1 | /*** Binary Heap Implementation ***/ |
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2 | /* |
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3 | * Shane Saunders |
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4 | */ |
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5 | /* This implementation stores the binary heap in a 1 dimensional array. */ |
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6 | #include <stdio.h> |
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7 | #include <stdlib.h> |
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8 | #include "../include/bheap.h" |
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9 | |
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10 | |
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11 | /*** Prototypes for functions internal to the implementation. ***/ |
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12 | |
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13 | void bh_siftup(bheap_t *h, int p, int q); |
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14 | |
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15 | |
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16 | |
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17 | /*** Definitions for visible functions. ***/ |
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18 | |
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19 | void bh_dump(bheap_t *h) { |
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20 | int i; |
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21 | |
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22 | printf("Heap: \n"); |
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23 | for(i = 1; i <= h->n; i++) printf(" %d(%f)\n", h->a[i].item, h->a[i].key); |
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24 | printf("\n"); |
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25 | |
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26 | for(i = 2; i <= h->n; i++) { |
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27 | if(h->a[i].key < h->a[i/2].key) { |
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28 | printf("key error at entry %d, value %f\n", i, h->a[i].key); |
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29 | exit(1); |
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30 | } |
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31 | } |
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32 | for(i = 1; i <= h->n; i++) { |
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33 | if(h->p[h->a[i].item] != i) { |
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34 | printf("indexing error at entry %d", i); exit(1); |
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35 | } |
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36 | } |
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37 | } |
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38 | |
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39 | /* bh_alloc() allocates space for a binary heap of size n and initialises it. |
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40 | * Returns a pointer to the binary heap. |
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41 | */ |
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42 | bheap_t *bh_alloc(int n) |
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43 | { |
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44 | bheap_t *h; |
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45 | |
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46 | /* Create the binary heap. */ |
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47 | h = (bheap_t *)malloc(sizeof(bheap_t)); |
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48 | |
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49 | /* For the purpose of indexing the binary heap, we require n+1 elements in |
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50 | * a[] since the indexing used does not use a[0]. |
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51 | */ |
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52 | h->a = (bheap_item_t *)calloc(n+1, sizeof(bheap_item_t)); |
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53 | h->p = (int *)calloc(n, sizeof(int)); |
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54 | h->n = 0; |
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55 | h->key_comps = 0; |
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56 | |
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57 | return h; |
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58 | } |
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59 | |
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60 | |
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61 | /* bh_free() frees the space taken up by the binary heap pointed to by h. |
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62 | */ |
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63 | void bh_free(bheap_t *h) |
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64 | { |
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65 | free(h->a); |
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66 | free(h->p); |
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67 | free(h); |
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68 | } |
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69 | |
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70 | |
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71 | /* bh_min() returns the item with the minimum key in the binary heap pointed to |
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72 | * by h. |
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73 | */ |
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74 | int bh_min(bheap_t *h) |
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75 | { |
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76 | /* The item at the top of the binary heap has the minimum key value. */ |
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77 | return h->a[1].item; |
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78 | } |
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79 | |
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80 | |
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81 | /* bh_insert() inserts an item and its key value into the binary heap pointed |
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82 | * to by h. |
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83 | */ |
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84 | void bh_insert(bheap_t *h, int item, double key) |
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85 | { |
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86 | /* i - insertion point |
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87 | * j - parent of i |
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88 | * y - parent's entry in the heap. |
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89 | */ |
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90 | int i, j; |
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91 | bheap_item_t y; |
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92 | |
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93 | /* i initially indexes the new entry at the bottom of the heap. */ |
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94 | i = ++(h->n); |
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95 | |
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96 | /* Stop if the insertion point reaches the top of the heap. */ |
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97 | while(i >= 2) { |
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98 | /* j indexes the parent of i. y is the parent's entry. */ |
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99 | j = i / 2; |
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100 | y = h->a[j]; |
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101 | |
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102 | /* We have the correct insertion point when the item's key is >= parent |
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103 | * Otherwise we move the parent down and insertion point up. |
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104 | */ |
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105 | h->key_comps++; |
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106 | if(key >= y.key) break; |
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107 | |
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108 | h->a[i] = y; |
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109 | h->p[y.item] = i; |
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110 | i = j; |
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111 | } |
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112 | |
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113 | /* Insert the new item at the insertion point found. */ |
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114 | h->a[i].item = item; |
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115 | h->a[i].key = key; |
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116 | h->p[item] = i; |
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117 | } |
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118 | |
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119 | |
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120 | /* bh_delete() deletes an item from the binary heap pointed to by h. |
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121 | */ |
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122 | void bh_delete(bheap_t *h, int item) |
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123 | { |
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124 | int n; |
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125 | int p; |
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126 | |
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127 | /* Decrease the number of entries in the heap and record the position of |
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128 | * the item to be deleted. |
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129 | */ |
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130 | n = --(h->n); |
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131 | p = h->p[item]; |
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132 | |
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133 | /* Heap needs adjusting if the position of the deleted item was not at the |
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134 | * end of the heap. |
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135 | */ |
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136 | if(p <= n) { |
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137 | /* We put the item at the end of the heap in the place of the deleted |
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138 | * item and sift-up or sift-down to relocate it in the correct place in |
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139 | * the heap. |
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140 | */ |
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141 | h->key_comps++; |
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142 | if(h->a[p].key <= h->a[n + 1].key) { |
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143 | h->a[p] = h->a[n + 1]; |
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144 | h->p[h->a[p].item] = p; |
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145 | bh_siftup(h, p, n); |
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146 | } |
