16, 8, 9, 32, 84, 7, 87, 46, 
   19, 30, 37, 96, 6, 98, 40, 79, 97, 45, 64, 60, 29, 49, 36, 43, 
   55};
limits = {{-\[Infinity]}~Join~limits~Join~{\[Infinity]}};
BinCounts[data, limits]
MapThread[{#2, #1} &, {%, Partition[First[limits], 2, 1]}] // Grid

limits = {14, 18, 249, 312, 389, 392, 513, 591, 634, 720};
data = {445, 814, 519, 697, 700, 130, 255, 889, 481, 122, 932, 77, 
   323, 525, 570, 219, 367, 523, 442, 933, 416, 589, 930, 373, 202, 
   253, 775, 47, 731, 685, 293, 126, 133, 450, 545, 100, 741, 583, 
   763, 306, 655, 267, 248, 477, 549, 238, 62, 678, 98, 534, 622, 907,
    406, 714, 184, 391, 913, 42, 560, 247, 346, 860, 56, 138, 546, 38,
    985, 948, 58, 213, 799, 319, 390, 634, 458, 945, 733, 507, 916, 
   123, 345, 110, 720, 917, 313, 845, 426, 9, 457, 628, 410, 723, 354,
    895, 881, 953, 677, 137, 397, 97, 854, 740, 83, 216, 421, 94, 517,
    479, 292, 963, 376, 981, 480, 39, 257, 272, 157, 5, 316, 395, 787,
    942, 456, 242, 759, 898, 576, 67, 298, 425, 894, 435, 831, 241, 
   989, 614, 987, 770, 384, 692, 698, 765, 331, 487, 251, 600, 879, 
   342, 982, 527, 736, 795, 585, 40, 54, 901, 408, 359, 577, 237, 605,
    847, 353, 968, 832, 205, 838, 427, 876, 959, 686, 646, 835, 127, 
   621, 892, 443, 198, 988, 791, 466, 23, 707, 467, 33, 670, 921, 180,
    991, 396, 160, 436, 717, 918, 8, 374, 101, 684, 727, 749};
limits = {{-\[Infinity]}~Join~limits~Join~{\[Infinity]}};
BinCounts[data, limits]
MapThread[{#2, #1} &, {%, Partition[First[limits], 2, 1]}] // Grid
Output:
{11, 4, 2, 6, 9, 5, 13}
{-\[Infinity],23}	11
{23,37}	4
{37,43}	2
{43,53}	6
{53,67}	9
{67,83}	5
{83,\[Infinity]}	13

{3, 0, 44, 10, 16, 2, 28, 16, 6, 16, 59}
{-\[Infinity],14}	3
{14,18}	0
{18,249}	44
{249,312}	10
{312,389}	16
{389,392}	2
{392,513}	28
{513,591}	16
{591,634}	6
{634,720}	16
{720,\[Infinity]}	59

Nim[edit]

Translation of: Python
import algorithm, strformat

func binIt(limits, data: openArray[int]): seq[Natural] =
  result.setLen(limits.len + 1)
  for d in data:
    inc result[limits.upperBound(d)]

proc binPrint(limits: openArray[int]; bins: seq[Natural]) =
  echo &"          < {limits[0]:3} := {bins[0]:3}"
  for i in 1..limits.high:
    echo &">= {limits[i-1]:3} .. < {limits[i]:3} := {bins[i]:3}"
  echo &">= {limits[^1]:3}          := {bins[^1]:3}"


when isMainModule:

  echo "Example 1:"
  const
    Limits1  = [23, 37, 43, 53, 67, 83]
    Data1 = [95, 21, 94, 12, 99,  4, 70, 75, 83, 93,
             52, 80, 57,  5, 53, 86, 65, 17, 92, 83,
             71, 61, 54, 58, 47, 16,  8,  9, 32, 84,
              7, 87, 46, 19, 30, 37, 96,  6, 98, 40,
             79, 97, 45, 64, 60, 29, 49, 36, 43, 55]
  let bins1 = binIt(Limits1, Data1)
  binPrint(Limits1, bins1)

  echo ""
  echo "Example 2:"
  const
    Limits2 = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
    Data2 = [445, 814, 519, 697, 700, 130, 255, 889, 481, 122,
             932,  77, 323, 525, 570, 219, 367, 523, 442, 933,
             416, 589, 930, 373, 202, 253, 775,  47, 731, 685,
             293, 126, 133, 450, 545, 100, 741, 583, 763, 306,
             655, 267, 248, 477, 549, 238,  62, 678,  98, 534,
             622, 907, 406, 714, 184, 391, 913,  42, 560, 247,
             346, 860,  56, 138, 546,  38, 985, 948,  58, 213,
             799, 319, 390, 634, 458, 945, 733, 507, 916, 123,
             345, 110, 720, 917, 313, 845, 426,   9, 457, 628,
             410, 723, 354, 895, 881, 953, 677, 137, 397,  97,
             854, 740,  83, 216, 421,  94, 517, 479, 292, 963,
             376, 981, 480,  39, 257, 272, 157,   5, 316, 395,
             787, 942, 456, 242, 759, 898, 576,  67, 298, 425,
             894, 435, 831, 241, 989, 614, 987, 770, 384, 692,
             698, 765, 331, 487, 251, 600, 879, 342, 982, 527,
             736, 795, 585,  40,  54, 901, 408, 359, 577, 237,
             605, 847, 353, 968, 832, 205, 838, 427, 876, 959,
             686, 646, 835, 127, 621, 892, 443, 198, 988, 791,
             466,  23, 707, 467,  33, 670, 921, 180, 991, 396,
             160, 436, 717, 918,   8, 374, 101, 684, 727, 749]
  let bins2 = binIt(Limits2, Data2)
  binPrint(Limits2, bins2)
Output:
Example 1:
          <  23 :=  11
>=  23 .. <  37 :=   4
>=  37 .. <  43 :=   2
>=  43 .. <  53 :=   6
>=  53 .. <  67 :=   9
>=  67 .. <  83 :=   5
>=  83          :=  13

