/Modules/_heapqmodule.c
C | 647 lines | 528 code | 69 blank | 50 comment | 66 complexity | bfb9467ec2ac93622c8490c6325520f2 MD5 | raw file
Possible License(s): Unlicense, 0BSD, BSD-3-Clause
- /* Drop in replacement for heapq.py
- C implementation derived directly from heapq.py in Py2.3
- which was written by Kevin O'Connor, augmented by Tim Peters,
- annotated by Franรงois Pinard, and converted to C by Raymond Hettinger.
- */
- #include "Python.h"
- static int
- siftdown(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
- {
- PyObject *newitem, *parent, **arr;
- Py_ssize_t parentpos, size;
- int cmp;
- assert(PyList_Check(heap));
- size = PyList_GET_SIZE(heap);
- if (pos >= size) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return -1;
- }
- /* Follow the path to the root, moving parents down until finding
- a place newitem fits. */
- arr = _PyList_ITEMS(heap);
- newitem = arr[pos];
- while (pos > startpos) {
- parentpos = (pos - 1) >> 1;
- parent = arr[parentpos];
- cmp = PyObject_RichCompareBool(newitem, parent, Py_LT);
- if (cmp < 0)
- return -1;
- if (size != PyList_GET_SIZE(heap)) {
- PyErr_SetString(PyExc_RuntimeError,
- "list changed size during iteration");
- return -1;
- }
- if (cmp == 0)
- break;
- arr = _PyList_ITEMS(heap);
- parent = arr[parentpos];
- newitem = arr[pos];
- arr[parentpos] = newitem;
- arr[pos] = parent;
- pos = parentpos;
- }
- return 0;
- }
- static int
- siftup(PyListObject *heap, Py_ssize_t pos)
- {
- Py_ssize_t startpos, endpos, childpos, limit;
- PyObject *tmp1, *tmp2, **arr;
- int cmp;
- assert(PyList_Check(heap));
- endpos = PyList_GET_SIZE(heap);
- startpos = pos;
- if (pos >= endpos) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return -1;
- }
- /* Bubble up the smaller child until hitting a leaf. */
- arr = _PyList_ITEMS(heap);
- limit = endpos >> 1; /* smallest pos that has no child */
- while (pos < limit) {
- /* Set childpos to index of smaller child. */
- childpos = 2*pos + 1; /* leftmost child position */
- if (childpos + 1 < endpos) {
- cmp = PyObject_RichCompareBool(
- arr[childpos],
- arr[childpos + 1],
- Py_LT);
- if (cmp < 0)
- return -1;
- childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
- arr = _PyList_ITEMS(heap); /* arr may have changed */
- if (endpos != PyList_GET_SIZE(heap)) {
- PyErr_SetString(PyExc_RuntimeError,
- "list changed size during iteration");
- return -1;
- }
- }
- /* Move the smaller child up. */
- tmp1 = arr[childpos];
- tmp2 = arr[pos];
- arr[childpos] = tmp2;
- arr[pos] = tmp1;
- pos = childpos;
- }
- /* Bubble it up to its final resting place (by sifting its parents down). */
- return siftdown(heap, startpos, pos);
- }
- static PyObject *
- heappush(PyObject *self, PyObject *args)
- {
- PyObject *heap, *item;
- if (!PyArg_UnpackTuple(args, "heappush", 2, 2, &heap, &item))
- return NULL;
- if (!PyList_Check(heap)) {
- PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
- return NULL;
- }
- if (PyList_Append(heap, item))
- return NULL;
- if (siftdown((PyListObject *)heap, 0, PyList_GET_SIZE(heap)-1))
- return NULL;
- Py_RETURN_NONE;
- }
- PyDoc_STRVAR(heappush_doc,
- "heappush(heap, item) -> None. Push item onto heap, maintaining the heap invariant.");
- static PyObject *
- heappop_internal(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
- {
- PyObject *lastelt, *returnitem;
- Py_ssize_t n;
- if (!PyList_Check(heap)) {
- PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
- return NULL;
- }
- /* raises IndexError if the heap is empty */
- n = PyList_GET_SIZE(heap);
- if (n == 0) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return NULL;
- }
- lastelt = PyList_GET_ITEM(heap, n-1) ;
- Py_INCREF(lastelt);
- if (PyList_SetSlice(heap, n-1, n, NULL)) {
- Py_DECREF(lastelt);
