025 (#39)

025-factorize.dfy

@@ -0,0 +1,40 @@
+function prod(s: seq<int>) : int {
+  if |s| == 0 then 1 else prod(s[..|s| - 1]) * s[|s| - 1]
+}
+
+method factorize(n: nat) returns (factors: seq<nat>)
+  requires n > 0
+  ensures prod(factors) == n
+{
+  factors := [];
+  ghost var taken := 1;
+  var cur := n;
+  var i := 2;
+  while i * i <= cur
+    invariant prod(factors) == taken
+    invariant taken * cur == n
+    invariant cur >= 1
+  {
+    ghost var pre := cur;
+    ghost var temp := 1;
+    while cur % i == 0 
+      invariant cur >= 1
+      invariant temp * cur == pre
+      invariant prod(factors) == taken * temp 
+      decreases cur - 1
+    {
+      factors := factors + [i];
+
+      cur := cur / i;
+      temp := temp * i;
+      assert 2 <= i && 2 * cur <= i * cur;
+    }
+    taken := taken * temp;
+    i := i + 1;
+  }
+  if cur > 1 {
+    factors := factors + [cur];
+    taken := taken * cur;
+  }
+  assert taken == n;
+}

README.md

@@ -27,7 +27,7 @@ Current status:
 - [ ] 22. filter_integers - ill-typed
 - [x] 23. strlen
 - [x] 24. largest_divisor
-- [ ] 25. factorize
+- [x] 25. factorize
 - [x] 26. remove_duplicates
 - [x] 27. flip_case
 - [ ] 28. concatenate

REMAINING.md

@@ -3,7 +3,6 @@
 Current status:
 
 ## Priority
-- [ ] 25. factorize
 - [ ] 147. get_max_triples
 
 ## Other