/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/**
* A sorted tree with optimal access times, where recently-accessed elements
* are faster to access again.
*/
#ifndef mozilla_SplayTree_h
#define mozilla_SplayTree_h
#include "mozilla/Assertions.h"
#include "mozilla/Attributes.h"
namespace mozilla {
template <class T, class C>
class SplayTree;
template <typename T>
class SplayTreeNode {
public:
template <class A, class B>
friend class SplayTree;
SplayTreeNode() : mLeft(nullptr), mRight(nullptr), mParent(nullptr) {}
private:
T* mLeft;
T* mRight;
T* mParent;
};
/**
* Class which represents a splay tree.
* Splay trees are balanced binary search trees for which search, insert and
* remove are all amortized O(log n), but where accessing a node makes it
* faster to access that node in the future.
*
* T indicates the type of tree elements, Comparator must have a static
* compare(const T&, const T&) method ordering the elements. The compare
* method must be free from side effects.
*/
template <typename T, class Comparator>
class SplayTree {
T* mRoot;
public:
constexpr SplayTree() : mRoot(nullptr) {}
bool empty() const { return !mRoot; }
T* find(const T& aValue) {
if (empty()) {
return nullptr;
}
T* last = lookup(aValue);
splay(last);
return Comparator::compare(aValue, *last) == 0 ? last : nullptr;
}
void insert(T* aValue) {
MOZ_ASSERT(!find(*aValue), "Duplicate elements are not allowed.");
if (!mRoot) {
mRoot = aValue;
return;
}
T* last = lookup(*aValue);
int cmp = Comparator::compare(*aValue, *last);
finishInsertion(last, cmp, aValue);
}
T* findOrInsert(const T& aValue);
T* remove(const T& aValue) {
T* last = lookup(aValue);
MOZ_ASSERT(last, "This tree must contain the element being removed.");
MOZ_ASSERT(Comparator::compare(aValue, *last) == 0);
// Splay the tree so that the item to remove is the root.
splay(last);
MOZ_ASSERT(last == mRoot);
// Find another node which can be swapped in for the root: either the
// rightmost child of the root's left, or the leftmost child of the
// root's right.
T* swap;
T* swapChild;
if (mRoot->mLeft) {
swap = mRoot->mLeft;
while (swap->mRight) {
swap = swap->mRight;
}
swapChild = swap->mLeft;
} else if (mRoot->mRight) {
swap = mRoot->mRight;
while (swap->mLeft) {
swap = swap->mLeft;
}
swapChild = swap->mRight;
} else {
T* result = mRoot;
mRoot = nullptr;
return result;
}
// The selected node has at most one child, in swapChild. Detach it
// from the subtree by replacing it with that child.
if (swap == swap->mParent->mLeft) {
swap->mParent->mLeft = swapChild;
} else {
swap->mParent->mRight = swapChild;
}
if (swapChild) {
swapChild->mParent = swap->mParent;
}
// Make the selected node the new root.
mRoot = swap;
mRoot->mParent = nullptr;
mRoot->mLeft = last->mLeft;
mRoot->mRight = last->mRight;
if (mRoot->mLeft) {
mRoot->mLeft->mParent = mRoot;
}
if (mRoot->mRight) {
mRoot->mRight->mParent = mRoot;
}
return last;
}
T* removeMin() {
MOZ_ASSERT(mRoot, "No min to remove!");
T* min = mRoot;
while (min->mLeft) {
min = min->mLeft;
}
return remove(*min);
}
// For testing purposes only.
void checkCoherency() { checkCoherency(mRoot, nullptr); }
private:
/**
* Returns the node in this comparing equal to |aValue|, or a node just
* greater or just less than |aValue| if there is no such node.
