Day 8 Part 2

1 files changed, 11 insertions, 0 deletions

diff --git a/Common/Euclid.lean b/Common/Euclid.lean
new file mode 100644
index 0000000..58c8210
--- /dev/null
+++ b/Common/Euclid.lean
@@ -0,0 +1,11 @@
+namespace Euclid
+-- Extended Euclidean algorithm, stolen from Wikipedia.
+-- The signature is stolen from Wikipedia too. As in, the values a and b are Nat, but s and t are Int.
+def xgcd (a b: Nat) : Nat × Int × Int :=
+  if p : b > 0 then
+    have : a % b < b := by simp[p, Nat.mod_lt]
+    let (d, ss, tt) := xgcd b (a%b)
+    (d, tt ,ss - tt * (a / b))
+  else
+    (a,1,0)
+  termination_by xgcd a b => b