+++ /dev/null
-# -*- coding: Latin-1 -*-
-
-"""Heap queue algorithm (a.k.a. priority queue).
-
-Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
-all k, counting elements from 0. For the sake of comparison,
-non-existing elements are considered to be infinite. The interesting
-property of a heap is that a[0] is always its smallest element.
-
-Usage:
-
-heap = [] # creates an empty heap
-heappush(heap, item) # pushes a new item on the heap
-item = heappop(heap) # pops the smallest item from the heap
-item = heap[0] # smallest item on the heap without popping it
-heapify(x) # transforms list into a heap, in-place, in linear time
-item = heapreplace(heap, item) # pops and returns smallest item, and adds
- # new item; the heap size is unchanged
-
-Our API differs from textbook heap algorithms as follows:
-
-- We use 0-based indexing. This makes the relationship between the
- index for a node and the indexes for its children slightly less
- obvious, but is more suitable since Python uses 0-based indexing.
-
-- Our heappop() method returns the smallest item, not the largest.
-
-These two make it possible to view the heap as a regular Python list
-without surprises: heap[0] is the smallest item, and heap.sort()
-maintains the heap invariant!
-"""
-
-# Original code by Kevin O'Connor, augmented by Tim Peters
-
-__about__ = """Heap queues
-
-[explanation by François Pinard]
-
-Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
-all k, counting elements from 0. For the sake of comparison,
-non-existing elements are considered to be infinite. The interesting
-property of a heap is that a[0] is always its smallest element.
-
-The strange invariant above is meant to be an efficient memory
-representation for a tournament. The numbers below are `k', not a[k]:
-
- 0
-
- 1 2
-
- 3 4 5 6
-
- 7 8 9 10 11 12 13 14
-
- 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
-
-
-In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'. In
-an usual binary tournament we see in sports, each cell is the winner
-over the two cells it tops, and we can trace the winner down the tree
-to see all opponents s/he had. However, in many computer applications
-of such tournaments, we do not need to trace the history of a winner.
-To be more memory efficient, when a winner is promoted, we try to
-replace it by something else at a lower level, and the rule becomes
-that a cell and the two cells it tops contain three different items,
-but the top cell "wins" over the two topped cells.
-
-If this heap invariant is protected at all time, index 0 is clearly
-the overall winner. The simplest algorithmic way to remove it and
-find the "next" winner is to move some loser (let's say cell 30 in the
-diagram above) into the 0 position, and then percolate this new 0 down
-the tree, exchanging values, until the invariant is re-established.
-This is clearly logarithmic on the total number of items in the tree.
-By iterating over all items, you get an O(n ln n) sort.
-
-A nice feature of this sort is that you can efficiently insert new
-items while the sort is going on, provided that the inserted items are
-not "better" than the last 0'th element you extracted. This is
-especially useful in simulation contexts, where the tree holds all
-incoming events, and the "win" condition means the smallest scheduled
-time. When an event schedule other events for execution, they are
-scheduled into the future, so they can easily go into the heap. So, a
-heap is a good structure for implementing schedulers (this is what I
-used for my MIDI sequencer :-).
-
-Various structures for implementing schedulers have been extensively
-studied, and heaps are good for this, as they are reasonably speedy,
-the speed is almost constant, and the worst case is not much different
-than the average case. However, there are other representations which
-are more efficient overall, yet the worst cases might be terrible.
-
-Heaps are also very useful in big disk sorts. You most probably all
-know that a big sort implies producing "runs" (which are pre-sorted
-sequences, which size is usually related to the amount of CPU memory),
-followed by a merging passes for these runs, which merging is often
-very cleverly organised[1]. It is very important that the initial
-sort produces the longest runs possible. Tournaments are a good way
-to that. If, using all the memory available to hold a tournament, you
-replace and percolate items that happen to fit the current run, you'll
-produce runs which are twice the size of the memory for random input,
-and much better for input fuzzily ordered.
