698 lines
19 KiB
C
698 lines
19 KiB
C
/* 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"
|
|
|
|
/* Older implementations of heapq used Py_LE for comparisons. Now, it uses
|
|
Py_LT so it will match min(), sorted(), and bisect(). Unfortunately, some
|
|
client code (Twisted for example) relied on Py_LE, so this little function
|
|
restores compatability by trying both.
|
|
*/
|
|
static int
|
|
cmp_lt(PyObject *x, PyObject *y)
|
|
{
|
|
int cmp;
|
|
static PyObject *lt = NULL;
|
|
|
|
if (lt == NULL) {
|
|
lt = PyString_FromString("__lt__");
|
|
if (lt == NULL)
|
|
return -1;
|
|
}
|
|
if (PyObject_HasAttr(x, lt))
|
|
return PyObject_RichCompareBool(x, y, Py_LT);
|
|
cmp = PyObject_RichCompareBool(y, x, Py_LE);
|
|
if (cmp != -1)
|
|
cmp = 1 - cmp;
|
|
return cmp;
|
|
}
|
|
|
|
static int
|
|
_siftdown(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
|
|
{
|
|
PyObject *newitem, *parent;
|
|
int cmp;
|
|
Py_ssize_t parentpos;
|
|
|
|
assert(PyList_Check(heap));
|
|
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 = cmp_lt(newitem, parent);
|
|
if (cmp == -1) {
|
|
Py_DECREF(newitem);
|
|
return -1;
|
|
}
|
|
if (cmp == 0)
|
|
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;
|
|
}
|
|
|
|
static int
|
|
_siftup(PyListObject *heap, Py_ssize_t pos)
|
|
{
|
|
Py_ssize_t startpos, endpos, childpos, rightpos;
|
|
int cmp;
|
|
PyObject *newitem, *tmp;
|
|
|
|
assert(PyList_Check(heap));
|
|
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 = cmp_lt(
|
|
PyList_GET_ITEM(heap, childpos),
|
|
PyList_GET_ITEM(heap, rightpos));
|
|
if (cmp == -1) {
|
|
Py_DECREF(newitem);
|
|
return -1;
|
|
}
|
|
if (cmp == 0)
|
|
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);
|
|
}
|
|
|
|
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) == -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.");
|
|
|
|
static PyObject *
|
|
heappop(PyObject *self, PyObject *heap)
|
|
{
|
|
PyObject *lastelt, *returnitem;
|
|
Py_ssize_t n;
|
|
|
|
if (!PyList_Check(heap)) {
|
|
PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
|
|
return NULL;
|
|
}
|
|
|
|
/* # 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.");
|
|
|
|
static 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_TypeError, "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 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) < 1) {
|
|
Py_INCREF(item);
|
|
return item;
|
|
}
|
|
|
|
cmp = cmp_lt(PyList_GET_ITEM(heap, 0), item);
|
|
if (cmp == -1)
|
|
return NULL;
|
|
if (cmp == 0) {
|
|
Py_INCREF(item);
|
|
return item;
|
|
}
|
|
|
|
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(heappushpop_doc,
|
|
"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 PyObject *
|
|
heapify(PyObject *self, PyObject *heap)
|
|
{
|
|
Py_ssize_t i, n;
|
|
|
|
if (!PyList_Check(heap)) {
|
|
PyErr_SetString(PyExc_TypeError, "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 PyObject *
|
|
nlargest(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *heap=NULL, *elem, *iterable, *sol, *it, *oldelem;
|
|
Py_ssize_t i, n;
|
|
int cmp;
|
|
|
|
if (!PyArg_ParseTuple(args, "nO:nlargest", &n, &iterable))
|
|
return NULL;
|
|
|
|
it = PyObject_GetIter(iterable);
|
|
if (it == NULL)
|
|
return NULL;
|
|
|
|
heap = PyList_New(0);
|
|
if (heap == NULL)
|
|
goto fail;
|
|
|
|
for (i=0 ; i<n ; i++ ){
|
|
elem = PyIter_Next(it);
|
|
if (elem == NULL) {
|
|
if (PyErr_Occurred())
|
|
goto fail;
|
|
else
|
|
goto sortit;
|
|
}
|
|
if (PyList_Append(heap, elem) == -1) {
|
|
Py_DECREF(elem);
|
|
goto fail;
|
|
}
|
|
Py_DECREF(elem);
|
|
}
|
|
if (PyList_GET_SIZE(heap) == 0)
|
|
goto sortit;
|
|
|
|
for (i=n/2-1 ; i>=0 ; i--)
|
|
if(_siftup((PyListObject *)heap, i) == -1)
|
|
goto fail;
|
|
|
|
sol = PyList_GET_ITEM(heap, 0);
|
|
while (1) {
|
|
elem = PyIter_Next(it);
|
|
if (elem == NULL) {
|
|
if (PyErr_Occurred())
|
|
goto fail;
|
|
else
|
|
goto sortit;
|
|
}
