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Van Emde Boas.c
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Van Emde Boas.c
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#include <stdio.h>
#include <stdbool.h>
#include <math.h>
#include <stdlib.h>
typedef struct VEBTree {
int universeSize;
int minimum;
int maximum;
struct VEBTree* summary;
struct VEBTree** cluster;
} VEBTree;
VEBTree* createVEBTree(int size) {
VEBTree* tree = (VEBTree*)malloc(sizeof(VEBTree));
tree->universeSize = size;
tree->minimum = -1;
tree->maximum = -1;
tree->summary = NULL;
tree->cluster = NULL;
if (size > 2) {
int upperSize = (int)ceil(sqrt(size));
int lowerSize = (int)floor(sqrt(size));
tree->summary = createVEBTree(upperSize);
tree->cluster = (VEBTree**)malloc(sizeof(VEBTree*) * upperSize);
for (int i = 0; i < upperSize; i++)
tree->cluster[i] = createVEBTree(lowerSize);
}
return tree;
}
void insert(VEBTree* tree, int key) {
if (tree->minimum == -1) {
tree->minimum = key;
tree->maximum = key;
return;
}
if (key < tree->minimum) {
int temp = key;
key = tree->minimum;
tree->minimum = temp;
}
if (tree->universeSize > 2) {
if (tree->cluster[key / (int)ceil(sqrt(tree->universeSize))]->minimum == -1)
insert(tree->summary, key / (int)ceil(sqrt(tree->universeSize)));
insert(tree->cluster[key / (int)ceil(sqrt(tree->universeSize))], key % (int)ceil(sqrt(tree->universeSize)));
}
if (key > tree->maximum)
tree->maximum = key;
}
void remove(VEBTree* tree, int key) {
if (tree->minimum == tree->maximum) {
tree->minimum = -1;
tree->maximum = -1;
return;
}
if (tree->universeSize == 2) {
if (key == 0)
tree->minimum = 1;
else
tree->minimum = 0;
tree->maximum = tree->minimum;
return;
}
if (key == tree->minimum) {
int firstCluster = tree->summary->minimum;
key = firstCluster * (int)ceil(sqrt(tree->universeSize)) + tree->cluster[firstCluster]->minimum;
tree->minimum = key;
}
remove(tree->cluster[key / (int)ceil(sqrt(tree->universeSize))], key % (int)ceil(sqrt(tree->universeSize)));
if (tree->cluster[key / (int)ceil(sqrt(tree->universeSize))]->minimum == -1)
remove(tree->summary, key / (int)ceil(sqrt(tree->universeSize)));
if (key == tree->maximum) {
if (tree->summary->minimum == -1)
tree->maximum = tree->minimum;
else {
int lastCluster = tree->summary->maximum;
tree->maximum = lastCluster * (int)ceil(sqrt(tree->universeSize)) + tree->cluster[lastCluster]->maximum;
}
}
}
int successor(VEBTree* tree, int key) {
if (tree->universeSize == 2) {
if (key == 0 && tree->maximum == 1)
return 1;
else
return -1;
}
if (tree->minimum != -1 && key < tree->minimum)
return tree->minimum;
int maxLow = tree->cluster[key / (int)ceil(sqrt(tree->universeSize))]->maximum;
if (maxLow != -1 && key % (int)ceil(sqrt(tree->universeSize)) < maxLow) {
int offset = successor(tree->cluster[key / (int)ceil(sqrt(tree->universeSize))], key % (int)ceil(sqrt(tree->universeSize)));
return key / (int)ceil(sqrt(tree->universeSize)) * (int)ceil(sqrt(tree->universeSize)) + offset;
}
int succCluster = successor(tree->summary, key / (int)ceil(sqrt(tree->universeSize)));
if (succCluster == -1)
return -1;
int offset = tree->cluster[succCluster]->minimum;
return succCluster * (int)ceil(sqrt(tree->universeSize)) + offset;
}
int predecessor(VEBTree* tree, int key) {
if (tree->universeSize == 2) {
if (key == 1 && tree->minimum == 0)
return 0;
else
return -1;
}
if (tree->maximum != -1 && key > tree->maximum)
return tree->maximum;
int minLow = tree->cluster[key / (int)ceil(sqrt(tree->universeSize))]->minimum;
if (minLow != -1 && key % (int)ceil(sqrt(tree->universeSize)) > minLow) {
int offset = predecessor(tree->cluster[key / (int)ceil(sqrt(tree->universeSize))], key % (int)ceil(sqrt(tree->universeSize)));
return key / (int)ceil(sqrt(tree->universeSize)) * (int)ceil(sqrt(tree->universeSize)) + offset;
}
int predCluster = predecessor(tree->summary, key / (int)ceil(sqrt(tree->universeSize)));
if (predCluster == -1) {
if (tree->minimum != -1 && key > tree->minimum)
return tree->minimum;
else
return -1;
}
int offset = tree->cluster[predCluster]->maximum;
return predCluster * (int)ceil(sqrt(tree->universeSize)) + offset;
}
bool contains(VEBTree* tree, int key) {
if (key == tree->minimum || key == tree->maximum)
return true;
if (tree->universeSize == 2)
return false;
return contains(tree->cluster[key / (int)ceil(sqrt(tree->universeSize))], key % (int)ceil(sqrt(tree->universeSize)));
}
void destroyVEBTree(VEBTree* tree) {
if (tree->summary != NULL)
destroyVEBTree(tree->summary);
if (tree->cluster != NULL) {
int upperSize = (int)ceil(sqrt(tree->universeSize));
for (int i = 0; i < upperSize; i++)
destroyVEBTree(tree->cluster[i]);
free(tree->cluster);
}
free(tree);
}
int main() {
VEBTree* vebTree = createVEBTree(16);
insert(vebTree, 4);
insert(vebTree, 1);
insert(vebTree, 8);
insert(vebTree, 10);
printf("%d\n", contains(vebTree, 4)); // Output: 1 (true)
printf("%d\n", contains(vebTree, 5)); // Output: 0 (false)
printf("%d\n", successor(vebTree, 4)); // Output: 8
printf("%d\n", predecessor(vebTree, 4)); // Output: 1
remove(vebTree, 4);
printf("%d\n", contains(vebTree, 4)); // Output: 0 (false)
destroyVEBTree(vebTree);
return 0;
}