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Dafny Task 1 complete

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Aadi Desai 2022-11-21 13:50:18 +00:00
parent d2614f4946
commit 30874e2405
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GPG key ID: CFFFE425830EF4D9
1 changed files with 12 additions and 4 deletions
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dafny/submission.dfy
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@ -4,22 +4,30 @@
// Authors: John Wickerson // Authors: John Wickerson
method countsquares(n:nat) returns (result:nat) method countsquares(n:nat) returns (result:nat)
//ensures result == ... ensures result == (n * (n + 1) * (2 * n + 1)) / 6;
{ {
var i := 0; var i := 0;
result := 0; result := 0;
while i < n { while i < n
invariant 0 <= i <= n;
decreases n - i;
invariant result == (i * (i + 1) * (2 * i + 1)) / 6;
{
i := i + 1; i := i + 1;
result := result + i * i; result := result + i * i;
} }
} }
method countsquares2(n:nat) returns (result:nat) method countsquares2(n:nat) returns (result:nat)
// ensures result == ... ensures result == (n * (n + 1) * (2 * n + 1)) / 6;
{ {
var i := n; var i := n;
result := 0; result := 0;
while i > 0 { while i > 0
invariant 0 <= i <= n;
decreases i;
invariant result == ((n * (n + 1) * (2 * n + 1)) / 6) - ((i * (i + 1) * (2 * i + 1)) / 6);
{
result := result + i * i; result := result + i * i;
i := i - 1; i := i - 1;
} }