- return NULL;
- }
- n--;
- if (!n)
- return lastelt;
- returnitem = PyList_GET_ITEM(heap, 0);
- PyList_SET_ITEM(heap, 0, lastelt);
- if (siftup_func((PyListObject *)heap, 0)) {
- Py_DECREF(returnitem);
- return NULL;
- }
- return returnitem;
- }
- static PyObject *
- heappop(PyObject *self, PyObject *heap)
- {
- return heappop_internal(heap, siftup);
- }
- PyDoc_STRVAR(heappop_doc,
- "Pop the smallest item off the heap, maintaining the heap invariant.");
- static PyObject *
- heapreplace_internal(PyObject *args, int siftup_func(PyListObject *, Py_ssize_t))
- {
- PyObject *heap, *item, *returnitem;
- if (!PyArg_UnpackTuple(args, "heapreplace", 2, 2, &heap, &item))
- return NULL;
- if (!PyList_Check(heap)) {
- PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
- return NULL;
- }
- if (PyList_GET_SIZE(heap) == 0) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return NULL;
- }
- returnitem = PyList_GET_ITEM(heap, 0);
- Py_INCREF(item);
- PyList_SET_ITEM(heap, 0, item);
- if (siftup_func((PyListObject *)heap, 0)) {
- Py_DECREF(returnitem);
- return NULL;
- }
- return returnitem;
- }
- static PyObject *
- heapreplace(PyObject *self, PyObject *args)
- {
- return heapreplace_internal(args, siftup);
- }
- PyDoc_STRVAR(heapreplace_doc,
- "heapreplace(heap, item) -> value. Pop and return the current smallest value, and add the new item.\n\
- \n\
- This is more efficient than heappop() followed by heappush(), and can be\n\
- more appropriate when using a fixed-size heap. Note that the value\n\
- returned may be larger than item! That constrains reasonable uses of\n\
- this routine unless written as part of a conditional replacement:\n\n\
- if item > heap[0]:\n\
- item = heapreplace(heap, item)\n");
- static PyObject *
- heappushpop(PyObject *self, PyObject *args)
- {
- PyObject *heap, *item, *returnitem;
- int cmp;
- if (!PyArg_UnpackTuple(args, "heappushpop", 2, 2, &heap, &item))
- return NULL;
- if (!PyList_Check(heap)) {
- PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
- return NULL;
- }
- if (PyList_GET_SIZE(heap) == 0) {
- Py_INCREF(item);
- return item;
- }
- cmp = PyObject_RichCompareBool(PyList_GET_ITEM(heap, 0), item, Py_LT);
- if (cmp < 0)
- return NULL;
- if (cmp == 0) {
- Py_INCREF(item);
- return item;
- }
- if (PyList_GET_SIZE(heap) == 0) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return NULL;
- }
- returnitem = PyList_GET_ITEM(heap, 0);
- Py_INCREF(item);
- PyList_SET_ITEM(heap, 0, item);
- if (siftup((PyListObject *)heap, 0)) {
- Py_DECREF(returnitem);
- return NULL;
- }
- return returnitem;
- }
- PyDoc_STRVAR(heappushpop_doc,
- "heappushpop(heap, item) -> value. Push item on the heap, then pop and return the smallest item\n\
- from the heap. The combined action runs more efficiently than\n\
- heappush() followed by a separate call to heappop().");
- static Py_ssize_t
- keep_top_bit(Py_ssize_t n)
- {
- int i = 0;
- while (n > 1) {
- n >>= 1;
- i++;
- }
- return n << i;
- }
- /* Cache friendly version of heapify()
- -----------------------------------
- Build-up a heap in O(n) time by performing siftup() operations
- on nodes whose children are already heaps.
- The simplest way is to sift the nodes in reverse order from
- n//2-1 to 0 inclusive. The downside is that children may be
- out of cache by the time their parent is reached.
- A better way is to not wait for the children to go out of cache.
- Once a sibling pair of child nodes have been sifted, immediately
- sift their parent node (while the children are still in cache).
- Both ways build child heaps before their parents, so both ways
- do the exact same number of comparisons and produce exactly
- the same heap. The only difference is that the traversal
- order is optimized for cache efficiency.
