Add itertools.combinations().

Doc/library/itertools.rst

@@ -97,21 +97,21 @@ loops that truncate the stream.
 
         def combinations(iterable, r):
             pool = tuple(iterable)
-            if pool:
-                n = len(pool)
-                vec = range(r)
-                yield tuple(pool[i] for i in vec)
-                while 1:
-                    for i in reversed(range(r)):
-                        if vec[i] == i + n-r:
-                            continue
-                        vec[i] += 1
-                        for j in range(i+1, r):
-                            vec[j] = vec[j-1] + 1
-                        yield tuple(pool[i] for i in vec)
-                        break
-                    else:
-                        return
+            n = len(pool)
+            assert 0 <= r <= n
+            vec = range(r)
+            yield tuple(pool[i] for i in vec)
+            while 1:
+                for i in reversed(range(r)):
+                    if vec[i] == i + n-r:
+                        continue
+                    vec[i] += 1
+                    for j in range(i+1, r):
+                        vec[j] = vec[j-1] + 1
+                    yield tuple(pool[i] for i in vec)
+                    break
+                else:
+                    return
 
    .. versionadded:: 2.6
 

Lib/test/test_itertools.py

@@ -40,6 +40,10 @@ def take(n, seq):
     'Convenience function for partially consuming a long of infinite iterable'
     return list(islice(seq, n))
 
+def fact(n):
+    'Factorial'
+    return reduce(operator.mul, range(1, n+1), 1)
+
 class TestBasicOps(unittest.TestCase):
     def test_chain(self):
         self.assertEqual(list(chain('abc', 'def')), list('abcdef'))
@@ -48,6 +52,26 @@ class TestBasicOps(unittest.TestCase):
         self.assertEqual(take(4, chain('abc', 'def')), list('abcd'))
         self.assertRaises(TypeError, chain, 2, 3)
 
+    def test_combinations(self):
+        self.assertRaises(TypeError, combinations, 'abc')   # missing r argument
+        self.assertRaises(TypeError, combinations, 'abc', 2, 1) # too many arguments
+        self.assertRaises(ValueError, combinations, 'abc', -2)  # r is negative
+        self.assertRaises(ValueError, combinations, 'abc', 32)  # r is too big
+        self.assertEqual(list(combinations(range(4), 3)),
+                                           [(0,1,2), (0,1,3), (0,2,3), (1,2,3)])
+        for n in range(6):
+            values = [5*x-12 for x in range(n)]
+            for r in range(n+1):
+                result = list(combinations(values, r))
+                self.assertEqual(len(result), fact(n) / fact(r) / fact(n-r)) # right number of combs
+                self.assertEqual(len(result), len(set(result)))         # no repeats
+                self.assertEqual(result, sorted(result))                # lexicographic order
+                for c in result:
+                    self.assertEqual(len(c), r)                         # r-length combinations
+                    self.assertEqual(len(set(c)), r)                    # no duplicate elements
+                    self.assertEqual(list(c), sorted(c))                # keep original ordering
+                    self.assert_(all(e in values for e in c))           # elements taken from input iterable
+
     def test_count(self):
         self.assertEqual(zip('abc',count()), [('a', 0), ('b', 1), ('c', 2)])
         self.assertEqual(zip('abc',count(3)), [('a', 3), ('b', 4), ('c', 5)])

Misc/NEWS

@@ -670,6 +670,8 @@ Library
 - Added itertools.product() which forms the Cartesian product of
   the input iterables.
 
+- Added itertools.combinations().
+
 - Patch #1541463: optimize performance of cgi.FieldStorage operations.
 
 - Decimal is fully updated to the latest Decimal Specification (v1.66).