|
|
cmp = cmp_lt(sol, elem);
|
|
if (cmp == -1) {
|
|
Py_DECREF(elem);
|
|
goto fail;
|
|
}
|
|
if (cmp == 0) {
|
|
Py_DECREF(elem);
|
|
continue;
|
|
}
|
|
oldelem = PyList_GET_ITEM(heap, 0);
|
|
PyList_SET_ITEM(heap, 0, elem);
|
|
Py_DECREF(oldelem);
|
|
if (_siftup((PyListObject *)heap, 0) == -1)
|
|
goto fail;
|
|
sol = PyList_GET_ITEM(heap, 0);
|
|
}
|
|
sortit:
|
|
if (PyList_Sort(heap) == -1)
|
|
goto fail;
|
|
if (PyList_Reverse(heap) == -1)
|
|
goto fail;
|
|
Py_DECREF(it);
|
|
return heap;
|
|
|
|
fail:
|
|
Py_DECREF(it);
|
|
Py_XDECREF(heap);
|
|
return NULL;
|
|
}
|
|
|
|
PyDoc_STRVAR(nlargest_doc,
|
|
"Find the n largest elements in a dataset.\n\
|
|
\n\
|
|
Equivalent to: sorted(iterable, reverse=True)[:n]\n");
|
|
|
|
static int
|
|
_siftdownmax(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
|
|
{
|
|
PyObject *newitem, *parent;
|
|
int cmp;
|
|
Py_ssize_t parentpos;
|
|
|
|
assert(PyList_Check(heap));
|
|
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 = cmp_lt(parent, newitem);
|
|
if (cmp == -1) {
|
|
Py_DECREF(newitem);
|
|
return -1;
|
|
}
|
|
if (cmp == 0)
|
|
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;
|
|
}
|
|
|
|
static int
|
|
_siftupmax(PyListObject *heap, Py_ssize_t pos)
|
|
{
|
|
Py_ssize_t startpos, endpos, childpos, rightpos;
|
|
int cmp;
|
|
PyObject *newitem, *tmp;
|
|
|
|
assert(PyList_Check(heap));
|
|
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 = cmp_lt(
|
|
PyList_GET_ITEM(heap, rightpos),
|
|
PyList_GET_ITEM(heap, childpos));
|
|
if (cmp == -1) {
|
|
Py_DECREF(newitem);
|
|
return -1;
|
|
}
|
|
if (cmp == 0)
|
|
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 _siftdownmax(heap, startpos, pos);
|
|
}
|
|
|
|
static PyObject *
|
|
nsmallest(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *heap=NULL, *elem, *iterable, *los, *it, *oldelem;
|
|
Py_ssize_t i, n;
|
|
int cmp;
|
|
|
|
if (!PyArg_ParseTuple(args, "nO:nsmallest", &n, &iterable))
|
|
return NULL;
|
|
|
|
it = PyObject_GetIter(iterable);
|
|
if (it == NULL)
|
|
return NULL;
|
|
|
|
heap = PyList_New(0);
|
|
if (heap == NULL)
|
|
goto fail;
|
|
|
|
for (i=0 ; i<n ; i++ ){
|
|
elem = PyIter_Next(it);
|
|
if (elem == NULL) {
|
|
if (PyErr_Occurred())
|
|
goto fail;
|
|
else
|
|
goto sortit;
|
|
}
|
|
if (PyList_Append(heap, elem) == -1) {
|
|
Py_DECREF(elem);
|
|
goto fail;
|
|
}
|
|
Py_DECREF(elem);
|
|
}
|
|
n = PyList_GET_SIZE(heap);
|
|
if (n == 0)
|
|
goto sortit;
|
|
|
|
for (i=n/2-1 ; i>=0 ; i--)
|
|
if(_siftupmax((PyListObject *)heap, i) == -1)
|
|
goto fail;
|
|
|
|
los = PyList_GET_ITEM(heap, 0);
|
|
while (1) {
|
|
elem = PyIter_Next(it);
|
|
if (elem == NULL) {
|
|
if (PyErr_Occurred())
|
|
goto fail;
|
|
else
|
|
goto sortit;
|
|
}
|
|
cmp = cmp_lt(elem, los);
|
|
if (cmp == -1) {
|
|
Py_DECREF(elem);
|
|
goto fail;
|
|
}
|
|
if (cmp == 0) {
|
|
Py_DECREF(elem);
|
|
continue;
|
|
}
|
|
|
|
oldelem = PyList_GET_ITEM(heap, 0);
|
|
PyList_SET_ITEM(heap, 0, elem);
|
|
Py_DECREF(oldelem);
|
|
if (_siftupmax((PyListObject *)heap, 0) == -1)
|
|
goto fail;
|
|
los = PyList_GET_ITEM(heap, 0);
|
|
}
|
|
|
|
sortit:
|
|
if (PyList_Sort(heap) == -1)
|
|
goto fail;
|
|
Py_DECREF(it);
|
|
return heap;
|
|
|
|
fail:
|
|
Py_DECREF(it);
|
|
Py_XDECREF(heap);
|
|
return NULL;
|
|
}
|
|
|
|
PyDoc_STRVAR(nsmallest_doc,
|
|
"Find the n smallest elements in a dataset.\n\
|
|
\n\
|
|
Equivalent to: sorted(iterable)[:n]\n");
|
|
|
|
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},
|
|
{"nlargest", (PyCFunction)nlargest,
|
|
METH_VARARGS, nlargest_doc},
|
|
{"nsmallest", (PyCFunction)nsmallest,
|
|
METH_VARARGS, nsmallest_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
|
|
init_heapq(void)
|
|
{
|
|
PyObject *m;
|
|
|
|
m = Py_InitModule3("_heapq", heapq_methods, module_doc);
|
|
if (m == NULL)
|
|
return;
|
|
PyModule_AddObject(m, "__about__", PyString_FromString(__about__));
|
|
}
|
|
|