Python code coverage for Modules/_heapqmodule.c

#	count	content
1	n/a	/* Drop in replacement for heapq.py
2	n/a
3	n/a	C implementation derived directly from heapq.py in Py2.3
4	n/a	which was written by Kevin O'Connor, augmented by Tim Peters,
5	n/a	annotated by FranÃ§ois Pinard, and converted to C by Raymond Hettinger.
6	n/a
7	n/a	*/
8	n/a
9	n/a	#include "Python.h"
10	n/a
11	n/a	static int
12	n/a	siftdown(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
13	n/a	{
14	n/a	PyObject newitem, parent, **arr;
15	n/a	Py_ssize_t parentpos, size;
16	n/a	int cmp;
17	n/a
18	n/a	assert(PyList_Check(heap));
19	n/a	size = PyList_GET_SIZE(heap);
20	n/a	if (pos >= size) {
21	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
22	n/a	return -1;
23	n/a	}
24	n/a
25	n/a	/* Follow the path to the root, moving parents down until finding
26	n/a	a place newitem fits. */
27	n/a	arr = _PyList_ITEMS(heap);
28	n/a	newitem = arr[pos];
29	n/a	while (pos > startpos) {
30	n/a	parentpos = (pos - 1) >> 1;
31	n/a	parent = arr[parentpos];
32	n/a	cmp = PyObject_RichCompareBool(newitem, parent, Py_LT);
33	n/a	if (cmp < 0)
34	n/a	return -1;
35	n/a	if (size != PyList_GET_SIZE(heap)) {
36	n/a	PyErr_SetString(PyExc_RuntimeError,
37	n/a	"list changed size during iteration");
38	n/a	return -1;
39	n/a	}
40	n/a	if (cmp == 0)
41	n/a	break;
42	n/a	arr = _PyList_ITEMS(heap);
43	n/a	parent = arr[parentpos];
44	n/a	newitem = arr[pos];
45	n/a	arr[parentpos] = newitem;
46	n/a	arr[pos] = parent;
47	n/a	pos = parentpos;
48	n/a	}
49	n/a	return 0;
50	n/a	}
51	n/a
52	n/a	static int
53	n/a	siftup(PyListObject *heap, Py_ssize_t pos)
54	n/a	{
55	n/a	Py_ssize_t startpos, endpos, childpos, limit;
56	n/a	PyObject tmp1, tmp2, **arr;
57	n/a	int cmp;
58	n/a
59	n/a	assert(PyList_Check(heap));
60	n/a	endpos = PyList_GET_SIZE(heap);
61	n/a	startpos = pos;
62	n/a	if (pos >= endpos) {
63	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
64	n/a	return -1;
65	n/a	}
66	n/a
67	n/a	/* Bubble up the smaller child until hitting a leaf. */
68	n/a	arr = _PyList_ITEMS(heap);
69	n/a	limit = endpos >> 1; /* smallest pos that has no child */
70	n/a	while (pos < limit) {
71	n/a	/* Set childpos to index of smaller child. */
72	n/a	childpos = 2pos + 1; / leftmost child position */
73	n/a	if (childpos + 1 < endpos) {
74	n/a	cmp = PyObject_RichCompareBool(
75	n/a	arr[childpos],
76	n/a	arr[childpos + 1],
77	n/a	Py_LT);
78	n/a	if (cmp < 0)
79	n/a	return -1;
80	n/a	childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
81	n/a	arr = _PyList_ITEMS(heap); /* arr may have changed */
82	n/a	if (endpos != PyList_GET_SIZE(heap)) {
83	n/a	PyErr_SetString(PyExc_RuntimeError,
84	n/a	"list changed size during iteration");
85	n/a	return -1;
86	n/a	}
87	n/a	}
88	n/a	/* Move the smaller child up. */
89	n/a	tmp1 = arr[childpos];
90	n/a	tmp2 = arr[pos];
91	n/a	arr[childpos] = tmp2;
92	n/a	arr[pos] = tmp1;
93	n/a	pos = childpos;
94	n/a	}
95	n/a	/* Bubble it up to its final resting place (by sifting its parents down). */
96	n/a	return siftdown(heap, startpos, pos);
97	n/a	}