-
-Moreover, if you output the 0'th item on disk and get an input which
-may not fit in the current tournament (because the value "wins" over
-the last output value), it cannot fit in the heap, so the size of the
-heap decreases. The freed memory could be cleverly reused immediately
-for progressively building a second heap, which grows at exactly the
-same rate the first heap is melting. When the first heap completely
-vanishes, you switch heaps and start a new run. Clever and quite
-effective!
-
-In a word, heaps are useful memory structures to know. I use them in
-a few applications, and I think it is good to keep a `heap' module
-around. :-)
-
---------------------
-[1] The disk balancing algorithms which are current, nowadays, are
-more annoying than clever, and this is a consequence of the seeking
-capabilities of the disks. On devices which cannot seek, like big
-tape drives, the story was quite different, and one had to be very
-clever to ensure (far in advance) that each tape movement will be the
-most effective possible (that is, will best participate at
-"progressing" the merge). Some tapes were even able to read
-backwards, and this was also used to avoid the rewinding time.
-Believe me, real good tape sorts were quite spectacular to watch!
-From all times, sorting has always been a Great Art! :-)
-"""
-
-__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace']
-
-def heappush(heap, item):
- """Push item onto heap, maintaining the heap invariant."""
- heap.append(item)
- _siftdown(heap, 0, len(heap)-1)
-
-def heappop(heap):
- """Pop the smallest item off the heap, maintaining the heap invariant."""
- lastelt = heap.pop() # raises appropriate IndexError if heap is empty
- if heap:
- returnitem = heap[0]
- heap[0] = lastelt
- _siftup(heap, 0)
- else:
- returnitem = lastelt
- return returnitem
-
-def heapreplace(heap, item):
- """Pop and return the current smallest value, and add the new item.
-
- This is more efficient than heappop() followed by heappush(), and can be
- more appropriate when using a fixed-size heap. Note that the value
- returned may be larger than item! That constrains reasonable uses of
- this routine.
- """
- returnitem = heap[0] # raises appropriate IndexError if heap is empty
- heap[0] = item
- _siftup(heap, 0)
- return returnitem
-
-def heapify(x):
- """Transform list into a heap, in-place, in O(len(heap)) time."""
- n = len(x)
- # 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 in reversed(xrange(n//2)):
- _siftup(x, i)
-
-# 'heap' is a heap at all indices >= startpos, except possibly for pos. pos
-# is the index of a leaf with a possibly out-of-order value. Restore the
-# heap invariant.
-def _siftdown(heap, startpos, pos):
- newitem = heap[pos]
- # Follow the path to the root, moving parents down until finding a place
- # newitem fits.
- while pos > startpos:
- parentpos = (pos - 1) >> 1
- parent = heap[parentpos]
- if parent <= newitem:
- break
- heap[pos] = parent
- pos = parentpos
- heap[pos] = newitem
-
-# The child indices of heap index pos are already heaps, and we want to make
-# a heap at index pos too. We do this by bubbling the smaller child of
-# pos up (and so on with that child's children, etc) until hitting a leaf,
-# then using _siftdown to move the oddball originally at index pos into place.
-#
-# We *could* break out of the loop as soon as we find a pos where newitem <=
-# both its children, but turns out that's not a good idea, and despite that
-# many books write the algorithm that way. During a heap pop, the last array
-# element is sifted in, and that tends to be large, so that comparing it
-# against values starting from the root usually doesn't pay (= usually doesn't
-# get us out of the loop early). See Knuth, Volume 3, where this is
-# explained and quantified in an exercise.
-#
-# Cutting the # of comparisons is important, since these routines have no
-# way to extract "the priority" from an array element, so that intelligence
-# is likely to be hiding in custom __cmp__ methods, or in array elements
-# storing (priority, record) tuples. Comparisons are thus potentially
-# expensive.