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147 | else { |
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148 | /* Use insert to sift-down, temporarily adjusting the size of the |
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149 | * heap for the call to insert. |
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150 | */ |
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151 | h->n = p - 1; |
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152 | bh_insert(h, h->a[n + 1].item, h->a[n+1].key); |
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153 | h->n = n; |
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154 | } |
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155 | } |
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156 | } |
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157 | /* bh_mark() marks an item from the binary heap pointed to by h. |
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158 | */ |
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159 | void bh_mark(bheap_t *h, int item, int flag) |
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160 | { |
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161 | h->a[h->p[item]].dirty = flag; |
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162 | } |
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163 | /* bh_get_key() returns the key value of an item from the binary heap h. |
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164 | */ |
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165 | double bh_get_key(bheap_t *h, int item) |
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166 | { |
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167 | return h->a[h->p[item]].key; |
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168 | } |
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169 | /* bh_is_dirty() returns the dirty value of an item from the binary heap h. |
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170 | */ |
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171 | int bh_is_dirty(bheap_t *h, int item) |
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172 | { |
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173 | return h->a[h->p[item]].dirty; |
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174 | } |
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175 | |
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176 | |
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177 | /* bh_decrease_key() decreases the value of 'item's key and then performs |
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178 | * sift-down until 'item' has been relocated to the correct position in the |
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179 | * binary heap. |
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180 | */ |
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181 | void bh_decrease_key(bheap_t *h, int item, double new_key) |
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182 | { |
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183 | int n; |
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184 | |
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185 | n = h->n; |
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186 | h->n = h->p[item] - 1; |
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187 | |
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188 | bh_insert(h, item, new_key); |
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189 | |
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190 | h->n = n; |
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191 | } |
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192 | |
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193 | |
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194 | /*** Definitions for internal functions ***/ |
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195 | |
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196 | /* siftup() considers the sub-tree rooted at p that ends at q and moves |
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197 | * the root down, sifting up the minimum child until it is located in the |
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198 | * correct part of the binary heap. |
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199 | */ |
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200 | void bh_siftup(bheap_t *h, int p, int q) |
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201 | { |
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202 | /* y - the heap entry of the root. |
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203 | * j - the current insertion point for the root. |
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204 | * k - the child of the insertion point. |
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205 | * z - heap entry of the child of the insertion point. |
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206 | */ |
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207 | int j, k; |
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208 | bheap_item_t y, z; |
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209 | |
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210 | /* Get the value of the root and initialise the insertion point and child. |
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211 | */ |
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212 | y = h->a[p]; |
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213 | j = p; |
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214 | k = 2 * p; |
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215 | |
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216 | /* sift-up only if there is a child of the insertion point. */ |
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217 | while(k <= q) { |
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218 | |
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219 | /* Choose the minimum child unless there is only one. */ |
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220 | z = h->a[k]; |
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221 | if(k < q) { |
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222 | h->key_comps++; |
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223 | if(z.key > h->a[k + 1].key) z = h->a[++k]; |
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224 | } |
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225 | |
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226 | /* We stop if the insertion point for the root is in the correct place. |
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227 | * Otherwise the child goes up and the root goes down. (i.e. swap) |
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228 | */ |
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229 | if(y.key <= z.key) break; |
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230 | h->a[j] = z; |
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231 | h->p[z.item] = j; |
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232 | j = k; |
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233 | k = 2 * j; |
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234 | } |
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235 | |
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236 | /* Insert the root in the correct place in the heap. */ |
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237 | h->a[j] = y; |
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238 | h->p[y.item] = j; |
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239 | } |
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240 | |
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241 | |
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242 | |
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243 | |
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244 | /*** Implement the universal heap structure type ***/ |
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245 | |
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246 | /* Binary heap wrapper functions. */ |
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247 | |
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248 | int _bh_delete_min(void *h) { |
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249 | int v; |
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250 | v = bh_min((bheap_t *)h); |
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251 | bh_delete((bheap_t *)h, v); |
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252 | return v; |
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253 | } |
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254 | |
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255 | void _bh_insert(void *h, int v, double k) { |
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256 | bh_insert((bheap_t *)h, v, k); |
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257 | } |
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258 | |
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259 | void _bh_decrease_key(void *h, int v, double k) { |
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260 | bh_decrease_key((bheap_t *)h, v, k); |
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261 | } |
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262 | |
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263 | int _bh_n(void *h) { |
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264 | return ((bheap_t *)h)->n; |
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265 | } |
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266 | |
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267 | long _bh_key_comps(void *h) { |
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268 | return ((bheap_t *)h)->key_comps; |
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269 | } |
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270 | |
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271 | void *_bh_alloc(int n) { |
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272 | return bh_alloc(n); |
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273 | } |
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274 | |
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275 | void _bh_free(void *h) { |
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276 | bh_free((bheap_t *)h); |
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277 | } |
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278 | |
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279 | void _bh_dump(void *h) { |
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280 | bh_dump((bheap_t *)h); |
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281 | } |
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282 | |
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283 | /* Binary heap info. */ |
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284 | const heap_info_t BHEAP_info = { |
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285 | _bh_delete_min, |
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286 | _bh_insert, |
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287 | _bh_decrease_key, |
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288 | _bh_n, |
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289 | _bh_key_comps, |
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290 | _bh_alloc, |
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291 | _bh_free, |
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292 | _bh_dump |
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293 | }; |
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