98	n/a
99	n/a	static PyObject *
100	n/a	heappush(PyObject self, PyObject args)
101	n/a	{
102	n/a	PyObject heap, item;
103	n/a
104	n/a	if (!PyArg_UnpackTuple(args, "heappush", 2, 2, &heap, &item))
105	n/a	return NULL;
106	n/a
107	n/a	if (!PyList_Check(heap)) {
108	n/a	PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
109	n/a	return NULL;
110	n/a	}
111	n/a
112	n/a	if (PyList_Append(heap, item))
113	n/a	return NULL;
114	n/a
115	n/a	if (siftdown((PyListObject *)heap, 0, PyList_GET_SIZE(heap)-1))
116	n/a	return NULL;
117	n/a	Py_RETURN_NONE;
118	n/a	}
119	n/a
120	n/a	PyDoc_STRVAR(heappush_doc,
121	n/a	"heappush(heap, item) -> None. Push item onto heap, maintaining the heap invariant.");
122	n/a
123	n/a	static PyObject *
124	n/a	heappop_internal(PyObject heap, int siftup_func(PyListObject , Py_ssize_t))
125	n/a	{
126	n/a	PyObject lastelt, returnitem;
127	n/a	Py_ssize_t n;
128	n/a
129	n/a	if (!PyList_Check(heap)) {
130	n/a	PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
131	n/a	return NULL;
132	n/a	}
133	n/a
134	n/a	/* raises IndexError if the heap is empty */
135	n/a	n = PyList_GET_SIZE(heap);
136	n/a	if (n == 0) {
137	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
138	n/a	return NULL;
139	n/a	}
140	n/a
141	n/a	lastelt = PyList_GET_ITEM(heap, n-1) ;
142	n/a	Py_INCREF(lastelt);
143	n/a	if (PyList_SetSlice(heap, n-1, n, NULL)) {
144	n/a	Py_DECREF(lastelt);
145	n/a	return NULL;
146	n/a	}
147	n/a	n--;
148	n/a
149	n/a	if (!n)
150	n/a	return lastelt;
151	n/a	returnitem = PyList_GET_ITEM(heap, 0);
152	n/a	PyList_SET_ITEM(heap, 0, lastelt);
153	n/a	if (siftup_func((PyListObject *)heap, 0)) {
154	n/a	Py_DECREF(returnitem);
155	n/a	return NULL;
156	n/a	}
157	n/a	return returnitem;
158	n/a	}
159	n/a
160	n/a	static PyObject *
161	n/a	heappop(PyObject self, PyObject heap)
162	n/a	{
163	n/a	return heappop_internal(heap, siftup);
164	n/a	}
165	n/a
166	n/a	PyDoc_STRVAR(heappop_doc,
167	n/a	"Pop the smallest item off the heap, maintaining the heap invariant.");
168	n/a
169	n/a	static PyObject *
170	n/a	heapreplace_internal(PyObject args, int siftup_func(PyListObject , Py_ssize_t))
171	n/a	{
172	n/a	PyObject heap, item, *returnitem;
173	n/a
174	n/a	if (!PyArg_UnpackTuple(args, "heapreplace", 2, 2, &heap, &item))
175	n/a	return NULL;
176	n/a
177	n/a	if (!PyList_Check(heap)) {
178	n/a	PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
179	n/a	return NULL;
180	n/a	}
181	n/a
182	n/a	if (PyList_GET_SIZE(heap) == 0) {
183	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
184	n/a	return NULL;
185	n/a	}
186	n/a
187	n/a	returnitem = PyList_GET_ITEM(heap, 0);
188	n/a	Py_INCREF(item);
189	n/a	PyList_SET_ITEM(heap, 0, item);
190	n/a	if (siftup_func((PyListObject *)heap, 0)) {
191	n/a	Py_DECREF(returnitem);
192	n/a	return NULL;
193	n/a	}
194	n/a	return returnitem;
195	n/a	}
196	n/a
197	n/a	static PyObject *
198	n/a	heapreplace(PyObject self, PyObject args)
199	n/a	{
200	n/a	return heapreplace_internal(args, siftup);
201	n/a	}
202	n/a
203	n/a	PyDoc_STRVAR(heapreplace_doc,