- */
- static PyObject *
- cache_friendly_heapify(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
- {
- Py_ssize_t i, j, m, mhalf, leftmost;
- m = PyList_GET_SIZE(heap) >> 1; /* index of first childless node */
- leftmost = keep_top_bit(m + 1) - 1; /* leftmost node in row of m */
- mhalf = m >> 1; /* parent of first childless node */
- for (i = leftmost - 1 ; i >= mhalf ; i--) {
- j = i;
- while (1) {
- if (siftup_func((PyListObject *)heap, j))
- return NULL;
- if (!(j & 1))
- break;
- j >>= 1;
- }
- }
- for (i = m - 1 ; i >= leftmost ; i--) {
- j = i;
- while (1) {
- if (siftup_func((PyListObject *)heap, j))
- return NULL;
- if (!(j & 1))
- break;
- j >>= 1;
- }
- }
- Py_RETURN_NONE;
- }
- static PyObject *
- heapify_internal(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
- {
- Py_ssize_t i, n;
- if (!PyList_Check(heap)) {
- PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
- return NULL;
- }
- /* For heaps likely to be bigger than L1 cache, we use the cache
- friendly heapify function. For smaller heaps that fit entirely
- in cache, we prefer the simpler algorithm with less branching.
- */
- n = PyList_GET_SIZE(heap);
- if (n > 2500)
- return cache_friendly_heapify(heap, siftup_func);
- /* Transform bottom-up. The largest index there's any point to
- looking at is the largest with a child index in-range, so must
- have 2*i + 1 < n, or i < (n-1)/2. If n is even = 2*j, this is
- (2*j-1)/2 = j-1/2 so j-1 is the largest, which is n//2 - 1. If
- n is odd = 2*j+1, this is (2*j+1-1)/2 = j so j-1 is the largest,
- and that's again n//2-1.
- */
- for (i = (n >> 1) - 1 ; i >= 0 ; i--)
- if (siftup_func((PyListObject *)heap, i))
- return NULL;
- Py_RETURN_NONE;
- }
- static PyObject *
- heapify(PyObject *self, PyObject *heap)
- {
- return heapify_internal(heap, siftup);
- }
- PyDoc_STRVAR(heapify_doc,
- "Transform list into a heap, in-place, in O(len(heap)) time.");
- static int
- siftdown_max(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
- {
- PyObject *newitem, *parent, **arr;
- Py_ssize_t parentpos, size;
- int cmp;
- assert(PyList_Check(heap));
- size = PyList_GET_SIZE(heap);
- if (pos >= size) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return -1;
- }
- /* Follow the path to the root, moving parents down until finding
- a place newitem fits. */
- arr = _PyList_ITEMS(heap);
- newitem = arr[pos];
- while (pos > startpos) {
- parentpos = (pos - 1) >> 1;
- parent = arr[parentpos];
- cmp = PyObject_RichCompareBool(parent, newitem, Py_LT);
- if (cmp < 0)
- return -1;
- if (size != PyList_GET_SIZE(heap)) {
- PyErr_SetString(PyExc_RuntimeError,
- "list changed size during iteration");
- return -1;
- }
- if (cmp == 0)
- break;
- arr = _PyList_ITEMS(heap);
- parent = arr[parentpos];
- newitem = arr[pos];
- arr[parentpos] = newitem;
- arr[pos] = parent;
- pos = parentpos;
- }
- return 0;
- }
- static int
- siftup_max(PyListObject *heap, Py_ssize_t pos)
- {
- Py_ssize_t startpos, endpos, childpos, limit;
- PyObject *tmp1, *tmp2, **arr;
- int cmp;
- assert(PyList_Check(heap));
- endpos = PyList_GET_SIZE(heap);
- startpos = pos;
- if (pos >= endpos) {
- PyErr_SetString(PyExc_IndexError, "index out of range");
- return -1;
- }
- /* Bubble up the smaller child until hitting a leaf. */
- arr = _PyList_ITEMS(heap);
- limit = endpos >> 1; /* smallest pos that has no child */
- while (pos < limit) {
- /* Set childpos to index of smaller child. */
- childpos = 2*pos + 1; /* leftmost child position */
- if (childpos + 1 < endpos) {
- cmp = PyObject_RichCompareBool(
- arr[childpos + 1],
- arr[childpos],
- Py_LT);
- if (cmp < 0)
- return -1;
- childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
- arr = _PyList_ITEMS(heap); /* arr may have changed */
- if (endpos != PyList_GET_SIZE(heap)) {
- PyErr_SetString(PyExc_RuntimeError,
- "list changed size during iteration");
- return -1;
- }
- }
- /* Move the smaller child up. */
- tmp1 = arr[childpos];
- tmp2 = arr[pos];
- arr[childpos] = tmp2;
- arr[pos] = tmp1;
- pos = childpos;
- }
