Loop Invariant for linear array search

Question

int i = 0
boolean answer = false
while (i < a.length) {
    if a[i] == 0
        answer = true
    i = i + 1

where 'a' is an array of integers. I'm doing a question paper where it has asked me what the loop invariant of this is, I have already established that the code works out whether the array contains a 0. But so far I can only think of the invariant as being

i <= a.length

and the question states to include variables i, a and answer in the invariant so I know this can't be right. I have not come across loop invariants involving booleans before and am confused, could anyone help explaining?

I think this answer may help you: http://stackoverflow.com/a/5585221/1766140 — Sergio A., Jan 17 '14 at 00:02

score 0 · Answer 1 · answered May 12 '16 at 23:35

Here is an implementation of your loop in Microsoft Dafny with appropriate loop invariants specified:

method Main(a:array<int>) returns (answer:bool)
   requires a != null
   ensures answer <==> (exists i :: 0 <= i < a.Length && a[i] == 0) 
{
   var i:int := 0;
   answer := false;
   while (i < a.Length)
     invariant 0 <= i <= a.Length;
     invariant !answer ==> !(exists j :: 0 <= j < i && a[j] == 0)
     invariant answer ==> (exists j :: 0 <= j < i && a[j] == 0)  
   {
     if a[i] == 0 {
        answer := true;
     }
     i := i + 1;
   }
}

You can verify its correctness automatically in the online version of Dafny

Loop Invariant for linear array search

1 Answers1