Red Black Tree
Red Black Tree is balanced binary search tree with one extra bit of storage per node: color
Red Black Tree satisfies the Red-Black-Properties
Red-Black-Properties
- Every node is black or red
- The root is black
- Every leaf(NIL) is black
- if a node is red, then both its children are black
- For each node, all simple paths from the node to descendant leaves contains the same number of black nodes.
Operations & time complexity
$N$ = number of elements in Tree
| Member Function |
Running Time |
| insert() |
$\Omicron(\lg(N))$ |
| erase() |
$\Omicron(\lg(N))$ |
| inorder_tree_walk |
$\Theta(N)$ |
| find() |
$\Omicron(\lg(N))$ |
| minimum() |
$\Omicron(\lg(N))$ |
| maximum() |
$\Omicron(\lg(N))$ |
| successor() |
$\Omicron(\lg(N))$ |
| predecessor() |
$\Omicron(\lg(N))$ |
Note
Red Black Tree is Balanced Binary Search Tree
It is guaranteed that height of the tree is $\Omicron(\lg(N))$ in worst case
Implementation
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295 | #include <bits/stdc++.h>
using namespace std;
template<typename K, typename V>
class Map {
struct Node {
K key;
V val;
bool color; // 0: red, 1:black
Node* p;
Node* left;
Node* right;
Node(Map &out):
key(), val(), color(1),
p(out.NIL), left(out.NIL), right(out.NIL){}
Node(Map &out, K key, V val):
key(key), val(val), color(0),
p(out.NIL), left(out.NIL), right(out.NIL){}
};
Node* root;
void left_rotate(Node* x) {
Node* y = x->right; // y is x's right child
x->right = y->left; // set y's left child to x's right child;
x->right->p = x; // set parent
y->p = x->p;
//set x's parent pointing to y;
if (x->p == NIL) { // if x is root
this->root = y;
} else if(x == x->p->left) { //if x is left child
x->p->left = y;
} else {
x->p->right = y;
}
x->p = y; // y is x's parent
y->left = x; // x is y's left child
}
void right_rotate(Node* x) {
Node* y = x->left;
x->left = y->right;
x->left->p = x;
y->p = x->p;
if (x->p == NIL) {
this->root = y;
} else if(x == x->p->left) {
x->p->left = y;
} else {
x->p->right = y;
}
x->p = y;
y->right = x;
}
void transplant(Node* u, Node* v) {
// gives u's parent relations to v
if (u->p == NIL) {
root = v;
} else if (u == u->p->right) {
u->p->right = v;
} else {
u->p->left = v;
}
v->p = u->p; // unconditionally because NIL can have parent also;
}
public:
Node* NIL;
Map() {
NIL = new Node(*this);
root = NIL;
}
void insert_fixup(Node* &z) {
while (z->p->color == 0) {
Node* y; // z's uncle
if (z->p == z->p->p->left) { // when z's parent is left child
y = z->p->p->right;
if (y->color == 0) { // if uncle is red, uncles parent should be black
z->p->color = 1; // recoloring and goes up
y->color = 1;
z->p->p->color = 0;
z = z->p->p;
} else {
if (z == z->p->right) { // if uncle is black and z is right child
z = z->p;
left_rotate(z);
} // if uncle is black and z is right child
z->p->color = 1;
z->p->p->color = 0;
right_rotate(z->p->p);
}
} else { // when z's parent is right child
y = z->p->p->left;
if (y->color == 0) {
z->p->color = 1;
y->color = 1;
z->p->p->color = 0;
z = z->p->p;
} else { // if uncle's color is black
if (z == z->p->left) { //when z is right child
z = z->p;
right_rotate(z);
}
z->p->color = 1;
z->p->p->color = 0;
left_rotate(z->p->p);
}
}
}
this->root->color = 1;
}
void insert(K key, V val) {