- /* Bubble it up to its final resting place (by sifting its parents down). */
- return siftdown_max(heap, startpos, pos);
- }
- static PyObject *
- heappop_max(PyObject *self, PyObject *heap)
- {
- return heappop_internal(heap, siftup_max);
- }
- PyDoc_STRVAR(heappop_max_doc, "Maxheap variant of heappop.");
- static PyObject *
- heapreplace_max(PyObject *self, PyObject *args)
- {
- return heapreplace_internal(args, siftup_max);
- }
- PyDoc_STRVAR(heapreplace_max_doc, "Maxheap variant of heapreplace");
- static PyObject *
- heapify_max(PyObject *self, PyObject *heap)
- {
- return heapify_internal(heap, siftup_max);
- }
- PyDoc_STRVAR(heapify_max_doc, "Maxheap variant of heapify.");
- static PyMethodDef heapq_methods[] = {
- {"heappush", (PyCFunction)heappush,
- METH_VARARGS, heappush_doc},
- {"heappushpop", (PyCFunction)heappushpop,
- METH_VARARGS, heappushpop_doc},
- {"heappop", (PyCFunction)heappop,
- METH_O, heappop_doc},
- {"heapreplace", (PyCFunction)heapreplace,
- METH_VARARGS, heapreplace_doc},
- {"heapify", (PyCFunction)heapify,
- METH_O, heapify_doc},
- {"_heappop_max", (PyCFunction)heappop_max,
- METH_O, heappop_max_doc},
- {"_heapreplace_max",(PyCFunction)heapreplace_max,
- METH_VARARGS, heapreplace_max_doc},
- {"_heapify_max", (PyCFunction)heapify_max,
- METH_O, heapify_max_doc},
- {NULL, NULL} /* sentinel */
- };
- PyDoc_STRVAR(module_doc,
- "Heap queue algorithm (a.k.a. priority queue).\n\
- \n\
- Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for\n\
- all k, counting elements from 0. For the sake of comparison,\n\
- non-existing elements are considered to be infinite. The interesting\n\
- property of a heap is that a[0] is always its smallest element.\n\
- \n\
- Usage:\n\
- \n\
- heap = [] # creates an empty heap\n\
- heappush(heap, item) # pushes a new item on the heap\n\
- item = heappop(heap) # pops the smallest item from the heap\n\
- item = heap[0] # smallest item on the heap without popping it\n\
- heapify(x) # transforms list into a heap, in-place, in linear time\n\
- item = heapreplace(heap, item) # pops and returns smallest item, and adds\n\
- # new item; the heap size is unchanged\n\
- \n\
- Our API differs from textbook heap algorithms as follows:\n\
- \n\
- - We use 0-based indexing. This makes the relationship between the\n\
- index for a node and the indexes for its children slightly less\n\
- obvious, but is more suitable since Python uses 0-based indexing.\n\
- \n\
- - Our heappop() method returns the smallest item, not the largest.\n\
- \n\
- These two make it possible to view the heap as a regular Python list\n\
- without surprises: heap[0] is the smallest item, and heap.sort()\n\
- maintains the heap invariant!\n");
- PyDoc_STRVAR(__about__,
- "Heap queues\n\
- \n\
- [explanation by Fran\xc3\xa7ois Pinard]\n\
- \n\
- Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for\n\
- all k, counting elements from 0. For the sake of comparison,\n\
- non-existing elements are considered to be infinite. The interesting\n\
- property of a heap is that a[0] is always its smallest element.\n"
- "\n\
- The strange invariant above is meant to be an efficient memory\n\
- representation for a tournament. The numbers below are `k', not a[k]:\n\
- \n\
- 0\n\
- \n\
- 1 2\n\
- \n\
- 3 4 5 6\n\
- \n\
- 7 8 9 10 11 12 13 14\n\
- \n\
- 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n\
- \n\
- \n\
- In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'. In\n\
- a usual binary tournament we see in sports, each cell is the winner\n\
- over the two cells it tops, and we can trace the winner down the tree\n\
- to see all opponents s/he had. However, in many computer applications\n\
- of such tournaments, we do not need to trace the history of a winner.\n\
- To be more memory efficient, when a winner is promoted, we try to\n\
- replace it by something else at a lower level, and the rule becomes\n\
- that a cell and the two cells it tops contain three different items,\n\
- but the top cell \"wins\" over the two topped cells.\n"
- "\n\
- If this heap invariant is protected at all time, index 0 is clearly\n\
