Counting Digits

January 7, 2020

Here’s our solution:

(define (f lo hi)
  (define (is258 d) (or (= d 2) (= d 5) (= d 8)))
  (define (cnt n) (length (filter is258 (digits n))))
  (do ((n lo (+ n 1)) (c 0 (+ c (cnt n)))) ((< hi n) c))) > (f 295 395)
9
> (time (f 11 100000))
(time (f 11 ...))
2 collections
0.018759638s elapsed cpu time, including 0.000229760s collecting
0.018892309s elapsed real time, including 0.000238270s collecting
9539376 bytes allocated, including 16834208 bytes reclaimed
149997

You can run the program at https://ideone.com/FA3ADI.

Pages: 1 2

6 Responses to “Counting Digits”

  1. matthew said

    Happy new year & I hope everyone enjoyed the holiday break.

    I thought that should be a more direct way of counting the digits than enumerating the entire range. For simplicity, dcount counts all the digits in range(n) – ie. not including n itself:

    def dcount(digits,n):
        count = 0
        m,m1 = 1,10
        while n >= m:
            for k in digits:
                count += n//m1*m + min(m,max(n%m1-k*m,0))
            m,m1 = m1,10*m1
        return count
    
    digits = [2,5,8]
    
    print(dcount(digits,306)-dcount(digits,295)) # 9
    
  2. matthew said

    That needs some modification for digit ‘0’ (an exercise for the reader)- also the while condition can be ‘n > m’

  3. matthew said

    This is better (and the ‘0’ count is correct if we assume numbers are zero padded on the left to the same length):

    def dcount(digits,n):
        count = 0
        m,m1 = 1,10
        for _ in range(len(str(n-1))):
            count += n//m1*m*len(digits)
            for k in digits: count += min(m,max(n%m1-k*m,0))
            m,m1 = m1,10*m1
        return count
    
  4. matthew said

    Or wrap the whole thing up in a list comprehension:

    def dcount(digits,n):
        return sum(sum(n//m1*m + min(m,max(n%m1-k*m,0)) for k in digits)
                   for i in range(len(str(n-1))) for m in [10**i] for m1 in [10*m])
    
  5. Steve said

    Klong version

    ; $n                             - Change number to string
    ; ($n)?$x                        - Turn digit into string and store in a list the positions of digit in string
    ; #($n)?$x                       - Get number of positions
    ; {#($n)?$x}'"258"}              - Function to do the aboved for each digit in "258" and return list of number of positions/hits
    ; +/...                          - Return sum of hits
    ; {[n];n::x;+/{...}...}'x+!1+y-x - Function to goo through each of the number in the range and run the inner function, returning a list of sums
    ; +/{...{...}...                 - Return total sum of hits
    ; {+/...}(295;305)               - Run middle function ({}) with first and last number in range of numbers
    ; 
    {+/{[n];n::x;+/{#($n)?$x}'"258"}'x+!1+y-x}(295;305)
    
  6. Steve said

    Klong results:
    {+/{[n];n::x;+/{#($n)?$x}'”258″}’x+!1+y-x}(295;305)
    9

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