.

wcfs/internal/xbtree.py

@@ -556,6 +556,27 @@ def _iterSplitByN(lo, hi, nsplit): # -> i[] of [lo, s1, s2, ..., sn, hi)
         for tail in _iterSplitByN(s, hi, nsplit-1):
             yield [lo] + tail
 
+# _iterSplitKeyvByN is similar to _iterSplitByN but makes sure that every
+# splitted range contains at least one key from keyv.
+def _iterSplitKeyvByN(lo, hi, keyv, nsplit): # -> i[] of [lo, s1, s2, ..., sn, hi)
+    #print('_iterSplitKeyvByN [%s, %s) keyv=%r nsplit=%r' % (lo, hi, keyv, nsplit))
+    assert lo <= hi
+    assert 0 <= nsplit
+    _assertIncv(keyv)
+    assert lo <= keyv[0]
+    assert       keyv[-1] < hi
+
+    if nsplit >= len(keyv):
+        return  # no split exists
+    if nsplit == 0:
+        yield [lo, hi]
+        return
+
+    for i in range(len(keyv)-nsplit):
+        for s in range(keyv[i]+1, keyv[i+1]+1): # (ki, k_{i+1}]
+            for tail in _iterSplitKeyvByN(s, hi, keyv[i+1:], nsplit-1):
+                yield [lo] + tail
+
 
 # ---- topology encoding ----
 

wcfs/internal/xbtree_test.py

@@ -823,7 +823,6 @@ def test_iterSplitByN():
     def X(lo, hi, nsplit):
         return tuple(xbtree._iterSplitByN(lo, hi, nsplit))
 
-
     assert X(0,0, 0)    == ( [0,0], )
     assert X(0,0, 1)    == ()
     assert X(0,1, 0)    == ( [0,1], )
@@ -851,3 +850,12 @@ def test_iterSplitByN():
     assert X(0,5, 4)    == ( [0,1,2,3,4,5], )
     assert X(0,5, 5)    == ()
 
+def test_iterSplitKeyvByN():
+    keyv = [1,3,4]
+    def X(lo, hi, nsplit):
+        return tuple(xbtree._iterSplitKeyvByN(lo, hi, keyv, nsplit))
+
+    assert X(0,7, 0)    == ( [0,7], )
+    assert X(0,7, 1)    == ( [0,2,7], [0,3,7], [0,4,7] )
+    assert X(0,7, 2)    == ( [0,2,4,7], [0,3,4,7] )
+    assert X(0,7, 3)    == ()