Modules/itertoolsmodule.c

@@ -1982,6 +1982,229 @@ static PyTypeObject product_type = {
 };
 
 
+/* combinations object ************************************************************/
+
+typedef struct {
+	PyObject_HEAD
+	PyObject *pool;			/* input converted to a tuple */
+	Py_ssize_t *indices;            /* one index per result element */
+	PyObject *result;               /* most recently returned result tuple */
+	Py_ssize_t r;			/* size of result tuple */
+	int stopped;			/* set to 1 when the combinations iterator is exhausted */
+} combinationsobject;
+
+static PyTypeObject combinations_type;
+
+static PyObject *
+combinations_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+	combinationsobject *co;
+	Py_ssize_t n;
+	Py_ssize_t r;
+	PyObject *pool = NULL;
+	PyObject *iterable = NULL;
+	Py_ssize_t *indices = NULL;
+	Py_ssize_t i;
+	static char *kwargs[] = {"iterable", "r", NULL};
+ 
+ 	if (!PyArg_ParseTupleAndKeywords(args, kwds, "On:combinations", kwargs, 
+					 &iterable, &r))
+		return NULL;
+
+	pool = PySequence_Tuple(iterable);
+	if (pool == NULL)
+		goto error;
+	n = PyTuple_GET_SIZE(pool);
+	if (r < 0) {
+		PyErr_SetString(PyExc_ValueError, "r must be non-negative");
+		goto error;
+	}
+	if (r > n) {
+		PyErr_SetString(PyExc_ValueError, "r cannot be bigger than the iterable");
+		goto error;
+	}
+
+	indices = PyMem_Malloc(r * sizeof(Py_ssize_t));
+	if (indices == NULL) {
+    		PyErr_NoMemory();
+		goto error;
+	}
+
+	for (i=0 ; i<r ; i++)
+		indices[i] = i;
+
+	/* create combinationsobject structure */
+	co = (combinationsobject *)type->tp_alloc(type, 0);
+	if (co == NULL)
+		goto error;
+
+	co->pool = pool;
+	co->indices = indices;
+	co->result = NULL;
+	co->r = r;
+	co->stopped = 0;
+
+	return (PyObject *)co;
+
+error:
+	if (indices != NULL)
+		PyMem_Free(indices);
+	Py_XDECREF(pool);
+	return NULL;
+}
+
+static void
+combinations_dealloc(combinationsobject *co)
+{
+	PyObject_GC_UnTrack(co);
+	Py_XDECREF(co->pool);
+	Py_XDECREF(co->result);
+	PyMem_Free(co->indices);
+	Py_TYPE(co)->tp_free(co);
+}
+
+static int
+combinations_traverse(combinationsobject *co, visitproc visit, void *arg)
+{
+	Py_VISIT(co->pool);
+	Py_VISIT(co->result);
+	return 0;
+}
+
+static PyObject *
+combinations_next(combinationsobject *co)
+{
+	PyObject *elem;
+	PyObject *oldelem;
+	PyObject *pool = co->pool;
+	Py_ssize_t *indices = co->indices;
+	PyObject *result = co->result;
+	Py_ssize_t n = PyTuple_GET_SIZE(pool);
+	Py_ssize_t r = co->r;
+	Py_ssize_t i, j, index;
+
+	if (co->stopped)
+		return NULL;
+
+	if (result == NULL) {
+                /* On the first pass, initialize result tuple using the indices */
+		result = PyTuple_New(r);
+		if (result == NULL)
+            		goto empty;
+		co->result = result;
+		for (i=0; i<r ; i++) {
+			index = indices[i];
+    			elem = PyTuple_GET_ITEM(pool, index);
+    			Py_INCREF(elem);
+    			PyTuple_SET_ITEM(result, i, elem);
+		}
+	} else {
+		/* Copy the previous result tuple or re-use it if available */
+		if (Py_REFCNT(result) > 1) {
+			PyObject *old_result = result;
+			result = PyTuple_New(r);
+			if (result == NULL)
+				goto empty;
+			co->result = result;
+			for (i=0; i<r ; i++) {
+				elem = PyTuple_GET_ITEM(old_result, i);
+    				Py_INCREF(elem);
+    				PyTuple_SET_ITEM(result, i, elem);