Example 2:
          <  14 :=   3
>=  14 .. <  18 :=   0
>=  18 .. < 249 :=  44
>= 249 .. < 312 :=  10
>= 312 .. < 389 :=  16
>= 389 .. < 392 :=   2
>= 392 .. < 513 :=  28
>= 513 .. < 591 :=  16
>= 591 .. < 634 :=   6
>= 634 .. < 720 :=  16
>= 720          :=  59

Objective-C[edit]

#import <Foundation/Foundation.h>

NSArray<NSNumber *> *bins(NSArray<NSNumber *> *limits, NSArray<NSNumber *> *data) {
  NSMutableArray<NSNumber *> *result = [[NSMutableArray alloc] initWithCapacity:[limits count] + 1];
  for (NSInteger i = 0; i <= [limits count]; i++) {
    [result addObject:@0];
  }
  for (NSNumber *n in data) {
    NSUInteger i = [limits indexOfObject:n
                           inSortedRange:NSMakeRange(0, [limits count])
                                 options:NSBinarySearchingInsertionIndex|NSBinarySearchingLastEqual
                         usingComparator:^(NSNumber *x, NSNumber *y){ return [x compare: y]; }];
    result[i] = @(result[i].integerValue + 1);
  }
  return result;
}
 
void printBins(NSArray<NSNumber *> *limits, NSArray<NSNumber *> *bins) {
  NSUInteger n = [limits count];
  if (n == 0)
      return;
  NSCAssert(n + 1 == [bins count], @"Wrong size of bins");
  NSLog(@"           < %3@: %2@", limits[0], bins[0]);
  for (NSInteger i = 1; i < n; i++) {
    NSLog(@">= %3@ and < %3@: %2@", limits[i-1], limits[i], bins[i]);
  }
  NSLog(@">= %3@          : %2@", limits[n-1], bins[n]);
}

int main(void) {
  @autoreleasepool {
    NSArray<NSNumber *> *limits = @[@23, @37, @43, @53, @67, @83];
    NSArray<NSNumber *> *data = @[
      @95, @21, @94, @12, @99, @4,  @70, @75, @83, @93, @52, @80, @57, @5,  @53, @86, @65,
      @17, @92, @83, @71, @61, @54, @58, @47, @16, @8,  @9,  @32, @84, @7,  @87, @46, @19,
      @30, @37, @96, @6,  @98, @40, @79, @97, @45, @64, @60, @29, @49, @36, @43, @55];

    NSLog(@"Example 1:");
    printBins(limits, bins(limits, data));

    limits = @[@14,  @18,  @249, @312, @389, @392, @513, @591, @634, @720];
    data = @[
      @445, @814, @519, @697, @700, @130, @255, @889, @481, @122, @932, @77,  @323, @525,
      @570, @219, @367, @523, @442, @933, @416, @589, @930, @373, @202, @253, @775, @47,
      @731, @685, @293, @126, @133, @450, @545, @100, @741, @583, @763, @306, @655, @267,
      @248, @477, @549, @238, @62,  @678, @98,  @534, @622, @907, @406, @714, @184, @391,
      @913, @42,  @560, @247, @346, @860, @56,  @138, @546, @38,  @985, @948, @58,  @213,
      @799, @319, @390, @634, @458, @945, @733, @507, @916, @123, @345, @110, @720, @917,
      @313, @845, @426, @9,   @457, @628, @410, @723, @354, @895, @881, @953, @677, @137,
      @397, @97,  @854, @740, @83,  @216, @421, @94,  @517, @479, @292, @963, @376, @981,
      @480, @39,  @257, @272, @157, @5,   @316, @395, @787, @942, @456, @242, @759, @898,
      @576, @67,  @298, @425, @894, @435, @831, @241, @989, @614, @987, @770, @384, @692,
      @698, @765, @331, @487, @251, @600, @879, @342, @982, @527, @736, @795, @585, @40,
      @54,  @901, @408, @359, @577, @237, @605, @847, @353, @968, @832, @205, @838, @427,
      @876, @959, @686, @646, @835, @127, @621, @892, @443, @198, @988, @791, @466, @23,
      @707, @467, @33,  @670, @921, @180, @991, @396, @160, @436, @717, @918, @8,   @374,
      @101, @684, @727, @749];

    NSLog(@"");
    NSLog(@"Example 2:");
    printBins(limits, bins(limits, data));
  }
  return 0;
}
Output:
Example 1:
           <  23: 11
>=  23 and <  37:  4
>=  37 and <  43:  2
>=  43 and <  53:  6
>=  53 and <  67:  9
>=  67 and <  83:  5
>=  83          : 13

Example 2:
           <  14:  3
>=  14 and <  18:  0
>=  18 and < 249: 44
>= 249 and < 312: 10
>= 312 and < 389: 16
>= 389 and < 392:  2
>= 392 and < 513: 28
>= 513 and < 591: 16
>= 591 and < 634:  6
>= 634 and < 720: 16
>= 720          : 59

Perl[edit]

Borrowed bisect_right from Julia entry.

