A simple programming exercise: find out the most frequent value in an array

Using an external table (e.g. a hash table), we can easily do it in linear time and space.

However, if the array is sorted, we can do it in linear time and constant space.

Author: Jean-Christophe Filliâtre (CNRS)

use int.Int
use ref.Refint
use array.Array
use array.NumOfEq

let most_frequent (a: array int) : int
  requires { length a > 0 }
  requires { forall i j. 0 <= i <= j < length a -> a[i] <= a[j] }
  ensures  { numof a result 0 (length a) > 0 }
  ensures  { forall x. numof a x 0 (length a) <= numof a result 0 (length a) }
= let ref r = a[0] in
  let ref c = 1 in
  let ref m = 1 in
  for i = 1 to length a - 1 do
    invariant { c = numof a a[i-1] 0 i }
    invariant { m = numof a r 0 i }
    invariant { forall x. numof a x 0 i <= m }
    if a[i] = a[i-1] then begin
      incr c;
      if c > m then begin m <- c; r <- a[i] end
    end else
      c <- 1
  done;
  r