+			}
+			Py_DECREF(old_result);
+		}
+		/* Now, we've got the only copy so we can update it in-place */
+		assert (Py_REFCNT(result) == 1);
+
+                /* Scan indices right-to-left until finding one that is not
+                   at its maximum (i + n - r). */
+		for (i=r-1 ; i >= 0 && indices[i] == i+n-r ; i--)
+			;
+
+		/* If i is negative, then the indices are all at
+                   their maximum value and we're done. */
+		if (i < 0)
+			goto empty;
+
+		/* Increment the current index which we know is not at its
+                   maximum.  Then move back to the right setting each index
+                   to its lowest possible value (one higher than the index
+                   to its left -- this maintains the sort order invariant). */
+		indices[i]++;
+		for (j=i+1 ; j<r ; j++)
+			indices[j] = indices[j-1] + 1;
+
+		/* Update the result tuple for the new indices
+		   starting with i, the leftmost index that changed */
+		for ( ; i<r ; i++) {
+			index = indices[i];
+			elem = PyTuple_GET_ITEM(pool, index);
+			Py_INCREF(elem);
+			oldelem = PyTuple_GET_ITEM(result, i);
+			PyTuple_SET_ITEM(result, i, elem);
+			Py_DECREF(oldelem);
+		}
+	}
+
+	Py_INCREF(result);
+	return result;
+
+empty:
+	co->stopped = 1;
+	return NULL;
+}
+
+PyDoc_STRVAR(combinations_doc,
+"combinations(iterables) --> combinations object\n\
+\n\
+Return successive r-length combinations of elements in the iterable.\n\n\
+combinations(range(4), 3) --> (0,1,2), (0,1,3), (0,2,3), (1,2,3)");
+
+static PyTypeObject combinations_type = {
+	PyVarObject_HEAD_INIT(NULL, 0)
+	"itertools.combinations",		/* tp_name */
+	sizeof(combinationsobject),	/* tp_basicsize */
+	0,				/* tp_itemsize */
+	/* methods */
+	(destructor)combinations_dealloc,	/* tp_dealloc */
+	0,				/* tp_print */
+	0,				/* tp_getattr */
+	0,				/* tp_setattr */
+	0,				/* tp_compare */
+	0,				/* tp_repr */
+	0,				/* tp_as_number */
+	0,				/* tp_as_sequence */
+	0,				/* tp_as_mapping */
+	0,				/* tp_hash */
+	0,				/* tp_call */
+	0,				/* tp_str */
+	PyObject_GenericGetAttr,	/* tp_getattro */
+	0,				/* tp_setattro */
+	0,				/* tp_as_buffer */
+	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC |
+		Py_TPFLAGS_BASETYPE,	/* tp_flags */
+	combinations_doc,			/* tp_doc */
+	(traverseproc)combinations_traverse,	/* tp_traverse */
+	0,				/* tp_clear */
+	0,				/* tp_richcompare */
+	0,				/* tp_weaklistoffset */
+	PyObject_SelfIter,		/* tp_iter */
+	(iternextfunc)combinations_next,	/* tp_iternext */
+	0,				/* tp_methods */
+	0,				/* tp_members */
+	0,				/* tp_getset */
+	0,				/* tp_base */
+	0,				/* tp_dict */
+	0,				/* tp_descr_get */
+	0,				/* tp_descr_set */
+	0,				/* tp_dictoffset */
+	0,				/* tp_init */
+	0,				/* tp_alloc */
+	combinations_new,			/* tp_new */
+	PyObject_GC_Del,		/* tp_free */
+};
+
+
 /* ifilter object ************************************************************/
 
 typedef struct {
@@ -3026,6 +3249,7 @@ inititertools(void)
 	PyObject *m;
 	char *name;
 	PyTypeObject *typelist[] = {
+		&combinations_type,
 		&cycle_type,
 		&dropwhile_type,
 		&takewhile_type,
@@ -3038,7 +3262,7 @@ inititertools(void)
 		&count_type,
 		&izip_type,
 		&iziplongest_type,
-		&product_type,          
+		&product_type,         
 		&repeat_type,
 		&groupby_type,
 		NULL