use strict;
use warnings; no warnings 'uninitialized';
use feature 'say';
use experimental 'signatures';
use constant Inf => 1e10;

my @tests = (
    {
        limits => [23, 37, 43, 53, 67, 83],
        data   => [
            95,21,94,12,99,4,70,75,83,93,52,80,57, 5,53,86,65,17,92,83,71,61,54,58,47,
            16, 8, 9,32,84,7,87,46,19,30,37,96, 6,98,40,79,97,45,64,60,29,49,36,43,55
        ]
    },
    {
        limits => [14, 18, 249, 312, 389, 392, 513, 591, 634, 720],
        data   => [
            445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
            416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
            655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
            346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
            345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
            854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
            787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
            698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
            605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
            466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749
        ]
    }
);

sub bisect_right ($x, $low, $high, @array) {
    my ($middle);
    while ($low < $high) {
        $middle = ($low + $high) / 2;
        $x < $array[$middle] ? $high = $middle : ($low = $middle + 1)
    }
    $low-1
}

sub bin_it ($limits, $data) {
    my @bins;
    ++$bins[ bisect_right($_, 0, @$limits-1, @$limits) ] for @$data;
    @bins
}

sub bin_format ($limits, @bins) {
    my @lim = @$limits;
    my(@formatted);
    push @formatted, sprintf "[%3d, %3d) => %3d\n", $lim[$_], ($lim[$_+1] == Inf ? 'Inf' : $lim[$_+1]), $bins[$_] for 0..@lim-2;
    @formatted
}

for (0..$#tests) {
    my @limits = (0, @{$tests[$_]{limits}}, Inf);
    say bin_format \@limits, bin_it(\@limits,\@{$tests[$_]{data}});
}
Output:
[  0,  23) =>  11
[ 23,  37) =>   4
[ 37,  43) =>   2
[ 43,  53) =>   6
[ 53,  67) =>   9
[ 67,  83) =>   5
[ 83, Inf) =>  13

[  0,  14) =>   3
[ 14,  18) =>   0
[ 18, 249) =>  44
[249, 312) =>  10
[312, 389) =>  16
[389, 392) =>   2
[392, 513) =>  28
[513, 591) =>  16
[591, 634) =>   6
[634, 720) =>  16
[720, Inf) =>  59

But if we were to take to heart the warning that the input data was scary-big, then perhaps using a more efficient routine to classify the data into bins would be prudent (boilerplate/input/output same as above).

use Math::SimpleHisto::XS;

for (@tests) {
    my @lim = (0, @{$$_{limits}}, Inf);
    my $hist = Math::SimpleHisto::XS->new( bins => \@lim );
    $hist->fill( \$$_{data}->@* );
    my $data_bins = $hist->all_bin_contents;
    printf "[%3d, %3d) => %3d\n", $lim[$_], ($lim[$_+1] == Inf ? 'Inf' : $lim[$_+1]), $$data_bins[$_] for 0..@lim-2;
    print "\n";
}

Phix[edit]

with javascript_semantics
function bin_it(sequence limits, data)
    -- Bin data according to (ascending) limits.
    sequence bins = repeat(0,length(limits)+1)  -- adds under/over range bins too
    for i=1 to length(data) do
        integer bdx = binary_search(data[i],limits)
        bdx = abs(bdx)+(bdx>0)
        bins[bdx] += 1
    end for
    return bins
end function
 
procedure bin_print(sequence limits, bins)
     printf(1,"           < %3d := %3d\n",{limits[1],bins[1]})
     for i=2 to length(limits) do
         printf(1,">= %3d and < %3d := %3d\n",{limits[i-1],limits[i],bins[i]})
     end for
     printf(1,">= %3d           := %3d\n\n",{limits[$],bins[$]})
end procedure
 
sequence limits, data
printf(1,"Example 1:\n")
limits = {23, 37, 43, 53, 67, 83}
data = {95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
        16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55}
bin_print(limits, bin_it(limits, data))
 
printf(1,"Example 2:\n")
limits = {14, 18, 249, 312, 389, 392, 513, 591, 634, 720}
data = {445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
        416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
        655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
        346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
        345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
        854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
        787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
        698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
        605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
        466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749}
bin_print(limits, bin_it(limits, data))
Output:
Example 1:
           <  23 :=  11
>=  23 and <  37 :=   4
>=  37 and <  43 :=   2
>=  43 and <  53 :=   6
>=  53 and <  67 :=   9
>=  67 and <  83 :=   5
>=  83           :=  13

Example 2:
           <  14 :=   3
>=  14 and <  18 :=   0
>=  18 and < 249 :=  44
>= 249 and < 312 :=  10
>= 312 and < 389 :=  16
>= 389 and < 392 :=   2
>= 392 and < 513 :=  28
>= 513 and < 591 :=  16
>= 591 and < 634 :=   6
>= 634 and < 720 :=  16
>= 720           :=  59

Python[edit]

This example uses binary search through the limits to assign each number to its bin, via standard module bisect.bisect_right.
The Counter module is not used as the number of bins is known allowing faster array access for incrementing bin counts versus dict lookup.

