Clasele 11-12 lecția 7 - 13 nov 2015
From Algopedia
Arbori binari echilibrați augmentați
#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <algorithm>
using std::pair;
class Treap {
public:
int value;
int priority; // Max-Heap
int size;
bool reversed;
Treap* left;
Treap* right;
};
Treap* duplicate(const Treap* node) {
Treap* answer = new Treap;
answer->value = node->value;
answer->priority = node->priority;
answer->size = node->size;
answer->reversed = node->reversed;
answer->left = node->left;
answer->right = node->right;
return answer;
}
Treap* propagate(Treap* node) {
Treap* newNode;
if (node != NULL && node->reversed) {
newNode = duplicate(node);
newNode->reversed = false;
if (node->left != NULL) {
newNode->right = duplicate(node->left);
newNode->right->reversed ^= 1;
} else {
newNode->right = NULL;
}
if (node->right != NULL) {
newNode->left = duplicate(node->right);
newNode->left->reversed ^= 1;
} else {
newNode->left = NULL;
}
} else {
newNode = node;
}
return newNode;
}
Treap* reverse(Treap* node) {
if (node == NULL) {
return NULL;
} else {
Treap* newNode = duplicate(node);
newNode->reversed ^= 1;
return newNode;
}
}
int getSize(Treap* node) {
if (node == NULL) {
return 0;
} else {
return node->size;
}
}
Treap* updateSize(Treap* node) {
if (node != NULL)
node->size =
getSize(node->left) + 1 + getSize(node->right);
return node;
}
Treap* find(Treap* node, int index) {
node = propagate(node);
if (node == NULL || node->size <= index) {
return NULL;
}
if (index < getSize(node->left)) {
return find(node->left, index);
} else if (index == getSize(node->left)) {
return node;
} else { // if (leftSize < index)
return find(node->right, index - getSize(node->left) - 1);
}
}
pair<Treap*, Treap*> split(Treap* node, int size1) {
node = propagate(node);
pair<Treap*, Treap*> answer;
if (node == NULL) {
answer.first = NULL;
answer.second = NULL;
} else {
assert(size1 <= node->size);
if (getSize(node->left) + 1 <= size1) {
answer.first = new Treap;
answer.first->value = node->value;
answer.first->priority = node->priority;
answer.first->reversed = false;
answer.first->left = node->left;
pair<Treap*, Treap*> splitAnswer =
split(node->right, size1 - (getSize(node->left) + 1));
answer.first->right = splitAnswer.first;
answer.second = splitAnswer.second;
} else { // size1 < leftSize + 1
answer.second = new Treap;
answer.second->value = node->value;
answer.second->priority = node->priority;
answer.second->reversed = false;
answer.second->right = node->right;
pair<Treap*, Treap*> splitAnswer =
split(node->left, size1);
answer.first = splitAnswer.first;
answer.second->left = splitAnswer.second;
}
updateSize(answer.first);
updateSize(answer.second);
}
return answer;
}
Treap* join(Treap* first, Treap* second) {
first = propagate(first);
second = propagate(second);
if (first == NULL) {
return second;
} else if (second == NULL) {
return first;
} else if (second->priority < first->priority) {
Treap* newNode = duplicate(first);
newNode->right = join(first->right, second);
updateSize(newNode);
return newNode;
} else { // if (first->priority < second->priority)
Treap* newNode = duplicate(second);
newNode->left = join(first, second->left);
updateSize(newNode);
return newNode;
}
}
int myRandom() {
return (rand() << 15) ^ rand();
}
Treap* insert(Treap* node, int index, int value, int priority = myRandom()) {
assert(index <= getSize(node));
node = propagate(node);
Treap* newNode = NULL;
if (node == NULL || node->priority < priority) {
newNode = new Treap;
pair<Treap*, Treap*> splitAnswer = split(node, index);
newNode->value = value;
newNode->priority = priority;
newNode->left = splitAnswer.first;
newNode->right = splitAnswer.second;
newNode->reversed = false;
} else if (getSize(node->left) < index) {
newNode = duplicate(node);
newNode->right = insert(node->right,
index - (getSize(node->left) + 1),
value, priority);
} else { // if (value <= node->value)
newNode = duplicate(node);
newNode->left = insert(node->left, index, value, priority);
}
updateSize(newNode);
return newNode;
}
Treap* erase(Treap* node, int index, int size) {
pair<Treap*, Treap*> aux;
aux = split(node, index);
Treap* t1 = aux.first;
aux = split(aux.second, size);
//Treap* t2 = aux.first;
Treap* t3 = aux.second;
return join(t1, t3);
}
Treap* reverse(Treap* node, int index, int size) {
pair<Treap*, Treap*> aux;
aux = split(node, index);
Treap* t1 = aux.first;
aux = split(aux.second, size);
Treap* t2 = reverse(aux.first);
Treap* t3 = aux.second;
return join(join(t1, t2), t3);
}
void dump(Treap* node, int depth = 0) {
node = propagate(node);
if (node != NULL) {
dump(node->left, depth + 1);
printf("%12d %2d ", node->priority, node->size);
for (int i = 0; i < depth; i++) {
printf(" ");
}
printf("%d\n", node->value);
dump(node->right, depth + 1);
}
}
int main(void) {
srand(time(NULL));
Treap* arb1 = NULL;
Treap* arb2 = insert(arb1, 0, 5);
Treap* arb3 = insert(arb2, 0, 3);
Treap* arb4 = insert(arb3, 1, 6);
Treap* arb5 = insert(arb4, 2, 4);
Treap* arb6 = insert(arb5, 3, 9);
Treap* arb7 = reverse(arb6);
Treap* arb8 = insert(arb7, 2, 1);
Treap* arb9 = insert(arb8, 1, 7);
Treap* arb10 = reverse(arb9, 2, 2);
Treap* arb11 = erase(arb10, 2, 2);
dump(arb1);
printf("\n");
dump(arb2);
printf("\n");
dump(arb3);
printf("\n");
dump(arb4);
printf("\n");
dump(arb5);
printf("\n");
dump(arb6);
printf("\n");
dump(arb7);
printf("\n");
dump(arb8);
printf("\n");
dump(arb9);
printf("\n");
dump(arb10);
printf("\n");
dump(arb11);
printf("\n");
return 0;
}
Temă
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