648 lines
21 KiB
C
648 lines
21 KiB
C
/* Drop in replacement for heapq.py
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C implementation derived directly from heapq.py in Py2.3
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which was written by Kevin O'Connor, augmented by Tim Peters,
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annotated by François Pinard, and converted to C by Raymond Hettinger.
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*/
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#include "Python.h"
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static int
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siftdown(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
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{
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PyObject *newitem, *parent, **arr;
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Py_ssize_t parentpos, size;
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int cmp;
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assert(PyList_Check(heap));
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size = PyList_GET_SIZE(heap);
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if (pos >= size) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return -1;
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}
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/* Follow the path to the root, moving parents down until finding
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a place newitem fits. */
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arr = _PyList_ITEMS(heap);
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newitem = arr[pos];
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while (pos > startpos) {
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parentpos = (pos - 1) >> 1;
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parent = arr[parentpos];
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cmp = PyObject_RichCompareBool(newitem, parent, Py_LT);
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if (cmp < 0)
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return -1;
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if (size != PyList_GET_SIZE(heap)) {
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PyErr_SetString(PyExc_RuntimeError,
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"list changed size during iteration");
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return -1;
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}
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if (cmp == 0)
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break;
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arr = _PyList_ITEMS(heap);
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parent = arr[parentpos];
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newitem = arr[pos];
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arr[parentpos] = newitem;
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arr[pos] = parent;
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pos = parentpos;
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}
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return 0;
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}
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static int
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siftup(PyListObject *heap, Py_ssize_t pos)
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{
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Py_ssize_t startpos, endpos, childpos, limit;
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PyObject *tmp1, *tmp2, **arr;
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int cmp;
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assert(PyList_Check(heap));
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endpos = PyList_GET_SIZE(heap);
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startpos = pos;
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if (pos >= endpos) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return -1;
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}
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/* Bubble up the smaller child until hitting a leaf. */
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arr = _PyList_ITEMS(heap);
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limit = endpos / 2; /* smallest pos that has no child */
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while (pos < limit) {
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/* Set childpos to index of smaller child. */
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childpos = 2*pos + 1; /* leftmost child position */
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if (childpos + 1 < endpos) {
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cmp = PyObject_RichCompareBool(
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arr[childpos],
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arr[childpos + 1],
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Py_LT);
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if (cmp < 0)
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return -1;
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childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
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if (endpos != PyList_GET_SIZE(heap)) {
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PyErr_SetString(PyExc_RuntimeError,
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"list changed size during iteration");
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return -1;
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}
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}
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/* Move the smaller child up. */
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arr = _PyList_ITEMS(heap);
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tmp1 = arr[childpos];
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tmp2 = arr[pos];
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arr[childpos] = tmp2;
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arr[pos] = tmp1;
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pos = childpos;
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}
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/* Bubble it up to its final resting place (by sifting its parents down). */
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return siftdown(heap, startpos, pos);
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}
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static PyObject *
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heappush(PyObject *self, PyObject *args)
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{
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PyObject *heap, *item;
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if (!PyArg_UnpackTuple(args, "heappush", 2, 2, &heap, &item))
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return NULL;
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if (!PyList_Check(heap)) {
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PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
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return NULL;
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}
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if (PyList_Append(heap, item))
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return NULL;
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if (siftdown((PyListObject *)heap, 0, PyList_GET_SIZE(heap)-1))
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return NULL;
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Py_RETURN_NONE;
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}
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PyDoc_STRVAR(heappush_doc,
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"heappush(heap, item) -> None. Push item onto heap, maintaining the heap invariant.");
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static PyObject *
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heappop_internal(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
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{
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PyObject *lastelt, *returnitem;
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Py_ssize_t n;
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if (!PyList_Check(heap)) {
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PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
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return NULL;
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}
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/* raises IndexError if the heap is empty */
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n = PyList_GET_SIZE(heap);
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if (n == 0) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return NULL;
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}
