ELEC70056-HSV-CW1/dafny/2020/tasks_2020.dfy

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2021-11-01 06:34:44 +00:00
// Dafny coursework tasks
// Autumn term, 2020
//
// Authors: John Wickerson and Matt Windsor
predicate sorted(A:array<int>)
reads A
{
forall m,n :: 0 <= m < n < A.Length ==> A[m] <= A[n]
}
// Task 1
method resetArray(A:array<int>)
ensures zeroes(A)
modifies A
{
var i := 0;
while i < A.Length {
A[i] := 0;
i := i + 1;
}
}
// Task 2
method backwards_selection_sort(A:array<int>)
ensures sorted(A)
modifies A
{
var i := A.Length;
while 0 < i {
var max := 0;
var j := 1;
while j < i {
if A[max] < A[j] {
max := j;
}
j := j+1;
}
A[max], A[i-1] := A[i-1], A[max];
i := i - 1;
}
}
// Task 3
method recursive_selection_sort_inner(A:array<int>, i:int)
modifies A
{
if i == A.Length {
return;
}
var k := i;
var j := i + 1;
while j < A.Length {
if A[k] > A[j] {
k := j;
}
j := j+1;
}
A[k], A[i] := A[i], A[k];
recursive_selection_sort_inner(A, i + 1);
}
method recursive_selection_sort(A:array<int>)
ensures sorted(A)
modifies A
{
recursive_selection_sort_inner(A, 0);
}
// Task 4
method bubble_sort_with_early_stop(A:array<int>)
ensures sorted(A)
modifies A
{
var stable := false;
var i := 0;
while !stable {
var j := 0;
stable := true;
while j + 1 < A.Length - i {
if A[j+1] < A[j] {
A[j], A[j+1] := A[j+1], A[j];
stable := false;
}
j := j+1;
}
i := i+1;
}
}
// Task 5
method cocktail_shaker_sort(A:array<int>)
ensures sorted(A)
modifies A
{
var i := 0;
while i < A.Length / 2 {
var j := i;
while j < A.Length - i - 1 {
if A[j+1] < A[j] {
A[j], A[j+1] := A[j+1], A[j];
}
j := j+1;
}
while i < j {
if A[j-1] > A[j] {
A[j-1], A[j] := A[j], A[j-1];
}
j := j-1;
}
i := i+1;
}
}
method Main() {
var A:array<int> := new int[7] [4,0,1,9,7,1,2];
print "Before: ", A[0], A[1], A[2], A[3],
A[4], A[5], A[6], "\n";
recursive_selection_sort(A);
print "After: ", A[0], A[1], A[2], A[3],
A[4], A[5], A[6], "\n";
}