204	n/a	"heapreplace(heap, item) -> value. Pop and return the current smallest value, and add the new item.\n\
205	n/a	\n\
206	n/a	This is more efficient than heappop() followed by heappush(), and can be\n\
207	n/a	more appropriate when using a fixed-size heap. Note that the value\n\
208	n/a	returned may be larger than item! That constrains reasonable uses of\n\
209	n/a	this routine unless written as part of a conditional replacement:\n\n\
210	n/a	if item > heap[0]:\n\
211	n/a	item = heapreplace(heap, item)\n");
212	n/a
213	n/a	static PyObject *
214	n/a	heappushpop(PyObject self, PyObject args)
215	n/a	{
216	n/a	PyObject heap, item, *returnitem;
217	n/a	int cmp;
218	n/a
219	n/a	if (!PyArg_UnpackTuple(args, "heappushpop", 2, 2, &heap, &item))
220	n/a	return NULL;
221	n/a
222	n/a	if (!PyList_Check(heap)) {
223	n/a	PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
224	n/a	return NULL;
225	n/a	}
226	n/a
227	n/a	if (PyList_GET_SIZE(heap) == 0) {
228	n/a	Py_INCREF(item);
229	n/a	return item;
230	n/a	}
231	n/a
232	n/a	cmp = PyObject_RichCompareBool(PyList_GET_ITEM(heap, 0), item, Py_LT);
233	n/a	if (cmp < 0)
234	n/a	return NULL;
235	n/a	if (cmp == 0) {
236	n/a	Py_INCREF(item);
237	n/a	return item;
238	n/a	}
239	n/a
240	n/a	if (PyList_GET_SIZE(heap) == 0) {
241	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
242	n/a	return NULL;
243	n/a	}
244	n/a
245	n/a	returnitem = PyList_GET_ITEM(heap, 0);
246	n/a	Py_INCREF(item);
247	n/a	PyList_SET_ITEM(heap, 0, item);
248	n/a	if (siftup((PyListObject *)heap, 0)) {
249	n/a	Py_DECREF(returnitem);
250	n/a	return NULL;
251	n/a	}
252	n/a	return returnitem;
253	n/a	}
254	n/a
255	n/a	PyDoc_STRVAR(heappushpop_doc,
256	n/a	"heappushpop(heap, item) -> value. Push item on the heap, then pop and return the smallest item\n\
257	n/a	from the heap. The combined action runs more efficiently than\n\
258	n/a	heappush() followed by a separate call to heappop().");
259	n/a
260	n/a	static Py_ssize_t
261	n/a	keep_top_bit(Py_ssize_t n)
262	n/a	{
263	n/a	int i = 0;
264	n/a
265	n/a	while (n > 1) {
266	n/a	n >>= 1;
267	n/a	i++;
268	n/a	}
269	n/a	return n << i;
270	n/a	}
271	n/a
272	n/a	/* Cache friendly version of heapify()
273	n/a	-----------------------------------
274	n/a
275	n/a	Build-up a heap in O(n) time by performing siftup() operations
276	n/a	on nodes whose children are already heaps.
277	n/a
278	n/a	The simplest way is to sift the nodes in reverse order from
279	n/a	n//2-1 to 0 inclusive. The downside is that children may be
280	n/a	out of cache by the time their parent is reached.
281	n/a
282	n/a	A better way is to not wait for the children to go out of cache.
283	n/a	Once a sibling pair of child nodes have been sifted, immediately
284	n/a	sift their parent node (while the children are still in cache).
285	n/a
286	n/a	Both ways build child heaps before their parents, so both ways
287	n/a	do the exact same number of comparisons and produce exactly
288	n/a	the same heap. The only difference is that the traversal
289	n/a	order is optimized for cache efficiency.