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lastelt = PyList_GET_ITEM(heap, n-1) ;
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Py_INCREF(lastelt);
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if (PyList_SetSlice(heap, n-1, n, NULL)) {
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Py_DECREF(lastelt);
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return NULL;
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}
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n--;
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if (!n)
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return lastelt;
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returnitem = PyList_GET_ITEM(heap, 0);
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PyList_SET_ITEM(heap, 0, lastelt);
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if (siftup_func((PyListObject *)heap, 0)) {
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Py_DECREF(returnitem);
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return NULL;
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}
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return returnitem;
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}
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static PyObject *
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heappop(PyObject *self, PyObject *heap)
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{
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return heappop_internal(heap, siftup);
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}
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PyDoc_STRVAR(heappop_doc,
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"Pop the smallest item off the heap, maintaining the heap invariant.");
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static PyObject *
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heapreplace_internal(PyObject *args, int siftup_func(PyListObject *, Py_ssize_t))
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{
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PyObject *heap, *item, *returnitem;
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if (!PyArg_UnpackTuple(args, "heapreplace", 2, 2, &heap, &item))
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return NULL;
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if (!PyList_Check(heap)) {
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PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
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return NULL;
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}
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if (PyList_GET_SIZE(heap) == 0) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return NULL;
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}
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returnitem = PyList_GET_ITEM(heap, 0);
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Py_INCREF(item);
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PyList_SET_ITEM(heap, 0, item);
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if (siftup_func((PyListObject *)heap, 0)) {
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Py_DECREF(returnitem);
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return NULL;
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}
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return returnitem;
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}
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static PyObject *
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heapreplace(PyObject *self, PyObject *args)
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{
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return heapreplace_internal(args, siftup);
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}
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PyDoc_STRVAR(heapreplace_doc,
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"heapreplace(heap, item) -> value. Pop and return the current smallest value, and add the new item.\n\
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\n\
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This is more efficient than heappop() followed by heappush(), and can be\n\
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more appropriate when using a fixed-size heap. Note that the value\n\
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returned may be larger than item! That constrains reasonable uses of\n\
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this routine unless written as part of a conditional replacement:\n\n\
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if item > heap[0]:\n\
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item = heapreplace(heap, item)\n");
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static PyObject *
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heappushpop(PyObject *self, PyObject *args)
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{
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PyObject *heap, *item, *returnitem;
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int cmp;
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if (!PyArg_UnpackTuple(args, "heappushpop", 2, 2, &heap, &item))
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return NULL;
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if (!PyList_Check(heap)) {
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PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
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return NULL;
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}
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if (PyList_GET_SIZE(heap) == 0) {
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Py_INCREF(item);
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return item;
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}
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cmp = PyObject_RichCompareBool(PyList_GET_ITEM(heap, 0), item, Py_LT);
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if (cmp < 0)
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return NULL;
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if (cmp == 0) {
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Py_INCREF(item);
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return item;
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}
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if (PyList_GET_SIZE(heap) == 0) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return NULL;
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}
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returnitem = PyList_GET_ITEM(heap, 0);
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Py_INCREF(item);
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PyList_SET_ITEM(heap, 0, item);
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if (siftup((PyListObject *)heap, 0)) {
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Py_DECREF(returnitem);
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return NULL;
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}
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return returnitem;
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}
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PyDoc_STRVAR(heappushpop_doc,
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"heappushpop(heap, item) -> value. Push item on the heap, then pop and return the smallest item\n\
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from the heap. The combined action runs more efficiently than\n\
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heappush() followed by a separate call to heappop().");
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static Py_ssize_t
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keep_top_bit(Py_ssize_t n)
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{
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int i = 0;
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while (n > 1) {
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n >>= 1;
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i++;
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}
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return n << i;
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}
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/* Cache friendly version of heapify()
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-----------------------------------
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Build-up a heap in O(n) time by performing siftup() operations
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on nodes whose children are already heaps.
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The simplest way is to sift the nodes in reverse order from
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n//2-1 to 0 inclusive. The downside is that children may be
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out of cache by the time their parent is reached.
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A better way is to not wait for the children to go out of cache.
