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.

#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))