| /* 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 François 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 / 2; /* 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 */ |
| if (endpos != PyList_GET_SIZE(heap)) { |
| PyErr_SetString(PyExc_RuntimeError, |
| "list changed size during iteration"); |
| return -1; |
| } |
| } |
| /* Move the smaller child up. */ |
| arr = _PyList_ITEMS(heap); |
| 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/2 - 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 / 2; /* 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 */ |
| if (endpos != PyList_GET_SIZE(heap)) { |
| PyErr_SetString(PyExc_RuntimeError, |
| "list changed size during iteration"); |
| return -1; |
| } |
| } |
| /* Move the smaller child up. */ |
| arr = _PyList_ITEMS(heap); |
| 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\ |
| an 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; |
| } |
| |