Insättning i ett rött-svart träd

I denna handledning lär du dig hur en ny nod kan införas i ett rött-svart träd. Du hittar också arbetsexempel på infogningar utförda på ett rött-svart träd i C, C ++, Java och Python.

Röd-svart träd är ett självbalanserande binärt sökträd där varje nod innehåller en extra bit för att beteckna nodens färg, antingen röd eller svart.

Innan du läser den här artikeln, se artikeln om rött-svart träd.

När du sätter in en ny nod infogas den nya noden alltid som en RÖD nod. Efter införande av en ny nod, om trädet bryter mot egenskaperna för det rödsvarta trädet, gör vi följande åtgärder.

  1. Återfärg
  2. Rotation

Algoritm för att infoga en ny nod

Följande steg följs för att infoga ett nytt element i ett rött-svart träd:

  1. Den newNodevare: ny nod
  2. Låt y vara bladet (dvs. NIL) och xvara trädets rot. Den nya noden infogas i följande träd. Initialt träd
  3. Kontrollera om trädet är tomt (dvs. om det xär NIL). Om ja, infoga newNodesom en rotnod och färg den svart.
  4. Annars, upprepa stegen efter stegen tills blad ( NIL) når.
    1. Jämför newKeymed rootKey.
    2. Om newKeyär större än rootKey, gå igenom rätt subtree.
    3. Annars korsar du genom vänster subtree. Sökväg som leder till noden där newNode ska infogas
  5. Tilldela bladets förälder som förälder till newNode.
  6. Om leafKeyär större än newKey, gör newNodesom rightChild.
  7. Annars, gör newNodesom leftChild. Ny nod infogad
  8. Tilldela NULLtill vänster och rightChildtill newNode.
  9. Tilldela RÖD färg till newNode. Ställ in färgen på newNode röd och tilldela barnen null
  10. Ring InsertFix-algoritmen för att bibehålla egenskapen för rött-svart träd om det bryts.

Varför nyinsatta noder är alltid röda i ett rött-svart träd?

Detta beror på att infogning av en röd nod inte bryter mot djupegenskapen för ett rött-svart träd.

Om du bifogar en röd nod till en röd nod bryts regeln men det är lättare att åtgärda problemet än det problem som introducerades genom att bryta mot djupegenskapen.

Algoritm för att bibehålla röd-svart egendom efter infogning

Denna algoritm används för att upprätthålla egenskapen för ett rött-svart träd om insättning av en newNode bryter mot den här egenskapen.

  1. Gör följande tills föräldern till newNode pär RÖD.
  2. Om pär det vänstra barnet grandParent gPtill newNode, gör följande.
    Fall-I:
    1. Om färgen på rätt barn gPmed newNodeär röd, sätta färg på både barn gPsom svart och färg gPsom rött. Färgbyte
    2. Tilldela gPtill newNode. Omfördela newNode
      Case-II:
    3. (Innan du går vidare till det här steget, medan loop kontrolleras. Om villkoren inte är uppfyllda, är loopn trasig.)
      Annars om det newNodeär rätt barn av pdå, tilldela ptill newNode. Tilldelar förälder till newNode som newNode
    4. Vänster-rotera newNode. Vänster rotera
      fall-III:
    5. (Innan du går vidare till det här steget, medan loop kontrolleras. Om villkoren inte är uppfyllda, är loopen trasig.)
      Ställ in färgen psom SVART och färgen gPsom RÖD. Färgbyte
    6. Högerrotera gP. Höger Rotera
  3. Annars, gör följande.
    1. Om färgen på vänstra barn gPav zär röd, sätta färg på både barn gPsom svart och färg gPsom rött.
    2. Tilldela gPtill newNode.
    3. Annars om newNodeär den vänstra barn psedan tilldela ptill newNodeoch höger Rotera newNode.
    4. Ställ in färgen psom SVART och färgen gPRÖD.
    5. Vänster-rotera gP.
  4. (Detta steg utförs efter att ha kommit ut från stundslingan.)
    Ställ in roten på trädet som SVART. Ställ rotens färg svart

Det sista trädet ser ut så här:

Sista trädet

Python, Java och C / C ++ exempel

Python Java C C ++ 
# Implementing Red-Black Tree in Python import sys # Node creation class Node(): def __init__(self, item): self.item = item self.parent = None self.left = None self.right = None self.color = 1 class RedBlackTree(): def __init__(self): self.TNULL = Node(0) self.TNULL.color = 0 self.TNULL.left = None self.TNULL.right = None self.root = self.TNULL # Preorder def pre_order_helper(self, node): if node != TNULL: sys.stdout.write(node.item + " ") self.pre_order_helper(node.left) self.pre_order_helper(node.right) # Inorder def in_order_helper(self, node): if node != TNULL: self.in_order_helper(node.left) sys.stdout.write(node.item + " ") self.in_order_helper(node.right) # Postorder def post_order_helper(self, node): if node != TNULL: self.post_order_helper(node.left) self.post_order_helper(node.right) sys.stdout.write(node.item + " ") # Search the tree def search_tree_helper(self, node, key): if node == TNULL or key == node.item: return node if key < node.item: return self.search_tree_helper(node.left, key) return self.search_tree_helper(node.right, key) # Balance the tree after insertion def fix_insert(self, k): while k.parent.color == 1: if k.parent == k.parent.parent.right: u = k.parent.parent.left if u.color == 1: u.color = 0 k.parent.color = 0 k.parent.parent.color = 1 k = k.parent.parent else: if k == k.parent.left: k = k.parent self.right_rotate(k) k.parent.color = 0 k.parent.parent.color = 1 self.left_rotate(k.parent.parent) else: u = k.parent.parent.right if u.color == 1: u.color = 0 k.parent.color = 0 k.parent.parent.color = 1 k = k.parent.parent else: if k == k.parent.right: k = k.parent self.left_rotate(k) k.parent.color = 0 k.parent.parent.color = 1 self.right_rotate(k.parent.parent) if k == self.root: break self.root.color = 0 # Printing the tree def __print_helper(self, node, indent, last): if node != self.TNULL: sys.stdout.write(indent) if last: sys.stdout.write("R----") indent += " " else: sys.stdout.write("L----") indent += "| " s_color = "RED" if node.color == 1 else "BLACK" print(str(node.item) + "(" + s_color + ")") self.__print_helper(node.left, indent, False) self.__print_helper(node.right, indent, True) def preorder(self): self.pre_order_helper(self.root) def inorder(self): self.in_order_helper(self.root) def postorder(self): self.post_order_helper(self.root) def searchTree(self, k): return self.search_tree_helper(self.root, k) def minimum(self, node): while node.left != self.TNULL: node = node.left return node def maximum(self, node): while node.right != self.TNULL: node = node.right return node def successor(self, x): if x.right != self.TNULL: return self.minimum(x.right) y = x.parent while y != self.TNULL and x == y.right: x = y y = y.parent return y def predecessor(self, x): if (x.left != self.TNULL): return self.maximum(x.left) y = x.parent while y != self.TNULL and x == y.left: x = y y = y.parent return y def left_rotate(self, x): y = x.right x.right = y.left if y.left != self.TNULL: y.left.parent = x y.parent = x.parent if x.parent == None: self.root = y elif x == x.parent.left: x.parent.left = y else: x.parent.right = y y.left = x x.parent = y def right_rotate(self, x): y = x.left x.left = y.right if y.right != self.TNULL: y.right.parent = x y.parent = x.parent if x.parent == None: self.root = y elif x == x.parent.right: x.parent.right = y else: x.parent.left = y y.right = x x.parent = y def insert(self, key): node = Node(key) node.parent = None node.item = key node.left = self.TNULL node.right = self.TNULL node.color = 1 y = None x = self.root while x != self.TNULL: y = x if node.item < x.item: x = x.left else: x = x.right node.parent = y if y == None: self.root = node elif node.item < y.item: y.left = node else: y.right = node if node.parent == None: node.color = 0 return if node.parent.parent == None: return self.fix_insert(node) def get_root(self): return self.root def print_tree(self): self.