from bisect import bisect_right

def bin_it(limits: list, data: list) -> list:
    "Bin data according to (ascending) limits."
    bins = [0] * (len(limits) + 1)      # adds under/over range bins too
    for d in data:
        bins[bisect_right(limits, d)] += 1
    return bins

def bin_print(limits: list, bins: list) -> list:
    print(f"          < {limits[0]:3} := {bins[0]:3}")
    for lo, hi, count in zip(limits, limits[1:], bins[1:]):
        print(f">= {lo:3} .. < {hi:3} := {count:3}")
    print(f">= {limits[-1]:3}          := {bins[-1]:3}")


if __name__ == "__main__":
    print("RC FIRST EXAMPLE\n")
    limits  = [23, 37, 43, 53, 67, 83]
    data = [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
            16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]
    bins = bin_it(limits, data)
    bin_print(limits, bins)

    print("\nRC SECOND EXAMPLE\n")
    limits = [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
    data = [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
            416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
            655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
            346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
            345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
            854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
            787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
            698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
            605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
            466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]
    bins = bin_it(limits, data)
    bin_print(limits, bins)
Output:
RC FIRST EXAMPLE

          <  23 :=  11
>=  23 .. <  37 :=   4
>=  37 .. <  43 :=   2
>=  43 .. <  53 :=   6
>=  53 .. <  67 :=   9
>=  67 .. <  83 :=   5
>=  83          :=  13

RC SECOND EXAMPLE

          <  14 :=   3
>=  14 .. <  18 :=   0
>=  18 .. < 249 :=  44
>= 249 .. < 312 :=  10
>= 312 .. < 389 :=  16
>= 389 .. < 392 :=   2
>= 392 .. < 513 :=  28
>= 513 .. < 591 :=  16
>= 591 .. < 634 :=   6
>= 634 .. < 720 :=  16
>= 720          :=  59

R[edit]

This is R's bread and butter. Even with only the base library, the only thing stopping us from giving a one-line solution is the task's requirement of using two functions.

Code such as 0:length(limits) is generally considered bad practice, but it didn't cause any problems here. To my amazement, this code works even if limits is of size 0 or 1. Even the <= printing doesn't break!

limits1 <- c(23, 37, 43, 53, 67, 83)
data1 <- c(95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
         16,8,9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55)
limits2 <- c(14, 18, 249, 312, 389, 392, 513, 591, 634, 720)
data2 <- c(445,814,519,697,700,130,255,889,481,122,932,77,323,525,570,219,367,523,442,933,
         416,589,930,373,202,253,775,47,731,685,293,126,133,450,545,100,741,583,763,306,
         655,267,248,477,549,238,62,678,98,534,622,907,406,714,184,391,913,42,560,247,
         346,860,56,138,546,38,985,948,58,213,799,319,390,634,458,945,733,507,916,123,
         345,110,720,917,313,845,426,9,457,628,410,723,354,895,881,953,677,137,397,97,
         854,740,83,216,421,94,517,479,292,963,376,981,480,39,257,272,157,5,316,395,
         787,942,456,242,759,898,576,67,298,425,894,435,831,241,989,614,987,770,384,692,
         698,765,331,487,251,600,879,342,982,527,736,795,585,40,54,901,408,359,577,237,
         605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
         466,23,707,467,33,670,921,180,991,396,160,436,717,918,8,374,101,684,727,749)

createBin <- function(limits, data) sapply(0:length(limits), function(x) sum(findInterval(data, limits) == x))

#Contains some unicode magic so that we can get the infinity symbol and <= to print nicely.
#Half of the battle here is making sure that we're not being thrown by R being 1-indexed.
#The other half is avoiding the mathematical sin of saying that anything can be >=infinity.
printBin <- function(limits, bin)
{
  invisible(sapply(0:length(limits), function(x) cat("Bin", x, "covers the range:",
                                                    if(x == 0) "-\U221E < x <" else paste(limits[x], "\U2264 x <"),
                                                    if(x == length(limits)) "\U221E" else limits[x + 1],
                                                    "and contains", bin[x + 1], "elements.\n")))
}

#Showing off a one-line solution. Admittedly, calling the massive anonymous function "one-line" is generous.
oneLine <- function(limits, data)
{
  invisible(sapply(0:length(limits), function(x) cat("Bin", x, "covers the range:",
                                                    if(x == 0) "-\U221E < x <" else paste(limits[x], "\U2264 x <"),
                                                    if(x == length(limits)) "\U221E" else limits[x + 1],
                                                    "and contains", sum(findInterval(data, limits) == x),
                                                    "elements.\n")))
}

createBin(limits1, data1)
printBin(limits1, createBin(limits1, data1))
createBin(limits2, data2)
printBin(limits2, createBin(limits2, data2))
oneLine(limits2, c(data1, data2))#Not needed.
Output:
> createBin(limits1, data1)
[1] 11  4  2  6  9  5 13

> printBin(limits1, createBin(limits1, data1))
Bin 0 covers the range: -∞ < x < 23 and contains 11 elements.
Bin 1 covers the range: 23 ≤ x < 37 and contains 4 elements.
Bin 2 covers the range: 37 ≤ x < 43 and contains 2 elements.
Bin 3 covers the range: 43 ≤ x < 53 and contains 6 elements.
Bin 4 covers the range: 53 ≤ x < 67 and contains 9 elements.
Bin 5 covers the range: 67 ≤ x < 83 and contains 5 elements.
Bin 6 covers the range: 83 ≤ x < ∞ and contains 13 elements.

> createBin(limits2, data2)
 [1]  3  0 44 10 16  2 28 16  6 16 59

> printBin(limits2, createBin(limits2, data2))
Bin 0 covers the range: -∞ < x < 14 and contains 3 elements.
Bin 1 covers the range: 14 ≤ x < 18 and contains 0 elements.
Bin 2 covers the range: 18 ≤ x < 249 and contains 44 elements.
Bin 3 covers the range: 249 ≤ x < 312 and contains 10 elements.
Bin 4 covers the range: 312 ≤ x < 389 and contains 16 elements.
Bin 5 covers the range: 389 ≤ x < 392 and contains 2 elements.
Bin 6 covers the range: 392 ≤ x < 513 and contains 28 elements.
Bin 7 covers the range: 513 ≤ x < 591 and contains 16 elements.
Bin 8 covers the range: 591 ≤ x < 634 and contains 6 elements.
Bin 9 covers the range: 634 ≤ x < 720 and contains 16 elements.
Bin 10 covers the range: 720 ≤ x < ∞ and contains 59 elements.

