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Initial commit for working on red-black tree algorithms

This commit is contained in:
Shaun Reed 2021-06-08 14:43:39 -04:00
parent 49eb64f320
commit f45e479603
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cpp/algorithms/trees/redblack/CMakeLists.txt Normal file
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###############################################################################
## Author: Shaun Reed ##
## Legal: All Content (c) 2021 Shaun Reed, all rights reserved ##
## About: A basic CMakeLists configuration to test RBT implementation ##
## ##
## Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 ##
##############################################################################
#
cmake_minimum_required(VERSION 3.15)
project (
#[[NAME]] RedBlackTree
VERSION 1.0
DESCRIPTION "A project for testing red-black tree algorithms"
LANGUAGES CXX
)
add_library(lib-redblack "redblack.cpp")
add_executable(test-redblack "driver.cpp")
target_link_libraries(test-redblack lib-redblack)

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cpp/algorithms/trees/redblack/driver.cpp Normal file
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/*#############################################################################
## Author: Shaun Reed ##
## Legal: All Content (c) 2021 Shaun Reed, all rights reserved ##
## About: Driver program to test RBT algorithms from MIT intro to algorithms ##
## ##
## Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 ##
###############################################################################
*/
#include "redblack.h"
#include <iostream>
#include <vector>
int main (const int argc, const char * argv[])
{
BinarySearchTree testTree;
std::vector<int> inputValues {2, 6, 9, 1, 5, 8, 10};
// Alternative input values
// std::vector<int> inputValues {10, 12, 6, 4, 20, 8, 7, 15, 13};
std::cout << "Building binary search tree with input: ";
for (const auto &value : inputValues) std::cout << value << ", ";
std::cout << std::endl;
for (const auto &value : inputValues) testTree.insert(value);
std::cout << "\nInorder traversal: \n";
testTree.printInOrder();
std::cout << std::endl;
std::cout << "Postorder traversal: \n";
testTree.printPostOrder();
std::cout << std::endl;
std::cout << "Preorder traversal: \n";
testTree.printPreOrder();
std::cout << std::endl;
std::cout << "\nMinimum value: " << testTree.findMin()->element << std::endl;
std::cout << "Maximum value: " << testTree.findMax()->element << std::endl;
// Test removing a node, printing the result in-order
std::cout << "\nRemoving root value...\n";
testTree.remove(testTree.getRoot()->element);
// Can use inline function to remove a value directly for testing -
// testTree.remove(6);
std::cout << "Inorder traversal: \n";
testTree.printInOrder();
std::cout << std::endl;
// Test copy constructor
std::cout << "\nCloning testTree to testTree2...\n";
BinarySearchTree testTree2 = testTree;
std::cout << "Inorder traversal of the cloned testTree2: \n";
testTree2.printInOrder();
std::cout << std::endl;
// Test assignment operator
std::cout << "\nCloning testTree to testTree3...\n";
BinarySearchTree testTree3;
testTree3 = testTree;
std::cout << "Inorder traversal of the cloned testTree3 tree: \n";
testTree3.printInOrder();
std::cout << std::endl;
// Test emptying the BST
std::cout << "\nEmptying testTree...\n";
testTree.makeEmpty();
std::cout << "testTree isEmpty: " << (testTree.isEmpty() ? "true" : "false");
std::cout << "\ntestTree2 isEmpty: " << (testTree2.isEmpty() ? "true" : "false");
std::cout << "\ntestTree3 isEmpty: " << (testTree3.isEmpty() ? "true" : "false");
// Testing integrity of deep copy (cloned) data after deletion of testTree
std::cout << "\n\nTesting integrity of previously cloned testTree2...\n";
std::cout << "Inorder traversal of the cloned testTree2: \n";
testTree2.printInOrder();
std::cout << std::endl;
std::cout << "Inorder traversal of the cloned testTree3: \n";
testTree3.printInOrder();
std::cout << std::endl;
std::cout << "\nChecking if tree contains value of 6: ";
std::cout << (testTree2.contains(6) ? "true" : "false") << std::endl;
std::cout << "Checking if tree contains value of 600: ";
std::cout << (testTree2.contains(600) ? "true" : "false") << std::endl;
std::cout << "\nSuccessor of node with value 6: "
<< testTree2.successor(testTree2.search(6))->element;
std::cout << "\nPredecessor of node with value 6: "
<< testTree2.predecessor(testTree2.search(6))->element;
std::cout << std::endl;
}

