Include partitions with no width in repartition

Previously when repartitioning a dataframe that had partitions of zero
width like the following:

    >>> df.divisions
    (1, 1, 1)

We would lose information about the earlier partitions.

Fixes dask#3911

dask/dataframe/core.py

@@ -4081,8 +4081,9 @@ def _is_single_last_div(x):
         else:
             d[(out1, k)] = (methods.boundary_slice, (name, i - 1), low, b[j], False)
             low = b[j]
+            if len(a) == i + 1 or a[i] < a[i + 1]:
+                j += 1
             i += 1
-            j += 1
         c.append(low)
         k += 1
 
@@ -4116,7 +4117,7 @@ def _is_single_last_div(x):
         while c[i] < b[j]:
             tmp.append((out1, i))
             i += 1
-        if last_elem and c[i] == b[-1] and (b[-1] != b[-2] or j == len(b) - 1) and i < k:
+        while last_elem and c[i] == b[-1] and (b[-1] != b[-2] or j == len(b) - 1) and i < k:
             # append if last split is not included
             tmp.append((out1, i))
             i += 1

dask/dataframe/tests/test_multi.py

@@ -1308,3 +1308,29 @@ def test_singleton_divisions():
     joined = ddf2.join(ddf2, rsuffix='r')
     assert joined.divisions == (1, 1)
     joined.compute()
+
+
+def test_repartition_repeated_divisions():
+    df = pd.DataFrame({'x': [0, 0, 0, 0]})
+    ddf = dd.from_pandas(df, npartitions=2).set_index('x')
+
+    ddf2 = ddf.repartition(divisions=(0, 0), force=True)
+    assert_eq(ddf2, df.set_index('x'))
+
+
+def test_multi_duplicate_divisions():
+    df1 = pd.DataFrame({'x': [0, 0, 0, 0]})
+    df2 = pd.DataFrame({'x': [0]})
+
+    ddf1 = dd.from_pandas(df1, npartitions=2).set_index('x')
+    ddf2 = dd.from_pandas(df2, npartitions=1).set_index('x')
+    assert ddf1.npartitions == 2
+    assert len(ddf1) == len(df1)
+
+    r1 = ddf1.merge(ddf2, how='left', left_index=True, right_index=True)
+
+    sf1 = df1.set_index('x')
+    sf2 = df2.set_index('x')
+    r2 = sf1.merge(sf2, how='left', left_index=True, right_index=True)
+
+    assert_eq(r1, r2)