> oneLine(limits2, c(data1, data2))#Not needed.
Bin 0 covers the range: -∞ < x < 14 and contains 10 elements.
Bin 1 covers the range: 14 ≤ x < 18 and contains 2 elements.
Bin 2 covers the range: 18 ≤ x < 249 and contains 85 elements.
Bin 3 covers the range: 249 ≤ x < 312 and contains 10 elements.
Bin 4 covers the range: 312 ≤ x < 389 and contains 16 elements.
Bin 5 covers the range: 389 ≤ x < 392 and contains 2 elements.
Bin 6 covers the range: 392 ≤ x < 513 and contains 28 elements.
Bin 7 covers the range: 513 ≤ x < 591 and contains 16 elements.
Bin 8 covers the range: 591 ≤ x < 634 and contains 6 elements.
Bin 9 covers the range: 634 ≤ x < 720 and contains 16 elements.
Bin 10 covers the range: 720 ≤ x < ∞ and contains 59 elements.

Racket[edit]

#lang racket

(define (find-bin-index limits v)
  (let inner ((l 0) (r (vector-length limits)))
    (let ((m (quotient (+ l r) 2)))
      (if (< v (vector-ref limits m))
          (if (= m l) l (inner l m))
          (if (= m (sub1 r)) r (inner m r))))))

(define ((bin-given-limits! limits) data (bins (make-vector (add1 (vector-length limits)) 0)))
  (for ((d data))
    (let ((i (find-bin-index limits d)))
      (vector-set! bins i (add1 (vector-ref bins i)))))
  bins)

(define (report-bins-given-limits limits data)
  (for ((b ((bin-given-limits! limits) data))
        (ge (in-sequences (in-value -Inf.0) limits))
        (lt (in-sequences limits (in-value +Inf.0))))
    (printf "~a <= v < ~a : ~a~%" ge lt b)))

(define (Bin-given-limits)
  (report-bins-given-limits
              #[23 37 43 53 67 83]
              (list 95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71 61 54 58 47 
                    16  8  9 32 84 7 87 46 19 30 37 96 6 98 40 79 97 45 64 60 29 49 36 43 55))
  (newline)
  (report-bins-given-limits
              #[14  18  249  312  389  392  513  591  634  720]
              (list 445 814 519 697 700 130 255 889 481 122 932  77 323 525 570 219 367 523 442 933 
                    416 589 930 373 202 253 775  47 731 685 293 126 133 450 545 100 741 583 763 306 
                    655 267 248 477 549 238  62 678  98 534 622 907 406 714 184 391 913  42 560 247 
                    346 860  56 138 546  38 985 948  58 213 799 319 390 634 458 945 733 507 916 123 
                    345 110 720 917 313 845 426   9 457 628 410 723 354 895 881 953 677 137 397  97 
                    854 740  83 216 421  94 517 479 292 963 376 981 480  39 257 272 157   5 316 395 
                    787 942 456 242 759 898 576  67 298 425 894 435 831 241 989 614 987 770 384 692 
                    698 765 331 487 251 600 879 342 982 527 736 795 585  40  54 901 408 359 577 237 
                    605 847 353 968 832 205 838 427 876 959 686 646 835 127 621 892 443 198 988 791 
                    466  23 707 467  33 670 921 180 991 396 160 436 717 918   8 374 101 684 727 749)))

(module+ main
  (Bin-given-limits))
Output:
-inf.0 <= v < 23 : 11
23 <= v < 37 : 4
37 <= v < 43 : 2
43 <= v < 53 : 6
53 <= v < 67 : 9
67 <= v < 83 : 5
83 <= v < +inf.0 : 13

-inf.0 <= v < 14 : 3
14 <= v < 18 : 0
18 <= v < 249 : 44
249 <= v < 312 : 10
312 <= v < 389 : 16
389 <= v < 392 : 2
392 <= v < 513 : 28
513 <= v < 591 : 16
591 <= v < 634 : 6
634 <= v < 720 : 16
720 <= v < +inf.0 : 59

Raku[edit]

sub bin_it ( @limits, @data ) {
    my @ranges = ( -Inf, |@limits, Inf ).rotor( 2 => -1 ).map: { .[0] ..^ .[1] };
    my @binned = @data.classify(-> $d { @ranges.grep(-> $r { $d ~~ $r }) });
    my %counts = @binned.map: { .key => .value.elems };
    return @ranges.map: { $_ => ( %counts{$_} // 0 ) };
}
sub bin_format ( @bins ) {
    return @bins.map: { .key.gist.fmt('%9s => ') ~ .value.fmt('%2d') };
}

my @tests =
    {
        limits => (23, 37, 43, 53, 67, 83),
        data   => (95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,16,8,9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55),
    },
    {
        limits => (14, 18, 249, 312, 389, 392, 513, 591, 634, 720),
        data   => (
            445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
            655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
            345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
            787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
            605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749
        ),
    },
;
for @tests -> ( :@limits, :@data ) {
    my @bins = bin_it( @limits, @data );
    .say for bin_format(@bins);
    say '';
}
Output:
-Inf..^23 => 11
  23..^37 =>  4
  37..^43 =>  2
  43..^53 =>  6
  53..^67 =>  9
  67..^83 =>  5
 83..^Inf => 13

-Inf..^14 =>  3
  14..^18 =>  0
 18..^249 => 44
249..^312 => 10
312..^389 => 16
389..^392 =>  2
392..^513 => 28
513..^591 => 16
591..^634 =>  6
634..^720 => 16
720..^Inf => 59

REXX[edit]

REXX programming note:   since the sets of numbers defined don't have any leading signs, no quotes (") are needed.