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cpp/algorithms/trees/redblack/redblack.cpp Normal file
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/*#############################################################################
## Author: Shaun Reed ##
## Legal: All Content (c) 2021 Shaun Reed, all rights reserved ##
## About: An example of a red-black tree implementation ##
## The algorithms in this example are seen in MIT Intro to Algorithms ##
## ##
## Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 ##
##############################################################################
*/
#include "redblack.h"
/*******************************************************************************
* Constructors, Destructors, Operators
*******************************************************************************/
/** BinarySearchTree Copy Assignment Operator
* @brief Empty the calling object's root BinaryNode, and copy the rhs data
*
* Runs in O( n ) time, since we visit each node in the BST once
* + Where n is the total number of nodes within the BST
*
* makeEmpty() and clone() are both O( n ), and we call each sequentially
* + This would appear to be O( 2n ), but we drop the constant of 2
*
* @param rhs The BST to copy, beginning from its root BinaryNode
* @return BinarySearchTree The copied BinarySearchTree object
*/
BinarySearchTree& BinarySearchTree::operator=(const BinarySearchTree &rhs)
{
// If the objects are already equal, do nothing
if (this == &rhs) return *this;
// Empty this->root
makeEmpty(root);
// Copy rhs to this->root
root = clone(rhs.root);
return *this;
}
/* BinaryNode Copy Constructor
*
* Runs in O( n ) time, since we visit each node in the BST once
* + Where n is the total number of nodes within the BST
*
* @param rhs An existing BST to initialize this node (and children) with
*/
BinarySearchTree::BinaryNode::BinaryNode(BinaryNode * toCopy)
{
// Base case, breaks recursion when we hit a null node
// + Returns to the previous call in the stack
if (toCopy == nullptr) return;
// Set the element of this BinaryNode to the value in toCopy->element
element = toCopy->element;
// If there is a left / right node, copy it using recursion
// + If there is no left / right node, set them to nullptr
if (toCopy->left != nullptr) {
left = new BinaryNode(toCopy->left);
left->parent = this;
}
if (toCopy->right != nullptr) {
right = new BinaryNode(toCopy->right);
right->parent = this;
}
}
/*******************************************************************************
* Public Member Functions
*******************************************************************************/
/** contains
* @brief Determines if value exists within a BinaryNode and its children
*
* Runs in O( height ) time, given the height of the current BST
* + In the worst case, we search for a node at the bottom of the BST
*
* @param value The value to search for within the BST
* @param start The root BinaryNode to begin the search
* @return true If the value is found within the root node or its children
* @return false If the value is not found within the root node or its children
*/
bool BinarySearchTree::contains(const int &value, BinaryNode *start) const
{
// If tree is empty
if (start == nullptr) return false;
// If x is smaller than our current value
else if (value < start->element) return contains(value, start->left);
// If x is larger than our current value, check the right node
else if (value > start->element) return contains(value, start->right);
else return true;
}
/** makeEmpty
* @brief Recursively delete the given root BinaryNode and all of its children
*
* Runs in O( n ) time, since we need to visit each node in the tree once
* + Where n is the total number of nodes in the tree
*
* @param tree The root BinaryNode to delete, along with all child nodes
*/
void BinarySearchTree::makeEmpty(BinarySearchTree::BinaryNode * & tree)
{
// Base case: When all nodes have been deleted, tree is a nullptr
// + Breaks from recursion
if (tree != nullptr) {
makeEmpty(tree->left);
makeEmpty(tree->right);
delete tree;
tree = nullptr;
}
}
/** isEmpty
* @brief Determine whether or not the calling BST object is empty
*
* Runs in constant time, O( 1 )
*
* @return true If this->root node points to an empty tree (nullptr)
* @return false If this->root node points to a constructed BinaryNode
*/
bool BinarySearchTree::isEmpty() const
{
return root == nullptr;
}
/** insert
* @brief Insert a value into the tree starting at a given BinaryNode
* + Uses recursion
*
* Runs in O( height ) time, since in the worst case we insert the node at the
* + bottom of the BST.