Node* z = new Node(*this, key, val);
Node* y = NIL;
Node* x = this->root;
while (x != NIL) {
y = x;
if (z->key < x->key) {
x = x->left;
} else {
x= x->right;
}
}
z->p = y;
if (y == NIL) {
this->root = z;
} else if (z->key < y->key) {
y->left = z;
} else {
y->right = z;
}
// z->left = NIL;
// z->right = ZIL;
// z->color = 0;
insert_fixup(z);
}
Node* find(K key) {
Node* x = root;
while (x!= NIL && x->key != key) {
if (key < x->key) {
x = x->left;
} else {
x = x->right;
}
}
return x;
}
Node* minimum(Node* x) {
while (x->left != NIL) {
x = x->left;
}
return x;
}
void erase_fixup(Node* x) {
Node * w; // sibling of x;
while (x != this->root && x->color == 1) { //only if x is black and not root
if (x == x->p->left) {
w = x->p->right;
if (w->color == 0) { // turns to case2, 3 or 4;
w->color = 1;
x->p->color = 0;
left_rotate(x->p);
w = x->p->right;
}
if (w->left->color == 1 && w->right->color == 1) { // case2
w->color = 0;
x = x->p;
} else {
if (w->right->color == 1) { //case3 -> turns to case4
w->left->color = 1;
w->color = 0;
right_rotate(w);
w = x->p->right;
}
w->color = x->p->color; // case4 -> we can make legit red-black tree
x->p->color = 1;
w->right->color = 1;
left_rotate(x->p);
x = root;
}
} else { // x == x->p->right
w = x->p->left;
if (w->color == 0) {
w->color = 1;
x->p->color = 0;
right_rotate(x->p);
w = x->p->left;
}
if (w->left->color == 1 && w->right->color == 1) {
w->color = 0;
x = x->p;
} else {
if (w->left->color == 1) {
w->color = 0;
w->right->color = 1;
left_rotate(w);
w = x->p->left;
}
w->color = w->p->color;
w->p->color = 1;
w->left->color = 1;
right_rotate(x->p);
x = root;
}
}
}
x->color = 1;
}
void erase(Node* z) {
Node* y = z;
bool y_original_color = y->color;
Node* x;
if (z->left == NIL) {
x = z->right;
transplant(z, z->right);
} else if (z->right == NIL) {
x = z->left;
transplant(z, z->left);
} else {
y = minimum(z->right);
y_original_color = y->color;
x = y->right;
if (y->p == z) {
x->p = y; // incase of x is NIL!! we need to find it's parent!
} else {
transplant(y, y->right);
y->right = z->right;
y->right->p = y;
}
transplant(z, y);
y->left = z->left;
y->left->p = y;
y->color = z->color;
}
if (y_original_color == 1) {
erase_fixup(x);
}
}
void rb_printer(Node* node, int indent) {
//prints red & black tree
int count = 4;
if (node == NIL) return;
indent += count;
rb_printer(node->right, indent);
cout << endl;
for (int i = count; i < indent; i++) {
cout << " ";
}
cout << (node->color == 0 ? "\033[1;31m":"") << (node == node->p->left ? "l":"r") << node->key << (node->color == 0 ? "\033[0m":"") << endl;
rb_printer(node->left, indent);
}
void print() {
rb_printer(this->root, 0);
}
};
int main() {
Map<int, int> m;
for (int i = 0; i < 20; i++) {
m.insert(rand()%20, 1);
}
m.print();
cout << "deleting ---" << endl;;
for (int i = 0; i < 20; i++) {
int key = rand()%20;
auto it = m.find(key);
cout << "delete: " << key << endl;
if (it != m.NIL) {
cout << "key exist... deleting...";
m.erase(it);
m.print();
} else {
cout << "key not exist" << endl;
}
}
return 0;
}
|
- NOT ADDED YET
BinarySearchTree
Analysis (Optional)
You can add some mathematical things here using KaTex
as a block tag
$$
T(N) = O(N*M)
$$
or as a inline tag $T(N) = O(N) $
Contributers (Optional)
08.18.2019 
JCHRYS
Source
RedBlackTree.cpp