-#
-# On random arrays of length 1000, making this change cut the number of
-# comparisons made by heapify() a little, and those made by exhaustive
-# heappop() a lot, in accord with theory. Here are typical results from 3
-# runs (3 just to demonstrate how small the variance is):
-#
-# Compares needed by heapify Compares needed by 1000 heappops
-# -------------------------- --------------------------------
-# 1837 cut to 1663 14996 cut to 8680
-# 1855 cut to 1659 14966 cut to 8678
-# 1847 cut to 1660 15024 cut to 8703
-#
-# Building the heap by using heappush() 1000 times instead required
-# 2198, 2148, and 2219 compares: heapify() is more efficient, when
-# you can use it.
-#
-# The total compares needed by list.sort() on the same lists were 8627,
-# 8627, and 8632 (this should be compared to the sum of heapify() and
-# heappop() compares): list.sort() is (unsurprisingly!) more efficient
-# for sorting.
-
-def _siftup(heap, pos):
- endpos = len(heap)
- startpos = pos
- newitem = heap[pos]
- # Bubble up the smaller child until hitting a leaf.
- childpos = 2*pos + 1 # leftmost child position
- while childpos < endpos:
- # Set childpos to index of smaller child.
- rightpos = childpos + 1
- if rightpos < endpos and heap[rightpos] <= heap[childpos]:
- childpos = rightpos
- # Move the smaller child up.
- heap[pos] = heap[childpos]
- pos = childpos
- childpos = 2*pos + 1
- # The leaf at pos is empty now. Put newitem there, and bubble it up
- # to its final resting place (by sifting its parents down).
- heap[pos] = newitem
- _siftdown(heap, startpos, pos)
-
-if __name__ == "__main__":
- # Simple sanity test
- heap = []
- data = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]
- for item in data:
- heappush(heap, item)
- sort = []
- while heap:
- sort.append(heappop(heap))
- print sort
--- /dev/null
+/* 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"
+
+int
+_siftdown(PyListObject *heap, int startpos, int pos)
+{
+ PyObject *newitem, *parent;
+ int cmp, parentpos;
+
+ if (pos >= PyList_GET_SIZE(heap)) {
+ PyErr_SetString(PyExc_IndexError, "index out of range");
+ return -1;
+ }
+
+ newitem = PyList_GET_ITEM(heap, pos);
+ Py_INCREF(newitem);
+ /* Follow the path to the root, moving parents down until finding
+ a place newitem fits. */
+ while (pos > startpos){
+ parentpos = (pos - 1) >> 1;
+ parent = PyList_GET_ITEM(heap, parentpos);
+ cmp = PyObject_RichCompareBool(parent, newitem, Py_LE);
+ if (cmp == -1)
+ return -1;
+ if (cmp == 1)
+ break;
+ Py_INCREF(parent);
+ Py_DECREF(PyList_GET_ITEM(heap, pos));
+ PyList_SET_ITEM(heap, pos, parent);
+ pos = parentpos;
+ }
+ Py_DECREF(PyList_GET_ITEM(heap, pos));
+ PyList_SET_ITEM(heap, pos, newitem);
+ return 0;
+}
+
+int
+_siftup(PyListObject *heap, int pos)
+{
+ int startpos, endpos, childpos, rightpos;
+ int cmp;
+ PyObject *newitem, *tmp;
+
+ endpos = PyList_GET_SIZE(heap);
+ startpos = pos;
+ if (pos >= endpos) {
+ PyErr_SetString(PyExc_IndexError, "index out of range");
+ return -1;
+ }
+ newitem = PyList_GET_ITEM(heap, pos);
+ Py_INCREF(newitem);
+
+ /* Bubble up the smaller child until hitting a leaf. */
+ childpos = 2*pos + 1; /* leftmost child position */
+ while (childpos < endpos) {
+ /* Set childpos to index of smaller child. */
+ rightpos = childpos + 1;
+ if (rightpos < endpos) {
