## Most Frequent Value in a Sorted Array

Search for the most frequent value in a sorted array, in constant space.

Authors: Jean-Christophe Filliâtre

Topics: Array Data Structure / Algorithms

Tools: Why3

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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 FilliĆ¢tre (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
```