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 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
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Why3 Proof Results for Project "array_most_frequent"
Theory "array_most_frequent.Top": fully verified
Obligations | Alt-Ergo 2.2.0 | CVC4 1.6 | Z3 4.6.0 | |
VC for most_frequent | --- | --- | --- | |
split_vc | ||||
index in array bounds | --- | 0.03 | --- | |
loop invariant init | --- | 0.04 | --- | |
loop invariant init | --- | 0.03 | --- | |
loop invariant init | --- | 0.04 | --- | |
index in array bounds | --- | 0.04 | --- | |
index in array bounds | --- | 0.03 | --- | |
index in array bounds | --- | 0.03 | --- | |
loop invariant preservation | --- | 0.07 | --- | |
loop invariant preservation | --- | 0.03 | --- | |
loop invariant preservation | --- | 0.17 | --- | |
loop invariant preservation | --- | 0.07 | --- | |
loop invariant preservation | --- | 0.06 | --- | |
loop invariant preservation | --- | 0.29 | --- | |
loop invariant preservation | --- | --- | 0.03 | |
loop invariant preservation | 0.46 | --- | --- | |
loop invariant preservation | --- | --- | 0.09 | |
postcondition | 0.26 | --- | --- | |
postcondition | --- | 0.03 | --- | |
out of loop bounds | --- | 0.03 | --- |