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033fd4e3 RK |
1 | /* |

2 | * This file is part of DisOrder. | |

3 | * Copyright (C) 2007 Richard Kettlewell | |

4 | * | |

5 | * This program is free software; you can redistribute it and/or modify | |

6 | * it under the terms of the GNU General Public License as published by | |

7 | * the Free Software Foundation; either version 2 of the License, or | |

8 | * (at your option) any later version. | |

9 | * | |

10 | * This program is distributed in the hope that it will be useful, but | |

11 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |

12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |

13 | * General Public License for more details. | |

14 | * | |

15 | * You should have received a copy of the GNU General Public License | |

16 | * along with this program; if not, write to the Free Software | |

17 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 | |

18 | * USA | |

19 | */ | |

20 | /** @file lib/heap.h @brief Binary heap template */ | |

21 | ||

22 | #ifndef HEAP_H | |

23 | #define HEAP_H | |

24 | ||

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) { \ | |

88 | assert(heap->nvec > 0); \ | |

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 | \ | |

119 | assert(heap->nvec > 0); \ | |

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 | */ |