*
* @param newValue The value to be inserted
* @param start The BinaryNode to begin insertion
* @param prevNode The last checked BinaryNode
* + prevNode is used to initialize new node's parent
*/
void BinarySearchTree::insert(const int &newValue,
BinaryNode *&start, BinaryNode *prevNode)
{
// Base case: We found a valid position which is empty for the newValue
if (start == nullptr) {
// Build a new node, place it at the current position
// + Breaks out of recursion
start = new BinaryNode(newValue, nullptr, nullptr, prevNode);
}
else if (newValue < start->element) insert(newValue, start->left, start);
else if (newValue > start->element) insert(newValue, start->right, start);
else return;
}
/** remove
* @brief Removes a value from the BST of the given BinaryNode
*
* Runs in O( height ) time, where findMin() is the limiting function
* + remove() and transplant() otherwise run in constant time, without findMin()
*
* @param removeNode The BinaryNode to remove from the BST
*/
void BinarySearchTree::remove(BinaryNode *removeNode)
{
if (removeNode->left == nullptr) {
// removeNode has no left node; Replace removeNode with removeNode->right
// + It doesn't matter if removeNode->right is nullptr or a valid node
// + Since there is no left node, this is the only possible valid transplant
// Transplant the right node and its subtree over this node
transplant(removeNode, removeNode->right);
}
else if (removeNode->right == nullptr) {
// removeNode has no right node; Replace removeNode with removeNode->right
// + removeNode->left exists, in this case
transplant(removeNode, removeNode->left);
}
else {
// removeNode has a right and left node, find the next value in-order
// + findMin(removeNode->right) returns the next largest value in the BST
BinaryNode *minNode = findMin(removeNode->right);
// If the next value in-order is not removeNode->right
if (minNode->parent != removeNode) {
// replace minNode with the next largest attached value, minNode->right
transplant(minNode, minNode->right);
// Set minNode->right to the node at removeNode->right
// + Update the parent of removeNode->right accordingly in the next line
minNode->right = removeNode->right;
minNode->right->parent = minNode;
}
// Replace removeNode with the next node in-order
// + Update the minNode's left and parent nodes in the following lines
transplant(removeNode, minNode);
minNode->left = removeNode->left;
minNode->left->parent = minNode;
}
}
/** printInOrder
* @brief Uses recursion to output left subtree, root node, then right subtrees
*
* Runs in O( n ) time, since we need to visit each node in the tree once
* + Where n is the total number of nodes within the BST
*
* @param start The root BinaryNode to begin the 'In Order' output
*/
void BinarySearchTree::printInOrder(BinaryNode *start) const
{
if(start != nullptr) {
printInOrder(start->left);
std::cout << start->element << " ";
printInOrder(start->right);
}
}
/** printPostOrder
* @brief Uses recursion to output left subtree, right subtree, then the root
*
* Runs in O( n ) time, since we need to visit each node in the tree once
* + Where n is the total number of nodes within the BST
*
* @param start The root BinaryNode to begin the 'Post Order' output
*/
void BinarySearchTree::printPostOrder(BinaryNode *start) const
{
if (start != nullptr) {
printPostOrder(start->left);
printPostOrder(start->right);
std::cout << start->element << " ";
}
}
/** printPreOrder
* @brief Uses recursion to output the root, then left subtree, right subtrees
*
* Runs in O( n ) time, since we need to visit each node in the tree once
* + Where n is the total number of nodes within the BST
*
* @param start The root BinaryNode to begin the 'Pre Order' output
*/
void BinarySearchTree::printPreOrder(BinaryNode *start) const
{
if (start != nullptr) {
std::cout << start->element << " ";
printPreOrder(start->left);
printPreOrder(start->right);
}
}
/** search
* @brief Search for a given value within a tree or subtree using recursion
*
* Runs in O( height ) time
* + In the worst case, we are searching for a node at the bottom of the BST
*
* @param value The value to search for
* @param start The node to start the search from; Can be a subtree
* @return A pointer to the BinaryNode containing the value within the BST
