Re: X in every language syndrome

The question is about so-called "bellied"
numbers, defined as 4-digit integers for which the sum of the two
"middle" digits is smaller than the sum of the two outer digits. So 1265
is bellied, while 4247 is not.

[ He means the sum of middle digits is larger. ]

 
This checking part is easy:
 
(defun bellied-number-p (n)
  (> (+ (mod (truncate n 10) 10) (mod (truncate n 100) 10))
     (+ (mod n 10) (truncate n 1000))))
 
Now the task is to find the longest, uninterrupted sequence of bellied
numbers within all 4-digit number, hence from 1000 to 9999. And this is
where I terribly screwed up:
 
While the following code does the job,
 
(let ((max-length 0)
      (current-length 0)
      (last-bellied-number 0))
  (dotimes (m 9000)
    (let ((n (+ 1000 m)))
      (if (bellied-number-p n)
          (incf current-length)
          (progn
            (when (> current-length max-length)
              (setf max-length current-length)
              (setf last-bellied-number (1- n)))
            (setf current-length 0)))))
  (print (format t "~&Longest sequence of ~a bellied numbers ends at ~a."
                 max-length last-bellied-number)))

[ Another poster: ]

TXR Lisp.
 
Having defined:
 
  (defun bellied-p (num)
    (let ((d (digits num)))
      (and (= 4 (len d))
   (< (+ [d 0] [d 3])
      (+ [d 1] [d 2])))))
 
We casually do this at the prompt:
 
  1> [find-max [partition-by bellied-p (range 1000 9999)] :
       [iff [chain car bellied-p] len (ret 0)]]
  (1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932
   1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
   1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958
   1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
   1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
   1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
   1998 1999)

Shorter.

Gauche Scheme:

(use gauche.sequence) ;; group-contiguous-sequence find-max
,print-mode pretty #t length #f width 64

(define (bellied? n)
  (define (d i) (mod (div n (expt 10 i)) 10))
  (> (+ (d 1) (d 2))
     (+ (d 0) (d 3))))

(find-max
  (group-contiguous-sequence (filter bellied? (iota 9000 1000)))
  :key length)

  ===>
(1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931
 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943
 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955
 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967
 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
 1992 1993 1994 1995 1996 1997 1998 1999)