*/
T* lookup(const T& aValue) {
MOZ_ASSERT(!empty());
T* node = mRoot;
T* parent;
do {
parent = node;
int c = Comparator::compare(aValue, *node);
if (c == 0) {
return node;
} else if (c < 0) {
node = node->mLeft;
} else {
node = node->mRight;
}
} while (node);
return parent;
}
void finishInsertion(T* aLast, int32_t aCmp, T* aNew) {
MOZ_ASSERT(aCmp, "Nodes shouldn't be equal!");
T** parentPointer = (aCmp < 0) ? &aLast->mLeft : &aLast->mRight;
MOZ_ASSERT(!*parentPointer);
*parentPointer = aNew;
aNew->mParent = aLast;
splay(aNew);
}
/**
* Rotate the tree until |node| is at the root of the tree. Performing
* the rotations in this fashion preserves the amortized balancing of
* the tree.
*/
void splay(T* aNode) {
MOZ_ASSERT(aNode);
while (aNode != mRoot) {
T* parent = aNode->mParent;
if (parent == mRoot) {
// Zig rotation.
rotate(aNode);
MOZ_ASSERT(aNode == mRoot);
return;
}
T* grandparent = parent->mParent;
if ((parent->mLeft == aNode) == (grandparent->mLeft == parent)) {
// Zig-zig rotation.
rotate(parent);
rotate(aNode);
} else {
// Zig-zag rotation.
rotate(aNode);
rotate(aNode);
}
}
}
void rotate(T* aNode) {
// Rearrange nodes so that aNode becomes the parent of its current
// parent, while preserving the sortedness of the tree.
T* parent = aNode->mParent;
if (parent->mLeft == aNode) {
// x y
// y c ==> a x
// a b b c
parent->mLeft = aNode->mRight;
if (aNode->mRight) {
aNode->mRight->mParent = parent;
}
aNode->mRight = parent;
} else {
MOZ_ASSERT(parent->mRight == aNode);
// x y
// a y ==> x c
// b c a b
parent->mRight = aNode->mLeft;
if (aNode->mLeft) {
aNode->mLeft->mParent = parent;
}
aNode->mLeft = parent;
}
aNode->mParent = parent->mParent;
parent->mParent = aNode;
if (T* grandparent = aNode->mParent) {
if (grandparent->mLeft == parent) {
grandparent->mLeft = aNode;
} else {
grandparent->mRight = aNode;
}
} else {
mRoot = aNode;
}
}
T* checkCoherency(T* aNode, T* aMinimum) {
if (mRoot) {
MOZ_RELEASE_ASSERT(!mRoot->mParent);
}
if (!aNode) {
MOZ_RELEASE_ASSERT(!mRoot);
return nullptr;
}
if (!aNode->mParent) {
MOZ_RELEASE_ASSERT(aNode == mRoot);
}
if (aMinimum) {
MOZ_RELEASE_ASSERT(Comparator::compare(*aMinimum, *aNode) < 0);
}
if (aNode->mLeft) {
MOZ_RELEASE_ASSERT(aNode->mLeft->mParent == aNode);
T* leftMaximum = checkCoherency(aNode->mLeft, aMinimum);
MOZ_RELEASE_ASSERT(Comparator::compare(*leftMaximum, *aNode) < 0);
}
if (aNode->mRight) {
MOZ_RELEASE_ASSERT(aNode->mRight->mParent == aNode);
return checkCoherency(aNode->mRight, aNode);
}
return aNode;
}
SplayTree(const SplayTree&) = delete;
void operator=(const SplayTree&) = delete;
};
template <typename T, class Comparator>
T* SplayTree<T, Comparator>::findOrInsert(const T& aValue) {
if (!mRoot) {
mRoot = new T(aValue);
return mRoot;
}
T* last = lookup(aValue);
int cmp = Comparator::compare(aValue, *last);
if (!cmp) {
return last;
}
T* t = new T(aValue);
finishInsertion(last, cmp, t);
return t;
}
} /* namespace mozilla */
#endif /* mozilla_SplayTree_h */