/* 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 compatibility 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; | |
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. */ | |
newitem = PyList_GET_ITEM(heap, pos); | |
while (pos > startpos) { | |
parentpos = (pos - 1) >> 1; | |
parent = PyList_GET_ITEM(heap, parentpos); | |
cmp = cmp_lt(newitem, parent); | |
if (cmp == -1) | |
return -1; | |
if (size != PyList_GET_SIZE(heap)) { | |
PyErr_SetString(PyExc_RuntimeError, | |
"list changed size during iteration"); | |
return -1; | |
} | |
if (cmp == 0) | |
break; | |
parent = PyList_GET_ITEM(heap, parentpos); | |
newitem = PyList_GET_ITEM(heap, pos); | |
PyList_SET_ITEM(heap, parentpos, newitem); | |
PyList_SET_ITEM(heap, pos, parent); | |
pos = parentpos; | |
} | |
return 0; | |
} | |
static int | |
_siftup(PyListObject *heap, Py_ssize_t pos) | |
{ | |
Py_ssize_t startpos, endpos, childpos, rightpos, limit; | |
PyObject *tmp1, *tmp2; | |
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. */ | |
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 */ | |
rightpos = childpos + 1; | |
if (rightpos < endpos) { | |
cmp = cmp_lt( | |
PyList_GET_ITEM(heap, childpos), | |
PyList_GET_ITEM(heap, rightpos)); | |
if (cmp == -1) | |
return -1; | |
if (cmp == 0) | |
childpos = rightpos; | |
if (endpos != PyList_GET_SIZE(heap)) { | |
PyErr_SetString(PyExc_RuntimeError, | |
"list changed size during iteration"); | |
return -1; | |
} | |
} | |
/* Move the smaller child up. */ | |
tmp1 = PyList_GET_ITEM(heap, childpos); | |
tmp2 = PyList_GET_ITEM(heap, pos); | |
PyList_SET_ITEM(heap, childpos, tmp2); | |
PyList_SET_ITEM(heap, 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) == -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, | |
"heappush(heap, item) -> None. 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, | |
"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) < 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, | |
"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 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, limit; | |
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. */ | |
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 */ | |
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; | |
} | |
/* The leaf at pos is empty now. Put newitem there, 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__)); | |
} | |