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Add verfication for partition

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ajs19 2022-11-21 17:30:48 +00:00
parent 88e407c8f7
commit b97546132c
1 changed files with 13 additions and 5 deletions
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10
dafny/2022/tasks_2022.dfy
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@ -62,7 +62,7 @@ method binarysearch_iter(A:array<int>, v:int) returns (result:bool)
method partition(A:array<int>, lo:int, hi:int) returns (pivot:int) method partition(A:array<int>, lo:int, hi:int) returns (pivot:int)
requires 0 <= lo < hi <= A.Length requires 0 <= lo < hi <= A.Length
ensures 0 <= lo <= pivot < hi ensures 0 <= lo <= pivot < hi <= A.Length
ensures forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k] ensures forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
modifies A modifies A
{ {
@ -71,6 +71,9 @@ method partition(A:array<int>, lo:int, hi:int) returns (pivot:int)
while i < hi while i < hi
invariant 0 <= lo <= pivot < i <= hi invariant 0 <= lo <= pivot < i <= hi
invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k] invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
invariant forall k :: (k==pivot) ==> A[k] == old(A[lo])
invariant forall k :: (lo <= k <= pivot) ==> A[k] <= A[pivot]
invariant forall k :: (pivot <= k < i) ==> A[k] >= A[pivot]
decreases hi - i decreases hi - i
{ {
if A[i] < A[pivot] { if A[i] < A[pivot] {
@ -79,6 +82,10 @@ method partition(A:array<int>, lo:int, hi:int) returns (pivot:int)
A[i] := A[j]; A[i] := A[j];
while pivot < j while pivot < j
invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k] invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
invariant forall k :: (k==pivot) ==> A[k] == old(A[lo])
invariant forall k :: (pivot <= k <= i) ==> A[k] >= A[pivot]
invariant forall k :: (lo <= k <= pivot) ==> A[k] <= A[pivot]
invariant A[pivot] > tmp
decreases j decreases j
{ {
A[j+1] := A[j]; A[j+1] := A[j];
@ -106,6 +113,7 @@ method quicksort_between(A:array<int>, lo:int, hi:int)
method quicksort(A:array<int>) method quicksort(A:array<int>)
modifies A modifies A
ensures sorted(A)
{ {
quicksort_between(A, 0, A.Length); quicksort_between(A, 0, A.Length);
} }