Commit | Line | Data |
---|---|---|
033fd4e3 RK |
1 | /* |
2 | * This file is part of DisOrder. | |
5aff007d | 3 | * Copyright (C) 2007, 2008 Richard Kettlewell |
033fd4e3 | 4 | * |
e7eb3a27 | 5 | * This program is free software: you can redistribute it and/or modify |
033fd4e3 | 6 | * it under the terms of the GNU General Public License as published by |
e7eb3a27 | 7 | * the Free Software Foundation, either version 3 of the License, or |
033fd4e3 | 8 | * (at your option) any later version. |
e7eb3a27 RK |
9 | * |
10 | * This program is distributed in the hope that it will be useful, | |
11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
13 | * GNU General Public License for more details. | |
14 | * | |
033fd4e3 | 15 | * You should have received a copy of the GNU General Public License |
e7eb3a27 | 16 | * along with this program. If not, see <http://www.gnu.org/licenses/>. |
033fd4e3 RK |
17 | */ |
18 | /** @file lib/heap.h @brief Binary heap template */ | |
19 | ||
20 | #ifndef HEAP_H | |
21 | #define HEAP_H | |
22 | ||
05b75f8d RK |
23 | #include "vector.h" |
24 | ||
033fd4e3 RK |
25 | /** @brief Binary heap template. |
26 | * @param NAME name of type to define | |
27 | * @param ETYPE element type | |
28 | * @param LT comparison function | |
29 | * | |
30 | * Defines a heap type called @c struct @p NAME and a number of functions to | |
31 | * operate on it. | |
32 | * | |
33 | * The element type of the heap will be @p ETYPE. | |
34 | * | |
35 | * @p LT will be called with two arguments of type @p ETYPE, and | |
36 | * implements a less-than comparison. | |
37 | * | |
38 | * The functions defined are: | |
39 | * - NAME_init(h) which initializes an empty heap at @p h | |
40 | * - NAME_count(h) which returns the number of elements in the heap | |
41 | * - NAME_insert(h, e) which inserts @p e into @p h | |
42 | * - NAME_first(g) which returns the least element of @p h | |
43 | * - NAME_remove(g) which removes and returns the least element of @p h | |
44 | * | |
45 | * The heap is implemented as a vector. Element 0 is the root. For any | |
46 | * element \f$i\f$, its children are elements \f$2i+1\f$ and \f$2i+2\f$ and | |
47 | * consequently its parent (if it is not the root) is | |
48 | * \f$\lfloor(i-1)/2\rfloor\f$. | |
49 | * | |
50 | * The insert and remove operations maintain two invariants: the @b | |
51 | * shape property (all levels of the tree are fully filled except the | |
52 | * deepest, and that is filled from the left), and the @b heap | |
53 | * property, that every element compares less than or equal to its | |
54 | * children. | |
55 | * | |
56 | * The shape property implies that the array representation has no gaps, which | |
57 | * is convenient. It is preserved by only adding or removing the final element | |
58 | * of the array and otherwise only modifying the array by swapping pairs of | |
59 | * elements. | |
60 | * | |
61 | * @b Insertion works by inserting the new element \f$N\f$ at the end and | |
62 | * bubbling it up the tree until it is in the right order for its branch. | |
63 | * - If, for its parent \f$P\f$, \f$P \le N\f$ then it is already in the right | |
64 | * place and the insertion is complete. | |
