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SplayTree.cpp
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SplayTree.cpp
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#include "SplayTree.h"
using namespace std;
SplayTree::SplayTree(size_t nElems) {
root = treeFor(0, nElems);
leftTree = nullptr;
rightTree = nullptr;
rightOfLeftTree = nullptr;
leftOfRightTree = nullptr;
}
/**
* Constructs a perfectly balanced tree for the values in the range
* [low, high).
*/
SplayTree::Node*
SplayTree::treeFor(size_t low, size_t high) {
/* Base Case: The empty range is represented by an empty tree. */
if (low == high) return nullptr;
/* Otherwise, pull out the middle, then recursively construct trees for the
* left and right ranges.
*/
size_t mid = low + (high - low) / 2;
return new Node {
mid,
treeFor(low, mid),
treeFor(mid + 1, high)
};
}
/**
* Frees all memory used by this tree.
*/
SplayTree::~SplayTree() {
/* This is the same algorithm we used in PS3. It takes time O(n) and uses
* only O(1) auxiliary memory.
*/
while (root != nullptr) {
/* If the root has no left subtree, just delete the root. */
if (root->left == nullptr) {
Node* next = root->right;
delete root;
root = next;
}
/* Otherwise, the root has a left subtree. Do a right rotation to move
* that child to the left.
*/
else {
Node* child = root->left;
root->left = child->right;
child->right = root;
root = child;
}
}
}
//Perform the assemble operation as detailed in the paper
void SplayTree::assemble() const {
Node * A = root->left;
Node * B = root->right;
link_right(A);
link_left(B);
root->left = leftTree;
root->right = rightTree;
leftTree = nullptr;
rightTree = nullptr;
rightOfLeftTree = nullptr;
leftOfRightTree = nullptr;
}
//This is the zig case for left
void SplayTree::case_one() const {
Node * x = root;
root = root->left;
x->left = nullptr;
link_left(x);
}
//This is the zig case for right
void SplayTree::case_one_opposite() const {
Node * x = root;
root = root->right;
x->right = nullptr;
link_right(x);
}
//Adds to leftmost node of right tree
void SplayTree::link_left(Node * n) const {
if(leftOfRightTree == nullptr) {
rightTree = n;
leftOfRightTree = n;
}
else {
leftOfRightTree->left = n;
leftOfRightTree = n;
}
}
//Adds to rightmost node of left tree
void SplayTree::link_right(Node * n) const {
if(rightOfLeftTree == nullptr) {
leftTree = n;
rightOfLeftTree = n;
}
else {
rightOfLeftTree->right = n;
rightOfLeftTree = n;
}
}
/**
* Determines whether the specified key is present in the splay tree.
*/
bool SplayTree::contains(size_t key) const {
//Base case, we found our element
if(root->key == key)
{
assemble();
return true;
} else if(key < root->key)
{
//Element not in tree
if(root->left == nullptr)
{
assemble();
return false;
}
size_t y_val = root->left->key;
//zig case and found it
if(key == y_val) //Case 1
{
case_one();
assemble();
return true;
}
else if(key < y_val) //Case 2
{
//not in tree
Node * z = root->left->left;
if(z == nullptr) { //Case 2.1
case_one();
assemble();
return false;
}
//zig-zig case
else { //Case 2.2
Node * x = root;
Node * y = root->left;
Node * B = y->right;
x->left = B;
y->left = nullptr;
y->right = x;
link_left(y);
root = z;
return contains(key);
}
}
else //Case 3
{ // key > y_val, or case 3
Node * z = root->left->right;
//not in tree
if(z == nullptr) {
case_one();
assemble();
return false;
}
//zig zag case
else { //Case 3.2
Node * x = root;
Node * y = root->left;
x->left = nullptr;
y->right = nullptr;
link_right(y);
link_left(x);
root = z;
return contains(key);
}
}
}
else
{
//not in tree
if(root->right == nullptr)
{
assemble();
return false;
}
size_t y_val = root->right->key;
//zig case
if(key == y_val) //Case 1
{
case_one_opposite();
assemble();
return true;
}
else if(key > y_val) //Case 2
{
Node * z = root->right->right;
//not in tree
if(z == nullptr) { //Case 2.1
case_one_opposite();
assemble();
return false;
}
//zig-zig case
else { //Case 2.2
Node * x = root;
Node * y = root->right;
Node * B = y->left;
x->right = B;
y->right = nullptr;
y->left = x;
link_right(y);
root = z;
return contains(key);
}
}
else //Case 3
{ // key > y_val, or case 3
Node * z = root->right->left;
//not in tree
if(z == nullptr) {
case_one_opposite();
assemble();
return false;
}
//zig-zag case
else { //Case 3.2
Node * x = root;
Node * y = root->right;
x->right = nullptr;
y->left = nullptr;
link_left(y);
link_right(x);
root = z;
return contains(key);
}
}
}
}