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Once a sibling pair of child nodes have been sifted, immediately
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sift their parent node (while the children are still in cache).
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Both ways build child heaps before their parents, so both ways
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do the exact same number of comparisons and produce exactly
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the same heap. The only difference is that the traversal
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order is optimized for cache efficiency.
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*/
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static PyObject *
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cache_friendly_heapify(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
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{
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Py_ssize_t i, j, m, mhalf, leftmost;
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m = PyList_GET_SIZE(heap) >> 1; /* index of first childless node */
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leftmost = keep_top_bit(m + 1) - 1; /* leftmost node in row of m */
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mhalf = m >> 1; /* parent of first childless node */
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for (i = leftmost - 1 ; i >= mhalf ; i--) {
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j = i;
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while (1) {
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if (siftup_func((PyListObject *)heap, j))
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return NULL;
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if (!(j & 1))
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break;
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j >>= 1;
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}
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}
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for (i = m - 1 ; i >= leftmost ; i--) {
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j = i;
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while (1) {
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if (siftup_func((PyListObject *)heap, j))
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return NULL;
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if (!(j & 1))
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break;
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j >>= 1;
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}
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}
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Py_RETURN_NONE;
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}
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static PyObject *
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heapify_internal(PyObject *heap, int siftup_func(PyListObject *, Py_ssize_t))
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{
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Py_ssize_t i, n;
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if (!PyList_Check(heap)) {
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PyErr_SetString(PyExc_TypeError, "heap argument must be a list");
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return NULL;
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}
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/* For heaps likely to be bigger than L1 cache, we use the cache
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friendly heapify function. For smaller heaps that fit entirely
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in cache, we prefer the simpler algorithm with less branching.
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*/
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n = PyList_GET_SIZE(heap);
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if (n > 2500)
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return cache_friendly_heapify(heap, siftup_func);
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/* Transform bottom-up. The largest index there's any point to
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looking at is the largest with a child index in-range, so must
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have 2*i + 1 < n, or i < (n-1)/2. If n is even = 2*j, this is
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(2*j-1)/2 = j-1/2 so j-1 is the largest, which is n//2 - 1. If
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n is odd = 2*j+1, this is (2*j+1-1)/2 = j so j-1 is the largest,
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and that's again n//2-1.
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*/
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for (i = n/2 - 1 ; i >= 0 ; i--)
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if (siftup_func((PyListObject *)heap, i))
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return NULL;
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Py_RETURN_NONE;
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}
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static PyObject *
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heapify(PyObject *self, PyObject *heap)
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{
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return heapify_internal(heap, siftup);
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}
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PyDoc_STRVAR(heapify_doc,
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"Transform list into a heap, in-place, in O(len(heap)) time.");
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static int
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siftdown_max(PyListObject *heap, Py_ssize_t startpos, Py_ssize_t pos)
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{
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PyObject *newitem, *parent, **arr;
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Py_ssize_t parentpos, size;
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int cmp;
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assert(PyList_Check(heap));
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size = PyList_GET_SIZE(heap);
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if (pos >= size) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return -1;
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}
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/* Follow the path to the root, moving parents down until finding
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a place newitem fits. */
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arr = _PyList_ITEMS(heap);
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newitem = arr[pos];
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while (pos > startpos) {
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parentpos = (pos - 1) >> 1;
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parent = arr[parentpos];
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cmp = PyObject_RichCompareBool(parent, newitem, Py_LT);
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if (cmp < 0)
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return -1;
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if (size != PyList_GET_SIZE(heap)) {
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PyErr_SetString(PyExc_RuntimeError,
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"list changed size during iteration");
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return -1;
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}
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if (cmp == 0)
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break;
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arr = _PyList_ITEMS(heap);
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parent = arr[parentpos];
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newitem = arr[pos];
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arr[parentpos] = newitem;
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arr[pos] = parent;
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pos = parentpos;
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}
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return 0;