65 | * - Otherwise \f$P > N\f$ and so \f$P\f$ and \f$N\f$ are exchanged. If | |
66 | * \f$P\f$ has a second child, \f$C\f$, then \f$N < P < C\f$ so the heap | |
67 | * property is now satisfied from \f$P\f$ down. | |
68 | * | |
69 | * @b Removal works by first swapping the root with the final element (and then | |
70 | * removing it) and then bubbling the new root \f$N\f$ down the tree until it | |
71 | * finds its proper place. At each stage it is compared with its children | |
72 | * \f$A\f$ and \f$B\f$. | |
73 | * - If \f$N \le A\f$ and \f$N \le B\f$ then it is in the | |
74 | * right place already. | |
75 | * - Otherwise \f$N > A\f$ or \f$N > B\f$ (or both). WLOG \f$A \le B\f$. | |
76 | * \f$N\f$ and \f$A\f$ are exchanged, so now \f$A\f$ has children \f$N\f$ and | |
77 | * \f$B\f$. \f$A < N\f$ and \f$A \le B\f$. | |
78 | */ | |
b8956e9e RK |
79 | #define HEAP_TYPE(NAME, ETYPE, LT) \ |
80 | typedef ETYPE NAME##_element; \ | |
81 | VECTOR_TYPE(NAME, NAME##_element, xrealloc); \ | |
82 | \ | |
83 | static inline int NAME##_count(struct NAME *heap) { \ | |
84 | return heap->nvec; \ | |
85 | } \ | |
86 | \ | |
87 | static inline NAME##_element NAME##_first(struct NAME *heap) { \ | |
4c672170 | 88 | assert(heap->nvec > 0 && "_first"); \ |
b8956e9e RK |
89 | return heap->vec[0]; \ |
90 | } \ | |
91 | \ | |
8e3fe3d8 | 92 | void NAME##_insert(struct NAME *heap, NAME##_element elt); \ |
93 | NAME##_element NAME##_remove(struct NAME *heap); \ | |
b8956e9e | 94 | \ |
033fd4e3 | 95 | struct heap_swallow_semicolon |
8e3fe3d8 | 96 | |
97 | /** @brief External-linkage definitions for @ref HEAP_TYPE */ | |
98 | #define HEAP_DEFINE(NAME, ETYPE, LT) \ | |
99 | void NAME##_insert(struct NAME *heap, NAME##_element elt) { \ | |
100 | int n = heap->nvec; \ | |
101 | NAME##_append(heap, elt); \ | |
102 | while(n > 0) { \ | |
103 | const int p = (n-1)/2; \ | |
104 | if(!LT(heap->vec[n],heap->vec[p])) \ | |
105 | break; \ | |
106 | else { \ | |
107 | const NAME##_element t = heap->vec[n]; \ | |
108 | heap->vec[n] = heap->vec[p]; \ | |
109 | heap->vec[p] = t; \ | |
110 | n = p; \ | |
111 | } \ | |
112 | } \ | |
113 | } \ | |
114 | \ | |
115 | NAME##_element NAME##_remove(struct NAME *heap) { \ | |
116 | int n = 0; \ | |
117 | NAME##_element r; \ | |
118 | \ | |
4c672170 | 119 | assert(heap->nvec > 0 && "_remove"); \ |
8e3fe3d8 | 120 | r = heap->vec[0]; \ |
121 | heap->vec[0] = heap->vec[--heap->nvec]; \ | |
122 | while(2 * n + 1 < heap->nvec) { \ | |
123 | int a = 2 * n + 1; \ | |
124 | int b = 2 * n + 2; \ | |
125 | \ | |
126 | if(b < heap->nvec && LT(heap->vec[b],heap->vec[a])) { \ | |
127 | ++a; \ | |
128 | --b; \ | |
129 | } \ | |
130 | if(LT(heap->vec[a], heap->vec[n])) { \ | |
131 | const NAME##_element t = heap->vec[n]; \ | |
132 | heap->vec[n] = heap->vec[a]; \ | |
133 | heap->vec[a] = t; \ | |
134 | n = a; \ | |
135 | } else \ | |
136 | break; \ | |
137 | } \ | |
138 | return r; \ | |
139 | } \ | |
140 | \ | |
141 | struct heap_swallow_semicolon \ | |
033fd4e3 RK |
142 | |
143 | ||
144 | #endif /* PQUEUE_H */ | |
145 | ||
146 | /* | |
147 | Local Variables: | |
148 | c-basic-offset:2 | |
149 | comment-column:40 | |
150 | fill-column:79 | |
151 | indent-tabs-mode:nil | |
152 | End: | |
153 | */ |