- the overall winner. The simplest algorithmic way to remove it and\n\
- find the \"next\" winner is to move some loser (let's say cell 30 in the\n\
- diagram above) into the 0 position, and then percolate this new 0 down\n\
- the tree, exchanging values, until the invariant is re-established.\n\
- This is clearly logarithmic on the total number of items in the tree.\n\
- By iterating over all items, you get an O(n ln n) sort.\n"
- "\n\
- A nice feature of this sort is that you can efficiently insert new\n\
- items while the sort is going on, provided that the inserted items are\n\
- not \"better\" than the last 0'th element you extracted. This is\n\
- especially useful in simulation contexts, where the tree holds all\n\
- incoming events, and the \"win\" condition means the smallest scheduled\n\
- time. When an event schedule other events for execution, they are\n\
- scheduled into the future, so they can easily go into the heap. So, a\n\
- heap is a good structure for implementing schedulers (this is what I\n\
- used for my MIDI sequencer :-).\n"
- "\n\
- Various structures for implementing schedulers have been extensively\n\
- studied, and heaps are good for this, as they are reasonably speedy,\n\
- the speed is almost constant, and the worst case is not much different\n\
- than the average case. However, there are other representations which\n\
- are more efficient overall, yet the worst cases might be terrible.\n"
- "\n\
- Heaps are also very useful in big disk sorts. You most probably all\n\
- know that a big sort implies producing \"runs\" (which are pre-sorted\n\
- sequences, which size is usually related to the amount of CPU memory),\n\
- followed by a merging passes for these runs, which merging is often\n\
- very cleverly organised[1]. It is very important that the initial\n\
- sort produces the longest runs possible. Tournaments are a good way\n\
- to that. If, using all the memory available to hold a tournament, you\n\
- replace and percolate items that happen to fit the current run, you'll\n\
- produce runs which are twice the size of the memory for random input,\n\
- and much better for input fuzzily ordered.\n"
- "\n\
- Moreover, if you output the 0'th item on disk and get an input which\n\
- may not fit in the current tournament (because the value \"wins\" over\n\
- the last output value), it cannot fit in the heap, so the size of the\n\
- heap decreases. The freed memory could be cleverly reused immediately\n\
- for progressively building a second heap, which grows at exactly the\n\
- same rate the first heap is melting. When the first heap completely\n\
- vanishes, you switch heaps and start a new run. Clever and quite\n\
- effective!\n\
- \n\
- In a word, heaps are useful memory structures to know. I use them in\n\
- a few applications, and I think it is good to keep a `heap' module\n\
- around. :-)\n"
- "\n\
- --------------------\n\
- [1] The disk balancing algorithms which are current, nowadays, are\n\
- more annoying than clever, and this is a consequence of the seeking\n\
- capabilities of the disks. On devices which cannot seek, like big\n\
- tape drives, the story was quite different, and one had to be very\n\
- clever to ensure (far in advance) that each tape movement will be the\n\
- most effective possible (that is, will best participate at\n\
- \"progressing\" the merge). Some tapes were even able to read\n\
- backwards, and this was also used to avoid the rewinding time.\n\
- Believe me, real good tape sorts were quite spectacular to watch!\n\
- From all times, sorting has always been a Great Art! :-)\n");
- static struct PyModuleDef _heapqmodule = {
- PyModuleDef_HEAD_INIT,
- "_heapq",
- module_doc,
- -1,
- heapq_methods,
- NULL,
- NULL,
- NULL,
- NULL
- };
- PyMODINIT_FUNC
- PyInit__heapq(void)
- {
- PyObject *m, *about;
- m = PyModule_Create(&_heapqmodule);
- if (m == NULL)
- return NULL;
- about = PyUnicode_DecodeUTF8(__about__, strlen(__about__), NULL);
- PyModule_AddObject(m, "__about__", about);
- return m;
- }