290	n/a	*/
291	n/a
292	n/a	static PyObject *
293	n/a	cache_friendly_heapify(PyObject heap, int siftup_func(PyListObject , Py_ssize_t))
294	n/a	{
295	n/a	Py_ssize_t i, j, m, mhalf, leftmost;
296	n/a
297	n/a	m = PyList_GET_SIZE(heap) >> 1; /* index of first childless node */
298	n/a	leftmost = keep_top_bit(m + 1) - 1; /* leftmost node in row of m */
299	n/a	mhalf = m >> 1; /* parent of first childless node */
300	n/a
301	n/a	for (i = leftmost - 1 ; i >= mhalf ; i--) {
302	n/a	j = i;
303	n/a	while (1) {
304	n/a	if (siftup_func((PyListObject *)heap, j))
305	n/a	return NULL;
306	n/a	if (!(j & 1))
307	n/a	break;
308	n/a	j >>= 1;
309	n/a	}
310	n/a	}
311	n/a
312	n/a	for (i = m - 1 ; i >= leftmost ; i--) {
313	n/a	j = i;
314	n/a	while (1) {
315	n/a	if (siftup_func((PyListObject *)heap, j))
316	n/a	return NULL;
317	n/a	if (!(j & 1))
318	n/a	break;
319	n/a	j >>= 1;
320	n/a	}
321	n/a	}
322	n/a	Py_RETURN_NONE;
323	n/a	}
324	n/a
325	n/a	static PyObject *
326	n/a	heapify_internal(PyObject heap, int siftup_func(PyListObject , Py_ssize_t))
327	n/a	{
328	n/a	Py_ssize_t i, n;
329	n/a
330	n/a	if (!PyList_Check(heap)) {
331	n/a	PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
332	n/a	return NULL;
333	n/a	}
334	n/a
335	n/a	/* For heaps likely to be bigger than L1 cache, we use the cache
336	n/a	friendly heapify function. For smaller heaps that fit entirely
337	n/a	in cache, we prefer the simpler algorithm with less branching.
338	n/a	*/
339	n/a	n = PyList_GET_SIZE(heap);
340	n/a	if (n > 2500)
341	n/a	return cache_friendly_heapify(heap, siftup_func);
342	n/a
343	n/a	/* Transform bottom-up. The largest index there's any point to
344	n/a	looking at is the largest with a child index in-range, so must
345	n/a	have 2i + 1 < n, or i < (n-1)/2. If n is even = 2j, this is
346	n/a	(2*j-1)/2 = j-1/2 so j-1 is the largest, which is n//2 - 1. If
347	n/a	n is odd = 2j+1, this is (2j+1-1)/2 = j so j-1 is the largest,
348	n/a	and that's again n//2-1.
349	n/a	*/
350	n/a	for (i = (n >> 1) - 1 ; i >= 0 ; i--)
351	n/a	if (siftup_func((PyListObject *)heap, i))
352	n/a	return NULL;
353	n/a	Py_RETURN_NONE;
354	n/a	}
355	n/a
356	n/a	static PyObject *
357	n/a	heapify(PyObject self, PyObject heap)
358	n/a	{
359	n/a	return heapify_internal(heap, siftup);
360	n/a	}
361	n/a
362	n/a	PyDoc_STRVAR(heapify_doc,
363	n/a	"Transform list into a heap, in-place, in O(len(heap)) time.");
364	n/a
365	n/a	static int
366	n/a	siftdown_max(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
367	n/a	{
368	n/a	PyObject newitem, parent, **arr;
369	n/a	Py_ssize_t parentpos, size;
370	n/a	int cmp;
371	n/a
372	n/a	assert(PyList_Check(heap));
373	n/a	size = PyList_GET_SIZE(heap);
374	n/a	if (pos >= size) {
375	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
376	n/a	return -1;
377	n/a	}
378	n/a
379	n/a	/* Follow the path to the root, moving parents down until finding
380	n/a	a place newitem fits. */
381	n/a	arr = _PyList_ITEMS(heap);
382	n/a	newitem = arr[pos];
383	n/a	while (pos > startpos) {
384	n/a	parentpos = (pos - 1) >> 1;
385	n/a	parent = arr[parentpos];
386	n/a	cmp = PyObject_RichCompareBool(parent, newitem, Py_LT);
387	n/a	if (cmp < 0)
388	n/a	return -1;
389	n/a	if (size != PyList_GET_SIZE(heap)) {
390	n/a	PyErr_SetString(PyExc_RuntimeError,
391	n/a	"list changed size during iteration");
392	n/a	return -1;
393	n/a	}
394	n/a	if (cmp == 0)
395	n/a	break;
396	n/a	arr = _PyList_ITEMS(heap);
397	n/a	parent = arr[parentpos];
398	n/a	newitem = arr[pos];
399	n/a	arr[parentpos] = newitem;
400	n/a	arr[pos] = parent;
401	n/a	pos = parentpos;
402	n/a	}
403	n/a	return 0;
404	n/a	}
405	n/a