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}
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static int
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siftup_max(PyListObject *heap, Py_ssize_t pos)
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{
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Py_ssize_t startpos, endpos, childpos, limit;
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PyObject *tmp1, *tmp2, **arr;
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int cmp;
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assert(PyList_Check(heap));
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endpos = PyList_GET_SIZE(heap);
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startpos = pos;
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if (pos >= endpos) {
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PyErr_SetString(PyExc_IndexError, "index out of range");
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return -1;
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}
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/* Bubble up the smaller child until hitting a leaf. */
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arr = _PyList_ITEMS(heap);
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limit = endpos / 2; /* smallest pos that has no child */
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while (pos < limit) {
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/* Set childpos to index of smaller child. */
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childpos = 2*pos + 1; /* leftmost child position */
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if (childpos + 1 < endpos) {
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cmp = PyObject_RichCompareBool(
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arr[childpos + 1],
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arr[childpos],
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Py_LT);
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if (cmp < 0)
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return -1;
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childpos += ((unsigned)cmp ^ 1); /* increment when cmp==0 */
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if (endpos != PyList_GET_SIZE(heap)) {
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PyErr_SetString(PyExc_RuntimeError,
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"list changed size during iteration");
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return -1;
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}
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}
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/* Move the smaller child up. */
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arr = _PyList_ITEMS(heap);
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tmp1 = arr[childpos];
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tmp2 = arr[pos];
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arr[childpos] = tmp2;
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arr[pos] = tmp1;
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pos = childpos;
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}
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/* Bubble it up to its final resting place (by sifting its parents down). */
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return siftdown_max(heap, startpos, pos);
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}
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static PyObject *
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heappop_max(PyObject *self, PyObject *heap)
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{
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return heappop_internal(heap, siftup_max);
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}
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PyDoc_STRVAR(heappop_max_doc, "Maxheap variant of heappop.");
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static PyObject *
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heapreplace_max(PyObject *self, PyObject *args)
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{
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return heapreplace_internal(args, siftup_max);
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}
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PyDoc_STRVAR(heapreplace_max_doc, "Maxheap variant of heapreplace");
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static PyObject *
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heapify_max(PyObject *self, PyObject *heap)
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{
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return heapify_internal(heap, siftup_max);
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}
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PyDoc_STRVAR(heapify_max_doc, "Maxheap variant of heapify.");
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static PyMethodDef heapq_methods[] = {
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{"heappush", (PyCFunction)heappush,
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METH_VARARGS, heappush_doc},
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{"heappushpop", (PyCFunction)heappushpop,
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METH_VARARGS, heappushpop_doc},
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{"heappop", (PyCFunction)heappop,
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METH_O, heappop_doc},
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{"heapreplace", (PyCFunction)heapreplace,
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METH_VARARGS, heapreplace_doc},
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{"heapify", (PyCFunction)heapify,
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METH_O, heapify_doc},
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{"_heappop_max", (PyCFunction)heappop_max,
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METH_O, heappop_max_doc},
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{"_heapreplace_max",(PyCFunction)heapreplace_max,
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METH_VARARGS, heapreplace_max_doc},
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{"_heapify_max", (PyCFunction)heapify_max,
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METH_O, heapify_max_doc},
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{NULL, NULL} /* sentinel */
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};
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PyDoc_STRVAR(module_doc,
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"Heap queue algorithm (a.k.a. priority queue).\n\
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\n\
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Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for\n\
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all k, counting elements from 0. For the sake of comparison,\n\
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non-existing elements are considered to be infinite. The interesting\n\
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property of a heap is that a[0] is always its smallest element.\n\
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\n\
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Usage:\n\
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\n\
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heap = [] # creates an empty heap\n\
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heappush(heap, item) # pushes a new item on the heap\n\
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item = heappop(heap) # pops the smallest item from the heap\n\
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item = heap[0] # smallest item on the heap without popping it\n\
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heapify(x) # transforms list into a heap, in-place, in linear time\n\
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item = heapreplace(heap, item) # pops and returns smallest item, and adds\n\
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# new item; the heap size is unchanged\n\
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\n\
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Our API differs from textbook heap algorithms as follows:\n\
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\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;
|
|
}
|
|
|