Clasele 11-12 lecția 7 - 13 nov 2015

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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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