406	n/a	static int
407	n/a	siftup_max(PyListObject *heap, Py_ssize_t pos)
408	n/a	{
409	n/a	Py_ssize_t startpos, endpos, childpos, limit;
410	n/a	PyObject tmp1, tmp2, **arr;
411	n/a	int cmp;
412	n/a
413	n/a	assert(PyList_Check(heap));
414	n/a	endpos = PyList_GET_SIZE(heap);
415	n/a	startpos = pos;
416	n/a	if (pos >= endpos) {
417	n/a	PyErr_SetString(PyExc_IndexError, "index out of range");
418	n/a	return -1;
419	n/a	}
420	n/a
421	n/a	/* Bubble up the smaller child until hitting a leaf. */
422	n/a	arr = _PyList_ITEMS(heap);
423	n/a	limit = endpos >> 1; /* smallest pos that has no child */
424	n/a	while (pos < limit) {
425	n/a	/* Set childpos to index of smaller child. */
426	n/a	childpos = 2pos + 1; / leftmost child position */
427	n/a	if (childpos + 1 < endpos) {
428	n/a	cmp = PyObject_RichCompareBool(
429	n/a	arr[childpos + 1],
430	n/a	arr[childpos],
431	n/a	Py_LT);
432	n/a	if (cmp < 0)
433	n/a	return -1;
434	n/a	childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
435	n/a	arr = _PyList_ITEMS(heap); /* arr may have changed */
436	n/a	if (endpos != PyList_GET_SIZE(heap)) {
437	n/a	PyErr_SetString(PyExc_RuntimeError,
438	n/a	"list changed size during iteration");
439	n/a	return -1;
440	n/a	}
441	n/a	}
442	n/a	/* Move the smaller child up. */
443	n/a	tmp1 = arr[childpos];
444	n/a	tmp2 = arr[pos];
445	n/a	arr[childpos] = tmp2;
446	n/a	arr[pos] = tmp1;
447	n/a	pos = childpos;
448	n/a	}
449	n/a	/* Bubble it up to its final resting place (by sifting its parents down). */
450	n/a	return siftdown_max(heap, startpos, pos);
451	n/a	}
452	n/a
453	n/a	static PyObject *
454	n/a	heappop_max(PyObject self, PyObject heap)
455	n/a	{
456	n/a	return heappop_internal(heap, siftup_max);
457	n/a	}
458	n/a
459	n/a	PyDoc_STRVAR(heappop_max_doc, "Maxheap variant of heappop.");
460	n/a
461	n/a	static PyObject *
462	n/a	heapreplace_max(PyObject self, PyObject args)
463	n/a	{
464	n/a	return heapreplace_internal(args, siftup_max);
465	n/a	}
466	n/a
467	n/a	PyDoc_STRVAR(heapreplace_max_doc, "Maxheap variant of heapreplace");
468	n/a
469	n/a	static PyObject *
470	n/a	heapify_max(PyObject self, PyObject heap)
471	n/a	{
472	n/a	return heapify_internal(heap, siftup_max);
473	n/a	}
474	n/a
475	n/a	PyDoc_STRVAR(heapify_max_doc, "Maxheap variant of heapify.");
476	n/a
477	n/a	static PyMethodDef heapq_methods[] = {
478	n/a	{"heappush", (PyCFunction)heappush,
479	n/a	METH_VARARGS, heappush_doc},
480	n/a	{"heappushpop", (PyCFunction)heappushpop,
481	n/a	METH_VARARGS, heappushpop_doc},
482	n/a	{"heappop", (PyCFunction)heappop,
483	n/a	METH_O, heappop_doc},
484	n/a	{"heapreplace", (PyCFunction)heapreplace,
485	n/a	METH_VARARGS, heapreplace_doc},
486	n/a	{"heapify", (PyCFunction)heapify,
487	n/a	METH_O, heapify_doc},
488	n/a	{"_heappop_max", (PyCFunction)heappop_max,
489	n/a	METH_O, heappop_max_doc},
490	n/a	{"_heapreplace_max",(PyCFunction)heapreplace_max,
491	n/a	METH_VARARGS, heapreplace_max_doc},
492	n/a	{"_heapify_max", (PyCFunction)heapify_max,
493	n/a	METH_O, heapify_max_doc},
494	n/a	{NULL, NULL} /* sentinel */
495	n/a	};
496	n/a
497	n/a	PyDoc_STRVAR(module_doc,
498	n/a	"Heap queue algorithm (a.k.a. priority queue).\n\
499	n/a	\n\
500	n/a	Heaps are arrays for which a[k] <= a[2k+1] and a[k] <= a[2k+2] for\n\
501	n/a	all k, counting elements from 0. For the sake of comparison,\n\
502	n/a	non-existing elements are considered to be infinite. The interesting\n\
503	n/a	property of a heap is that a[0] is always its smallest element.\n\
504	n/a	\n\
505	n/a	Usage:\n\
506	n/a	\n\
507	n/a	heap = [] # creates an empty heap\n\
508	n/a	heappush(heap, item) # pushes a new item on the heap\n\