* + Returns nullptr if the node was not found
*/
BinarySearchTree::BinaryNode *BinarySearchTree::search(
const int &value, BinaryNode *start) const
{
// Base case: If BST is empty, or holds the value we are searching for
// + Breaks out of recursion
if (start == nullptr || start->element == value) return start;
else if (start->element < value) return search(value, start->right);
else if (start->element > value) return search(value, start->left);
}
/** findMin
* @brief Find the minimum value within the BST of the given BinaryNode
* + This example uses a while loop; findMax uses recursion
*
* Runs in O( height ) time
* + In the worst case, we traverse to to the left-most bottom of the BST
*
* @param start The root BinaryNode to begin checking values
* @return A pointer to the BinaryNode which contains the smallest value
* + Returns nullptr if BST is empty
*/
BinarySearchTree::BinaryNode * BinarySearchTree::findMin(BinaryNode *start) const
{
// If our tree is empty
if (start == nullptr) return nullptr;
while (start->left != nullptr) start = start->left;
// If current node has no smaller children, it is min
return start;
}
/** findMax
* @brief Find the maximum value within the BST of the given BinaryNode
* + This example uses recursion; findMin uses a while loop
* ++ Both functions can be implemented using a loop or recursion
*
* Runs in O( height ) time
* + In the worst case, we traverse to to the right-most bottom of the BST
*
* @param start The root BinaryNode to begin checking values
* @return A pointer to the BinaryNode which contains the largest value
* + returns nullptr if BST is empty
*/
BinarySearchTree::BinaryNode * BinarySearchTree::findMax(BinaryNode *start) const
{
// If our tree is empty
if (start == nullptr) return nullptr;
// Base case: If current node has no larger children, it is max; Break recursion
if (start->right == nullptr) return start;
// Move down the right side of our tree and check again
return findMax(start->right);
}
/** predecessor
* @brief Finds the previous value in-order from the value at a given startNode
*
* Runs in O( height ) time
* + In the worst case we traverse to the bottom of the BST
*
* @param startNode The node containing the value to find predecessor of
* @return The node which is the predecessor of startNode
*/
BinarySearchTree::BinaryNode * BinarySearchTree::predecessor(BinaryNode *startNode) const
{
if (startNode->left != nullptr) return findMax(startNode->left);
// If startNode has a parent, walk up the tree until we reach the top
// + If startNode has no parent, we set it to nullptr and return
BinaryNode *temp = startNode->parent;
while (temp != nullptr && temp->left == startNode) {
startNode = temp;
temp = temp->parent;
}
return temp;
}
/** successor
* @brief Finds the next value in-order from the value at a given startNode
*
* Runs in O( height ) time
* + In the worst case we traverse to the bottom of the BST
*
* @param startNode The node containing the value to find successor of
* @return The node which is the successor of startNode
*/
BinarySearchTree::BinaryNode * BinarySearchTree::successor(BinaryNode *startNode) const
{
// If there is a right subtree, next value in-order is findMin(rightSubtree)
if (startNode->right != nullptr) return findMin(startNode->right);
// If startNode has a parent, walk up the tree until we reach the top
// + If startNode has no parent, we set it to nullptr and return
BinaryNode *temp = startNode->parent;
while (temp != nullptr && temp->right == startNode) {
startNode = temp;
temp = temp->parent;
}
return temp;
}
/*******************************************************************************
* Private Member Functions
*******************************************************************************/
/** clone
* @brief Clone a BST node and all its children using recursion
*
* Runs in O( n ) time, since each node must be copied individually
*
* @param start The node to begin cloning from
* @return A pointer to the BinaryNode which is root node of the copied tree
*/
BinarySearchTree::BinaryNode * BinarySearchTree::clone(BinaryNode *start)
{
// Base case: There is nothing to copy, break from recursion
if (start == nullptr) return nullptr;
// Construct all child nodes through recursion, return root node
return new BinaryNode(start);
}
/** transplant