/*REXX program counts how many   numbers of a set   that fall in the range of each bin. */
lims= 23 37 43 53 67 83                          /* ◄■■■■■■1st set of bin limits & data.*/
data= 95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71 61 54 58 47  ,
      16 8 9 32 84 7 87 46 19 30 37 96 6 98 40 79 97 45 64 60 29 49 36 43 55
call lims lims;     call bins data
call show 'the 1st set of bin counts for the specified data:'
                                                                  say;    say;    say
lims=  14  18 249 312 389 392 513 591 634 720    /* ◄■■■■■■2nd set of bin limits & data.*/
data= 445 814 519 697 700 130 255 889 481 122 932  77 323 525 570 219 367 523 442 933  ,
      416 589 930 373 202 253 775  47 731 685 293 126 133 450 545 100 741 583 763 306  ,
      655 267 248 477 549 238  62 678  98 534 622 907 406 714 184 391 913  42 560 247  ,
      346 860  56 138 546  38 985 948  58 213 799 319 390 634 458 945 733 507 916 123  ,
      345 110 720 917 313 845 426   9 457 628 410 723 354 895 881 953 677 137 397  97  ,
      854 740  83 216 421  94 517 479 292 963 376 981 480  39 257 272 157   5 316 395  ,
      787 942 456 242 759 898 576  67 298 425 894 435 831 241 989 614 987 770 384 692  ,
      698 765 331 487 251 600 879 342 982 527 736 795 585  40  54 901 408 359 577 237  ,
      605 847 353 968 832 205 838 427 876 959 686 646 835 127 621 892 443 198 988 791  ,
      466  23 707 467  33 670 921 180 991 396 160 436 717 918   8 374 101 684 727 749
call lims lims;     call bins data
call show 'the 2nd set of bin counts for the specified data:'
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
bins: parse arg nums; !.= 0;  datum= words(nums);  wc= length(datum)  /*max width count.*/
        do   j=1  for datum;  x= word(nums, j)
          do k=0  for #                          /*find the bin that this number is in. */
          if x < @.k  then do;  !.k= !.k + 1;  iterate j;  end        /*bump a bin count*/
          end   /*k*/
                                !.k= !.k + 1     /*number is > the highest bin specified*/
        end     /*j*/;                   return
/*──────────────────────────────────────────────────────────────────────────────────────*/
lims: parse arg limList;  #= words(limList);                 wb= 0    /*max width binLim*/
        do j=1  for #;  _= j - 1;   @._= word(limList, j);   wb= max(wb, length(@._) )
        end   /*j*/;                     return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: parse arg t;    say center(t,  51     );   $= left('', 9)  /*$:    for indentation*/
                      say center('', 51, "═")                    /*show title separator.*/
                          jp= # - 1;        ge= '≥';              le='<'; eq= '   count='
        do j=0  for #;    jm= j - 1;  bin= right(@.j, wb)
        if j==0  then say $ left('', length(ge) +3+wb+length(..) )le bin eq right(!.j, wc)
                 else say $                 ge right(@.jm, wb) .. le bin eq right(!.j, wc)
        if j==jp  then say $ ge right(@.jp,wb) left('', 3+length(..)+wb) eq right(!.#, wc)
        end   /*j*/;                     return
output   when using the internal default input:
 the 1st set of bin counts for the specified data:
═══════════════════════════════════════════════════
                  < 23    count= 11
          ≥ 23 .. < 37    count=  4
          ≥ 37 .. < 43    count=  2
          ≥ 43 .. < 53    count=  6
          ≥ 53 .. < 67    count=  9
          ≥ 67 .. < 83    count=  5
          ≥ 83            count= 13



 the 2nd set of bin counts for the specified data:
═══════════════════════════════════════════════════
                   <  14    count=   3
          ≥  14 .. <  18    count=   0
          ≥  18 .. < 249    count=  44
          ≥ 249 .. < 312    count=  10
          ≥ 312 .. < 389    count=  16
          ≥ 389 .. < 392    count=   2
          ≥ 392 .. < 513    count=  28
          ≥ 513 .. < 591    count=  16
          ≥ 591 .. < 634    count=   6
          ≥ 634 .. < 720    count=  16
          ≥ 720             count=  59

Ring[edit]

limit = [0, 23, 37, 43, 53, 67, 83]
data  = [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
         16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]
data  = sort(data)
dn    = list(len(limit))
see "Example 1:" + nl + nl
limits(limit,data,dn)
see nl

limit = [0, 14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
data   = [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
          416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
          655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
          346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
          345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
          854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
          787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
          698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
          605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
          466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749]
data  = sort(data)
dn    = list(len(limit))
see "Example 2:" + nl + nl
limits(limit,data,dn)

func limits(limit,data,dn)
     for n = 1 to len(data)
         for m = 1 to len(limit)-1
             if data[n] >= limit[m] and data[n] < limit[m+1]
                dn[m] += 1
              ok
         next
         if data[n] >= limit[len(limit)]
            dn[len(limit)] += 1
         ok    
     next

     for n = 1 to len(limit)-1
        see ">= " + limit[n] + " and < " + limit[n+1] + " := " + dn[n] + nl
     next     
     see ">= " + limit[n] + " := " + dn[n] + nl
Output:
Example 1:

>= 0  and < 23 := 11
>= 23 and < 37 :=  4
>= 37 and < 43 :=  2
>= 43 and < 53 :=  6
>= 53 and < 67 :=  9
>= 67 and < 83 :=  5
>= 83          := 13

Example 2:

>= 0   and < 14  :=  3
>= 14  and < 18  :=  0
>= 18  and < 249 := 44
>= 249 and < 312 := 10
>= 312 and < 389 := 16
>= 389 and < 392 :=  2
>= 392 and < 513 := 28
>= 513 and < 591 := 16
>= 591 and < 634 :=  6
>= 634 and < 720 := 16
>= 720           := 59

Ruby[edit]

Perform a binary search on the data to select the limit and keep a tally on that. Uses Ruby 3.0 end-less and begin-less Ranges.

Test = Struct.new(:limits, :data)
tests = Test.new( [23, 37, 43, 53, 67, 83],
                  [95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
                   16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55]),
        Test.new( [14, 18, 249, 312, 389, 392, 513, 591, 634, 720],
                  [445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
                   416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
                   655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
                   346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
                   345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
                   854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
                   787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
                   698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
                   605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
                   466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749])

def bin(limits, data)
  data.map{|d| limits.bsearch{|limit| limit > d} }.tally
end

def present_bins(limits, bins)
  ranges = ([nil]+limits+[nil]).each_cons(2).map{|low, high| Range.new(low, high, true) }
  ranges.each{|range| puts "#{range.to_s.ljust(12)} #{bins[range.end].to_i}"}
end

tests.each do |test|
  present_bins(test.limits, bin(test.limits, test.data))
  puts
end
Output:
...23        11
23...37      4
37...43      2
43...53      6
53...67      9
67...83      5
83...        13

...14        3
14...18      0
18...249     44
249...312    10
312...389    16
389...392    2
392...513    28
513...591    16
591...634    6
634...720    16
720...       59

Rust[edit]

Works with: rustc version 1.49.0

A very simple and naive algorithm that uses nested dynamic arrays.

fn make_bins(limits: &Vec<usize>, data: &Vec<usize>) -> Vec<Vec<usize>> {
    let mut bins: Vec<Vec<usize>> = Vec::with_capacity(limits.len() + 1);
    for _ in 0..=limits.len() {bins.push(Vec::new());}

    limits.iter().enumerate().for_each(|(idx, limit)| {
        data.iter().for_each(|elem| {
                 if idx == 0 && elem < limit              { bins[0].push(*elem); }             // smaller than the smallest limit
            else if idx == limits.len()-1 && elem >= limit { bins[limits.len()].push(*elem); } // larger than the largest limit
            else if elem < limit && elem >= &limits[idx-1] { bins[idx].push(*elem); }          // otherwise
        });
    });

    bins
}

fn print_bins(limits: &Vec<usize>, bins: &Vec<Vec<usize>>) {
    for (idx, bin) in bins.iter().enumerate() {
        if idx == 0 {
            println!("          < {:3} := {:3}", limits[idx], bin.len());
        } else if idx == limits.len() {
            println!(">= {:3}          := {:3}",  limits[idx-1], bin.len());
        }else {
            println!(">= {:3} .. < {:3} := {:3}", limits[idx-1], limits[idx], bin.len());
        }
    };
}

fn main() {
    let limits1  = vec![23, 37, 43, 53, 67, 83];
    let data1 = vec![95,21,94,12,99,4,70,75,83,93,52,80,57,5,53,86,65,17,92,83,71,61,54,58,47,
                     16, 8, 9,32,84,7,87,46,19,30,37,96,6,98,40,79,97,45,64,60,29,49,36,43,55];

   let limits2 = vec![14, 18, 249, 312, 389, 392, 513, 591, 634, 720];
   let data2 = vec![
       445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
       416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
       655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
       346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
       345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
       854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
       787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
       698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
       605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
       466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749
           ];


    // Why are we calling it RC anyways???
    println!("RC FIRST EXAMPLE");
    let bins1 = make_bins(&limits1, &data1);
    print_bins(&limits1, &bins1);

    println!("\nRC SECOND EXAMPLE");
    let bins2 = make_bins(&limits2, &data2);
    print_bins(&limits2, &bins2);
}
Output:
RC FIRST EXAMPLE
          <  23 :=  11
>=  23 .. <  37 :=   4
>=  37 .. <  43 :=   2
>=  43 .. <  53 :=   6
>=  53 .. <  67 :=   9
>=  67 .. <  83 :=   5
>=  83          :=  13

RC SECOND EXAMPLE
          <  14 :=   3
>=  14 .. <  18 :=   0
>=  18 .. < 249 :=  44
>= 249 .. < 312 :=  10
>= 312 .. < 389 :=  16
>= 389 .. < 392 :=   2
>= 392 .. < 513 :=  28
>= 513 .. < 591 :=  16
>= 591 .. < 634 :=   6
>= 634 .. < 720 :=  16
>= 720          :=  59

Tcl[edit]