+ cmp = PyObject_RichCompareBool(
+ PyList_GET_ITEM(heap, rightpos),
+ PyList_GET_ITEM(heap, childpos),
+ Py_LE);
+ if (cmp == -1)
+ return -1;
+ if (cmp == 1)
+ childpos = rightpos;
+ }
+ /* Move the smaller child up. */
+ tmp = PyList_GET_ITEM(heap, childpos);
+ Py_INCREF(tmp);
+ Py_DECREF(PyList_GET_ITEM(heap, pos));
+ PyList_SET_ITEM(heap, pos, tmp);
+ pos = childpos;
+ childpos = 2*pos + 1;
+ }
+
+ /* The leaf at pos is empty now. Put newitem there, and and bubble
+ it up to its final resting place (by sifting its parents down). */
+ Py_DECREF(PyList_GET_ITEM(heap, pos));
+ PyList_SET_ITEM(heap, pos, newitem);
+ return _siftdown(heap, startpos, pos);
+}
+
+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_ValueError, "heap argument must be a list");
+ return NULL;
+ }
+
+ if (PyList_Append(heap, item) == -1)
+ return NULL;
+
+ if (_siftdown((PyListObject *)heap, 0, PyList_GET_SIZE(heap)-1) == -1)
+ return NULL;
+ Py_INCREF(Py_None);
+ return Py_None;
+}
+
+PyDoc_STRVAR(heappush_doc,
+"Push item onto heap, maintaining the heap invariant.");
+
+PyObject *
+heappop(PyObject *self, PyObject *heap)
+{
+ PyObject *lastelt, *returnitem;
+ int n;
+
+ /* # raises appropriate IndexError if 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);
+ PyList_SetSlice(heap, n-1, n, NULL);
+ n--;
+
+ if (!n)
+ return lastelt;
+ returnitem = PyList_GET_ITEM(heap, 0);
+ PyList_SET_ITEM(heap, 0, lastelt);
+ if (_siftup((PyListObject *)heap, 0) == -1) {
+ Py_DECREF(returnitem);
+ return NULL;
+ }
+ return returnitem;
+}
+
+PyDoc_STRVAR(heappop_doc,
+"Pop the smallest item off the heap, maintaining the heap invariant.");
+
+PyObject *
+heapreplace(PyObject *self, PyObject *args)
+{
+ PyObject *heap, *item, *returnitem;
+
+ if (!PyArg_UnpackTuple(args, "heapreplace", 2, 2, &heap, &item))
+ return NULL;
+
+ if (!PyList_Check(heap)) {
+ PyErr_SetString(PyExc_ValueError, "heap argument must be a list");
+ return NULL;
+ }
+
+ if (PyList_GET_SIZE(heap) < 1) {
+ 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) == -1) {
+ Py_DECREF(returnitem);
+ return NULL;
+ }
+ return returnitem;
+}
+
+PyDoc_STRVAR(heapreplace_doc,
+"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.\n");
+
+PyObject *
+heapify(PyObject *self, PyObject *heap)
+{
+ int i, n;
+
+ if (!PyList_Check(heap)) {
+ PyErr_SetString(PyExc_ValueError, "heap argument must be a list");
+ return NULL;
+ }
+
+ n = PyList_GET_SIZE(heap);
+ /* 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((PyListObject *)heap, i) == -1)
+ return NULL;
+ Py_INCREF(Py_None);
+ return Py_None;
+}
+
+PyDoc_STRVAR(heapify_doc,
+"Transform list into a heap, in-place, in O(len(heap)) time.");
+
+static PyMethodDef heapq_methods[] = {
+ {"heappush", (PyCFunction)heappush,
+ METH_VARARGS, heappush_doc},
+ {"heappop", (PyCFunction)heappop,
+ METH_O, heappop_doc},
+ {"heapreplace", (PyCFunction)heapreplace,
+ METH_VARARGS, heapreplace_doc},
+ {"heapify", (PyCFunction)heapify,
+ METH_O, heapify_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 François 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");
+
+PyMODINIT_FUNC
+initheapq(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("heapq", heapq_methods, module_doc);
+ PyModule_AddObject(m, "__about__", PyString_FromString(__about__));
+}
+
projects / python / commitdiff