* @brief Replaces, or overwrites, a node and with a new node
* + The subtree attaches to oldNode is replace with that of newNode
*
* Runs in constant O( 1 ) time
* + We only need to check and update values immediately available
*
* @param oldNode The node to overwrite with newNode
* @param newNode The new node to take the place of oldNode
*/
void BinarySearchTree::transplant(BinaryNode *oldNode, BinaryNode *newNode)
{
// case 1: If oldNode is the root node at this->root
// + 2: if the oldNode is the left child of it's parent
// + 3: case if the oldNode is the right child of it's parent
if (oldNode->parent == nullptr) root = newNode;
else if (oldNode == oldNode->parent->left) {
// Update the parent of oldNode to reflect the transplant
oldNode->parent->left = newNode;
}
else if (oldNode == oldNode->parent->right) {
// Update the parent of oldNode to reflect the transplant
oldNode->parent->right = newNode;
}
// If we did not replace oldNode with a nullptr, update newNode's parent
if (newNode != nullptr) newNode->parent = oldNode->parent;
}

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cpp/algorithms/trees/redblack/redblack.h Normal file
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/*#############################################################################
## Author: Shaun Reed ##
## Legal: All Content (c) 2021 Shaun Reed, all rights reserved ##
## About: An example of a red black tree implementation ##
## The algorithms in this example are seen in MIT Intro to Algorithms ##
## ##
## Contact: shaunrd0@gmail.com | URL: www.shaunreed.com | GitHub: shaunrd0 ##
##############################################################################
*/
#ifndef REDBLACK_H
#define REDBLACK_H
#include <iostream>
// TODO: Add balance() method to balance overweight branches
class BinarySearchTree {
public:
// BinaryNode Structure
struct BinaryNode{
int element;
BinaryNode *left, *right, *parent;
// Ctor for specific element, lhs, rhs
BinaryNode(const int &el, BinaryNode *lt, BinaryNode *rt, BinaryNode *p)
:element(el), left(lt), right(rt), parent(p) {};
// Ctor for a node and any downstream nodes
explicit BinaryNode(BinaryNode * toCopy);
};
BinarySearchTree() : root(nullptr) {};
BinarySearchTree(const BinarySearchTree &rhs) : root(rhs.clone(rhs.root)) {};
BinarySearchTree& operator=(const BinarySearchTree& rhs);
~BinarySearchTree() { makeEmpty(root);};
inline BinaryNode * getRoot() const { return root;}
// Check if value is within the tree or subtree
inline bool contains(const int &value) const { return contains(value, root);}
bool contains(const int &value, BinaryNode *start) const;
// Empties a given tree or subtree
inline void makeEmpty() { makeEmpty(root);}
void makeEmpty(BinaryNode *&tree);
// Checks if this BST is empty
bool isEmpty() const;
// Insert and remove values from a tree or subtree
inline void insert(const int &x) { insert(x, root, nullptr);}
void insert(const int &newValue, BinaryNode *&start, BinaryNode *prevNode);
inline void remove(const int &x) { remove(search(x, root));}
void remove(BinaryNode *removeNode);
// Traversal functions
inline void printInOrder() const { printInOrder(root);}
inline void printPostOrder() const { printPostOrder(root);}
inline void printPreOrder() const { printPreOrder(root);}
// Overloaded to specify traversal of a subtree
void printInOrder(BinaryNode *start) const;
void printPostOrder(BinaryNode *start) const;
void printPreOrder(BinaryNode *start) const;
// Find a BinaryNode containing value starting at a given tree / subtree node
inline BinaryNode * search(const int &value) const { return search(value, root);}
BinaryNode * search(const int &value, BinaryNode *start) const;
inline BinaryNode * findMin() const { return findMin(root);}
inline BinaryNode * findMax() const { return findMax(root);}
// Find nodes with min / max values starting at a given tree / subtree node
BinaryNode * findMin(BinaryNode *start) const;
BinaryNode * findMax(BinaryNode *start) const;
BinaryNode * predecessor(BinaryNode *startNode) const;
BinaryNode * successor(BinaryNode *startNode) const;
private:
// BST Private Member Functions
static BinaryNode * clone(BinaryNode *start);
void transplant(BinaryNode *oldNode, BinaryNode *newNode);
BinaryNode *root;
};
#endif // REDBLACK_H