--- /dev/null
+/*
+ * This file is part of DisOrder.
+ * Copyright (C) 2007 Richard Kettlewell
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
+ * USA
+ */
+/** @file lib/heap.h @brief Binary heap template */
+
+#ifndef HEAP_H
+#define HEAP_H
+
+/** @brief Binary heap template.
+ * @param NAME name of type to define
+ * @param ETYPE element type
+ * @param LT comparison function
+ *
+ * Defines a heap type called @c struct @p NAME and a number of functions to
+ * operate on it.
+ *
+ * The element type of the heap will be @p ETYPE.
+ *
+ * @p LT will be called with two arguments of type @p ETYPE, and
+ * implements a less-than comparison.
+ *
+ * The functions defined are:
+ * - NAME_init(h) which initializes an empty heap at @p h
+ * - NAME_count(h) which returns the number of elements in the heap
+ * - NAME_insert(h, e) which inserts @p e into @p h
+ * - NAME_first(g) which returns the least element of @p h
+ * - NAME_remove(g) which removes and returns the least element of @p h
+ *
+ * The heap is implemented as a vector. Element 0 is the root. For any
+ * element \f$i\f$, its children are elements \f$2i+1\f$ and \f$2i+2\f$ and
+ * consequently its parent (if it is not the root) is
+ * \f$\lfloor(i-1)/2\rfloor\f$.
+ *
+ * The insert and remove operations maintain two invariants: the @b
+ * shape property (all levels of the tree are fully filled except the
+ * deepest, and that is filled from the left), and the @b heap
+ * property, that every element compares less than or equal to its
+ * children.
+ *
+ * The shape property implies that the array representation has no gaps, which
+ * is convenient. It is preserved by only adding or removing the final element
+ * of the array and otherwise only modifying the array by swapping pairs of
+ * elements.
+ *
+ * @b Insertion works by inserting the new element \f$N\f$ at the end and
+ * bubbling it up the tree until it is in the right order for its branch.
+ * - If, for its parent \f$P\f$, \f$P \le N\f$ then it is already in the right
+ * place and the insertion is complete.
+ * - Otherwise \f$P > N\f$ and so \f$P\f$ and \f$N\f$ are exchanged. If
+ * \f$P\f$ has a second child, \f$C\f$, then \f$N < P < C\f$ so the heap
+ * property is now satisfied from \f$P\f$ down.
+ *
+ * @b Removal works by first swapping the root with the final element (and then
+ * removing it) and then bubbling the new root \f$N\f$ down the tree until it
+ * finds its proper place. At each stage it is compared with its children
+ * \f$A\f$ and \f$B\f$.
+ * - If \f$N \le A\f$ and \f$N \le B\f$ then it is in the
+ * right place already.
+ * - Otherwise \f$N > A\f$ or \f$N > B\f$ (or both). WLOG \f$A \le B\f$.
+ * \f$N\f$ and \f$A\f$ are exchanged, so now \f$A\f$ has children \f$N\f$ and
+ * \f$B\f$. \f$A < N\f$ and \f$A \le B\f$.
+ */
+#define HEAP_TYPE(NAME, ETYPE, LT) \
+ typedef ETYPE NAME##_element; \
+ VECTOR_TYPE(NAME, NAME##_element, xrealloc) \
+ \
+ static inline int NAME##_count(struct NAME *heap) { \
+ return heap->nvec; \
+ } \
+ \
+ static inline NAME##_element NAME##_first(struct NAME *heap) { \
+ assert(heap->nvec > 0); \
+ return heap->vec[0]; \
+ } \
+ \
+ static void NAME##_insert(struct NAME *heap, NAME##_element elt) { \
+ int n = heap->nvec; \
+ NAME##_append(heap, elt); \
+ while(n > 0) { \
+ const int p = (n-1)/2; \
+ if(!LT(heap->vec[n],heap->vec[p])) \
+ break; \
+ else { \
+ const NAME##_element t = heap->vec[n]; \
+ heap->vec[n] = heap->vec[p]; \
+ heap->vec[p] = t; \
+ n = p; \
+ } \
+ } \
+ } \
+ \
+ static NAME##_element NAME##_remove(struct NAME *heap) { \
+ int n = 0; \
+ NAME##_element r; \
+ \
+ assert(heap->nvec > 0); \
+ r = heap->vec[0]; \
+ heap->vec[0] = heap->vec[--heap->nvec]; \
+ while(2 * n + 1 < heap->nvec) { \
+ int a = 2 * n + 1; \
+ int b = 2 * n + 2; \
+ \
+ if(b < heap->nvec && LT(heap->vec[b],heap->vec[a])) { \
+ ++a; \
+ --b; \
+ } \
+ if(LT(heap->vec[a], heap->vec[n])) { \
+ const NAME##_element t = heap->vec[n]; \
+ heap->vec[n] = heap->vec[a]; \
+ heap->vec[a] = t; \
+ n = a; \
+ } else \
+ break; \
+ } \
+ return r; \
+ } \
+ \
+ struct heap_swallow_semicolon
+
+
+#endif /* PQUEUE_H */
+
+/*
+Local Variables:
+c-basic-offset:2
+comment-column:40
+fill-column:79
+indent-tabs-mode:nil
+End:
+*/
~mdw / disorder / blobdiff