509	n/a	item = heappop(heap) # pops the smallest item from the heap\n\
510	n/a	item = heap[0] # smallest item on the heap without popping it\n\
511	n/a	heapify(x) # transforms list into a heap, in-place, in linear time\n\
512	n/a	item = heapreplace(heap, item) # pops and returns smallest item, and adds\n\
513	n/a	# new item; the heap size is unchanged\n\
514	n/a	\n\
515	n/a	Our API differs from textbook heap algorithms as follows:\n\
516	n/a	\n\
517	n/a	- We use 0-based indexing. This makes the relationship between the\n\
518	n/a	index for a node and the indexes for its children slightly less\n\
519	n/a	obvious, but is more suitable since Python uses 0-based indexing.\n\
520	n/a	\n\
521	n/a	- Our heappop() method returns the smallest item, not the largest.\n\
522	n/a	\n\
523	n/a	These two make it possible to view the heap as a regular Python list\n\
524	n/a	without surprises: heap[0] is the smallest item, and heap.sort()\n\
525	n/a	maintains the heap invariant!\n");
526	n/a
527	n/a
528	n/a	PyDoc_STRVAR(__about__,
529	n/a	"Heap queues\n\
530	n/a	\n\
531	n/a	[explanation by Fran\xc3\xa7ois Pinard]\n\
532	n/a	\n\
533	n/a	Heaps are arrays for which a[k] <= a[2k+1] and a[k] <= a[2k+2] for\n\
534	n/a	all k, counting elements from 0. For the sake of comparison,\n\
535	n/a	non-existing elements are considered to be infinite. The interesting\n\
536	n/a	property of a heap is that a[0] is always its smallest element.\n"
537	n/a	"\n\
538	n/a	The strange invariant above is meant to be an efficient memory\n\
539	n/a	representation for a tournament. The numbers below are `k', not a[k]:\n\
540	n/a	\n\
541	n/a	0\n\
542	n/a	\n\
543	n/a	1 2\n\
544	n/a	\n\
545	n/a	3 4 5 6\n\
546	n/a	\n\
547	n/a	7 8 9 10 11 12 13 14\n\
548	n/a	\n\
549	n/a	15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n\
550	n/a	\n\
551	n/a	\n\
552	n/a	In the tree above, each cell `k' is topping `2k+1' and `2k+2'. In\n\
553	n/a	a usual binary tournament we see in sports, each cell is the winner\n\
554	n/a	over the two cells it tops, and we can trace the winner down the tree\n\
555	n/a	to see all opponents s/he had. However, in many computer applications\n\
556	n/a	of such tournaments, we do not need to trace the history of a winner.\n\
557	n/a	To be more memory efficient, when a winner is promoted, we try to\n\
558	n/a	replace it by something else at a lower level, and the rule becomes\n\
559	n/a	that a cell and the two cells it tops contain three different items,\n\
560	n/a	but the top cell \"wins\" over the two topped cells.\n"
561	n/a	"\n\
562	n/a	If this heap invariant is protected at all time, index 0 is clearly\n\
563	n/a	the overall winner. The simplest algorithmic way to remove it and\n\
564	n/a	find the \"next\" winner is to move some loser (let's say cell 30 in the\n\
565	n/a	diagram above) into the 0 position, and then percolate this new 0 down\n\
566	n/a	the tree, exchanging values, until the invariant is re-established.\n\
567	n/a	This is clearly logarithmic on the total number of items in the tree.\n\
568	n/a	By iterating over all items, you get an O(n ln n) sort.\n"
569	n/a	"\n\
570	n/a	A nice feature of this sort is that you can efficiently insert new\n\
571	n/a	items while the sort is going on, provided that the inserted items are\n\
572	n/a	not \"better\" than the last 0'th element you extracted. This is\n\
573	n/a	especially useful in simulation contexts, where the tree holds all\n\
574	n/a	incoming events, and the \"win\" condition means the smallest scheduled\n\
575	n/a	time. When an event schedule other events for execution, they are\n\