For Tcl 8.6 (due to lsearch -bisect):

namespace path {::tcl::mathop ::tcl::mathfunc}

# Not necessary but useful helper
proc lincr {_list index} {
	upvar $_list list
	lset list $index [+ [lindex $list $index] 1]
}

proc distribute_bins {binlims data} {
	set bins [lrepeat [+ [llength $binlims] 1] 0]
	foreach val $data {
		lincr bins [+ [lsearch -exact -integer -sorted -bisect $binlims $val] 1]
	}
	return $bins
}

proc print_bins {binlims bins} {
	set binlims [list - {*}$binlims ]
	for {set i 0} {$i < [llength $bins]} {incr i} {
		puts "[lindex $binlims $i]..[lindex $binlims [+ $i 1]]: [lindex $bins $i]"
	}
}

set binlims {23  37  43  53  67  83}
set data {95 21 94 12 99 4 70 75 83 93 52 80 57 5 53 86 65 17 92 83 71 61 54 58 47
          16  8  9 32 84 7 87 46 19 30 37 96 6 98 40 79 97 45 64 60 29 49 36 43 55}
print_bins $binlims [distribute_bins $binlims $data]
puts ""

set binlims {14  18  249  312  389  392  513  591  634  720}
set data {445 814 519 697 700 130 255 889 481 122 932  77 323 525 570 219 367 523 442 933
          416 589 930 373 202 253 775  47 731 685 293 126 133 450 545 100 741 583 763 306
          655 267 248 477 549 238  62 678  98 534 622 907 406 714 184 391 913  42 560 247
          346 860  56 138 546  38 985 948  58 213 799 319 390 634 458 945 733 507 916 123
          345 110 720 917 313 845 426   9 457 628 410 723 354 895 881 953 677 137 397  97
          854 740  83 216 421  94 517 479 292 963 376 981 480  39 257 272 157   5 316 395
          787 942 456 242 759 898 576  67 298 425 894 435 831 241 989 614 987 770 384 692
          698 765 331 487 251 600 879 342 982 527 736 795 585  40  54 901 408 359 577 237
          605 847 353 968 832 205 838 427 876 959 686 646 835 127 621 892 443 198 988 791
          466  23 707 467  33 670 921 180 991 396 160 436 717 918   8 374 101 684 727 749}
print_bins $binlims [distribute_bins $binlims $data]
Output:
-∞..23: 11
23..37: 4
37..43: 2
43..53: 6
53..67: 9
67..83: 5
83..∞: 13

-∞..14: 3
14..18: 0
18..249: 44
249..312: 10
312..389: 16
389..392: 2
392..513: 28
513..591: 16
591..634: 6
634..720: 16
720..∞: 59

Wren[edit]

Library: Wren-sort
Library: Wren-fmt
import "/sort" for Find
import "/fmt" for Fmt

var getBins = Fn.new { |limits, data|
    var n = limits.count
    var bins = List.filled(n+1, 0)
    for (d in data) {
        var res = Find.all(limits, d) // uses binary search
        var found = res[0]
        var index = res[2].from
        if (found) index = index + 1
        bins[index] = bins[index] + 1
    }
    return bins
}

var printBins = Fn.new { |limits, bins|
    for (i in 0..limits.count) {
        if (i == 0) {
            Fmt.print("           < $3d = $2d", limits[0], bins[0])
        } else if (i == limits.count) {
            Fmt.print(">= $3d           = $2d", limits[i-1], bins[i])
        } else {
            Fmt.print(">= $3d and < $3d = $2d", limits[i-1], limits[i], bins[i])
        }
    }
    System.print()
}
                       
var limitsList  = [
    [23, 37, 43, 53, 67, 83],
    [14, 18, 249, 312, 389, 392, 513, 591, 634, 720]
]

var dataList = [
    [
        95,21,94,12,99,4,70,75,83,93,52,80,57, 5,53,86,65,17,92,83,71,61,54,58,47,
        16, 8, 9,32,84,7,87,46,19,30,37,96, 6,98,40,79,97,45,64,60,29,49,36,43,55
    ],
    [
       445,814,519,697,700,130,255,889,481,122,932, 77,323,525,570,219,367,523,442,933,
       416,589,930,373,202,253,775, 47,731,685,293,126,133,450,545,100,741,583,763,306,
       655,267,248,477,549,238, 62,678, 98,534,622,907,406,714,184,391,913, 42,560,247,
       346,860, 56,138,546, 38,985,948, 58,213,799,319,390,634,458,945,733,507,916,123,
       345,110,720,917,313,845,426,  9,457,628,410,723,354,895,881,953,677,137,397, 97,
       854,740, 83,216,421, 94,517,479,292,963,376,981,480, 39,257,272,157,  5,316,395,
       787,942,456,242,759,898,576, 67,298,425,894,435,831,241,989,614,987,770,384,692,
       698,765,331,487,251,600,879,342,982,527,736,795,585, 40, 54,901,408,359,577,237,
       605,847,353,968,832,205,838,427,876,959,686,646,835,127,621,892,443,198,988,791,
       466, 23,707,467, 33,670,921,180,991,396,160,436,717,918,  8,374,101,684,727,749
    ]
]

for (i in 0...limitsList.count) {
    System.print("Example %(i+1):\n")
    var bins = getBins.call(limitsList[i], dataList[i])
    printBins.call(limitsList[i], bins)
}
Output:
Example 1:

           <  23 = 11
>=  23 and <  37 =  4
>=  37 and <  43 =  2
>=  43 and <  53 =  6
>=  53 and <  67 =  9
>=  67 and <  83 =  5
>=  83           = 13

Example 2:

           <  14 =  3
>=  14 and <  18 =  0
>=  18 and < 249 = 44
>= 249 and < 312 = 10
>= 312 and < 389 = 16
>= 389 and < 392 =  2
>= 392 and < 513 = 28
>= 513 and < 591 = 16
>= 591 and < 634 =  6
>= 634 and < 720 = 16
>= 720           = 59