576	n/a	scheduled into the future, so they can easily go into the heap. So, a\n\
577	n/a	heap is a good structure for implementing schedulers (this is what I\n\
578	n/a	used for my MIDI sequencer :-).\n"
579	n/a	"\n\
580	n/a	Various structures for implementing schedulers have been extensively\n\
581	n/a	studied, and heaps are good for this, as they are reasonably speedy,\n\
582	n/a	the speed is almost constant, and the worst case is not much different\n\
583	n/a	than the average case. However, there are other representations which\n\
584	n/a	are more efficient overall, yet the worst cases might be terrible.\n"
585	n/a	"\n\
586	n/a	Heaps are also very useful in big disk sorts. You most probably all\n\
587	n/a	know that a big sort implies producing \"runs\" (which are pre-sorted\n\
588	n/a	sequences, which size is usually related to the amount of CPU memory),\n\
589	n/a	followed by a merging passes for these runs, which merging is often\n\
590	n/a	very cleverly organised[1]. It is very important that the initial\n\
591	n/a	sort produces the longest runs possible. Tournaments are a good way\n\
592	n/a	to that. If, using all the memory available to hold a tournament, you\n\
593	n/a	replace and percolate items that happen to fit the current run, you'll\n\
594	n/a	produce runs which are twice the size of the memory for random input,\n\
595	n/a	and much better for input fuzzily ordered.\n"
596	n/a	"\n\
597	n/a	Moreover, if you output the 0'th item on disk and get an input which\n\
598	n/a	may not fit in the current tournament (because the value \"wins\" over\n\
599	n/a	the last output value), it cannot fit in the heap, so the size of the\n\
600	n/a	heap decreases. The freed memory could be cleverly reused immediately\n\
601	n/a	for progressively building a second heap, which grows at exactly the\n\
602	n/a	same rate the first heap is melting. When the first heap completely\n\
603	n/a	vanishes, you switch heaps and start a new run. Clever and quite\n\
604	n/a	effective!\n\
605	n/a	\n\
606	n/a	In a word, heaps are useful memory structures to know. I use them in\n\
607	n/a	a few applications, and I think it is good to keep a `heap' module\n\
608	n/a	around. :-)\n"
609	n/a	"\n\
610	n/a	--------------------\n\
611	n/a	[1] The disk balancing algorithms which are current, nowadays, are\n\
612	n/a	more annoying than clever, and this is a consequence of the seeking\n\
613	n/a	capabilities of the disks. On devices which cannot seek, like big\n\
614	n/a	tape drives, the story was quite different, and one had to be very\n\
615	n/a	clever to ensure (far in advance) that each tape movement will be the\n\
616	n/a	most effective possible (that is, will best participate at\n\
617	n/a	\"progressing\" the merge). Some tapes were even able to read\n\
618	n/a	backwards, and this was also used to avoid the rewinding time.\n\
619	n/a	Believe me, real good tape sorts were quite spectacular to watch!\n\
620	n/a	From all times, sorting has always been a Great Art! :-)\n");
621	n/a
622	n/a
623	n/a	static struct PyModuleDef _heapqmodule = {
624	n/a	PyModuleDef_HEAD_INIT,
625	n/a	"_heapq",
626	n/a	module_doc,
627	n/a	-1,
628	n/a	heapq_methods,
629	n/a	NULL,
630	n/a	NULL,
631	n/a	NULL,
632	n/a	NULL
633	n/a	};
634	n/a
635	n/a	PyMODINIT_FUNC
636	n/a	PyInit__heapq(void)
637	n/a	{
638	n/a	PyObject m, about;
639	n/a
640	n/a	m = PyModule_Create(&_heapqmodule);
641	n/a	if (m == NULL)
642	n/a	return NULL;
643	n/a	about = PyUnicode_DecodeUTF8(__about__, strlen(__about__), NULL);
644	n/a	PyModule_AddObject(m, "__about__", about);
645	n/a	return m;
646	n/a	}
647	n/a