__print_helper(self.root, "", True) if __name__ == "__main__": bst = RedBlackTree() bst.insert(55) bst.insert(40) bst.insert(65) bst.insert(60) bst.insert(75) bst.insert(57) bst.print_tree()
// Implementing Red-Black Tree in Java class Node ( int data; Node parent; Node left; Node right; int color; ) public class RedBlackTree ( private Node root; private Node TNULL; // Preorder private void preOrderHelper(Node node) ( if (node != TNULL) ( System.out.print(node.data + " "); preOrderHelper(node.left); preOrderHelper(node.right); ) ) // Inorder private void inOrderHelper(Node node) ( if (node != TNULL) ( inOrderHelper(node.left); System.out.print(node.data + " "); inOrderHelper(node.right); ) ) // Post order private void postOrderHelper(Node node) ( if (node != TNULL) ( postOrderHelper(node.left); postOrderHelper(node.right); System.out.print(node.data + " "); ) ) // Search the tree private Node searchTreeHelper(Node node, int key) ( if (node == TNULL || key == node.data) ( return node; ) if (key < node.data) ( return searchTreeHelper(node.left, key); ) return searchTreeHelper(node.right, key); ) // Balance the tree after deletion of a node private void fixDelete(Node x) ( Node s; while (x != root && x.color == 0) ( if (x == x.parent.left) ( s = x.parent.right; if (s.color == 1) ( s.color = 0; x.parent.color = 1; leftRotate(x.parent); s = x.parent.right; ) if (s.left.color == 0 && s.right.color == 0) ( s.color = 1; x = x.parent; ) else ( if (s.right.color == 0) ( s.left.color = 0; s.color = 1; rightRotate(s); s = x.parent.right; ) s.color = x.parent.color; x.parent.color = 0; s.right.color = 0; leftRotate(x.parent); x = root; ) ) else ( s = x.parent.left; if (s.color == 1) ( s.color = 0; x.parent.color = 1; rightRotate(x.parent); s = x.parent.left; ) if (s.right.color == 0 && s.right.color == 0) ( s.color = 1; x = x.parent; ) else ( if (s.left.color == 0) ( s.right.color = 0; s.color = 1; leftRotate(s); s = x.parent.left; ) s.color = x.parent.color; x.parent.color = 0; s.left.color = 0; rightRotate(x.parent); x = root; ) ) ) x.color = 0; ) private void rbTransplant(Node u, Node v) ( if (u.parent == null) ( root = v; ) else if (u == u.parent.left) ( u.parent.left = v; ) else ( u.parent.right = v; ) v.parent = u.parent; ) // Balance the node after insertion private void fixInsert(Node k) ( Node u; while (k.parent.color == 1) ( if (k.parent == k.parent.parent.right) ( u = k.parent.parent.left; if (u.color == 1) ( u.color = 0; k.parent.color = 0; k.parent.parent.color = 1; k = k.parent.parent; ) else ( if (k == k.parent.left) ( k = k.parent; rightRotate(k); ) k.parent.color = 0; k.parent.parent.color = 1; leftRotate(k.parent.parent); ) ) else ( u = k.parent.parent.right; if (u.color == 1) ( u.color = 0; k.parent.color = 0; k.parent.parent.color = 1; k = k.parent.parent; ) else ( if (k == k.parent.right) ( k = k.parent; leftRotate(k); ) k.parent.color = 0; k.parent.parent.color = 1; rightRotate(k.parent.parent); ) ) if (k == root) ( break; ) ) root.color = 0; ) private void printHelper(Node root, String indent, boolean last) ( if (root != TNULL) ( System.out.print(indent); if (last) ( System.out.print("R----"); indent += " "; ) else ( System.out.print("L----"); indent += "| "; ) String sColor = root.color == 1 ? "RED" : "BLACK"; System.out.println(root.data + "(" + sColor + ")"); printHelper(root.left, indent, false); printHelper(root.right, indent, true); ) ) public RedBlackTree() ( TNULL = new Node(); TNULL.color = 0; TNULL.left = null; TNULL.right = null; root = TNULL; ) public void preorder() ( preOrderHelper(this.root); ) public void inorder() ( inOrderHelper(this.root); ) public void postorder() ( postOrderHelper(this.root); ) public Node searchTree(int k) ( return searchTreeHelper(this.root, k); ) public Node minimum(Node node) ( while (node.left != TNULL) ( node = node.left; ) return node; ) public Node maximum(Node node) ( while (node.right != TNULL) ( node = node.right; ) return node; ) public Node successor(Node x) ( if (x.right != TNULL) ( return minimum(x.right); ) Node y = x.parent; while (y != TNULL && x == y.right) ( x = y; y = y.parent; ) return y; ) public Node predecessor(Node x) ( if (x.left != TNULL) ( return maximum(x.left); ) Node y = x.parent; while (y != TNULL && x == y.left) ( x = y; y = y.parent; ) return y; ) public void leftRotate(Node x) ( Node y = x.right; x.right = y.left; if (y.left != TNULL) ( y.left.parent = x; ) y.parent = x.parent; if (x.parent == null) ( this.root = y; ) else if (x == x.parent.left) ( x.parent.left = y; ) else ( x.parent.right = y; ) y.left = x; x.parent = y; ) public void rightRotate(Node x) ( Node y = x.left; x.left = y.right; if (y.right != TNULL) ( y.right.parent = x; ) y.parent = x.parent; if (x.parent == null) ( this.root = y; ) else if (x == x.parent.right) ( x.parent.right = y; ) else ( x.parent.left = y; ) y.right = x; x.parent = y; ) public void insert(int key) ( Node node = new Node(); node.parent = null; node.data = key; node.left = TNULL; node.right = TNULL; node.color = 1; Node y = null; Node x = this.root; while (x != TNULL) ( y = x; if (node.data < x.data) ( x = x.left; ) else ( x = x.right; ) ) node.parent = y; if (y == null) ( root = node; ) else if (node.data < y.data) ( y.left = node; ) else ( y.right = node; ) if (node.parent == null) ( node.color = 0; return; ) if (node.parent.parent == null) ( return; ) fixInsert(node); ) public Node getRoot() ( return this.root; ) public void printTree() ( printHelper(this.root, "", true); ) public static void main(String() args) ( RedBlackTree bst = new RedBlackTree(); bst.insert(55); bst.insert(40); bst.insert(65); bst.insert(60); bst.insert(75); bst.insert(57); bst.printTree(); ) )
// Implementing Red-Black Tree in C #include #include enum nodeColor ( RED, BLACK ); struct rbNode ( int data, color; struct rbNode *link(2); ); struct rbNode *root = NULL; // Create a red-black tree struct rbNode *createNode(int data) ( struct rbNode *newnode; newnode = (struct rbNode *)malloc(sizeof(struct rbNode)); newnode->data = data; newnode->color = RED; newnode->link(0) = newnode->link(1) = NULL; return newnode; ) // Insert an node void insertion(int data) ( struct rbNode *stack(98), *ptr, *newnode, *xPtr, *yPtr; int dir(98), ht = 0, index; ptr = root; if (!root) ( root = createNode(data); return; ) stack(ht) = root; dir(ht++) = 0; while (ptr != NULL) ( if (ptr->data == data) ( printf("Duplicates Not Allowed!!"); return; ) index = (data - ptr->data)> 0 ? 1 : 0; stack(ht) = ptr; ptr = ptr->link(index); dir(ht++) = index; ) stack(ht - 1)->link(index) = newnode = createNode(data); while ((ht>= 3) && (stack(ht - 1)->color == RED)) ( if (dir(ht - 2) == 0) ( yPtr = stack(ht - 2)->link(1); if (yPtr != NULL && yPtr->color == RED) ( stack(ht - 2)->color = RED; stack(ht - 1)->color = yPtr->color = BLACK; ht = ht - 2; ) else ( if (dir(ht - 1) == 0) ( yPtr = stack(ht - 1); ) else ( xPtr = stack(ht - 1); yPtr = xPtr->link(1); xPtr->link(1) = yPtr->link(0); yPtr->link(0) = xPtr; stack(ht - 2)->link(0) = yPtr; ) xPtr = stack(ht - 2); xPtr->color = RED; yPtr->color = BLACK; xPtr->link(0) = yPtr->link(1); yPtr->link(1) = xPtr; if (xPtr == root) ( root = yPtr; ) else ( stack(ht - 3)->link(dir(ht - 3)) = yPtr; ) break; ) ) else ( yPtr = stack(ht - 2)->link(0); if ((yPtr != NULL) && (yPtr->color == RED)) ( stack(ht - 2)->color = RED; stack(ht - 1)->color = yPtr->color = BLACK; ht = ht - 2; ) else ( if (dir(ht - 1) == 1) ( yPtr = stack(ht - 1); ) else ( xPtr = stack(ht - 1); yPtr = xPtr->link(0); xPtr->link(0) = yPtr->link(1); yPtr->link(1) = xPtr; stack(ht - 2)->link(1) = yPtr; ) xPtr = stack(ht - 2); yPtr->color = BLACK; xPtr->color = RED; xPtr->link(1) = yPtr->link(0); yPtr->link(0) = xPtr; if (xPtr == root) ( root = yPtr; ) else ( stack(ht - 3)->link(dir(ht - 3)) = yPtr; ) break; ) ) ) root->color = BLACK; ) // Delete a node void deletion(int data) ( struct rbNode *stack(98), *ptr, *xPtr, *yPtr; struct rbNode *pPtr, *qPtr, *rPtr; int dir(98), ht = 0, diff, i; enum nodeColor color; if (!root) ( printf("Tree not available"); return; ) ptr = root; while (ptr != NULL) ( if ((data - ptr->data) == 0) break; diff = (data - ptr->data)> 0 ? 1 : 0; stack(ht) = ptr; dir(ht++) = diff; ptr = ptr->link(diff); ) if (ptr->link(1) == NULL) ( if ((ptr == root) && (ptr->link(0) == NULL)) ( free(ptr); root = NULL; ) else if (ptr == root) ( root = ptr->link(0); free(ptr); ) else ( stack(ht - 1)->link(dir(ht - 1)) = ptr->link(0); ) ) else ( xPtr = ptr->link(1); if (xPtr->link(0) == NULL) ( xPtr->link(0) = ptr->link(0); color = xPtr->color; xPtr->color = ptr->color; ptr->color = color; if (ptr == root) ( root = xPtr; ) else ( stack(ht - 1)->link(dir(ht - 1)) = xPtr; ) dir(ht) = 1; stack(ht++) = xPtr; ) else ( i = ht++; while (1) ( dir(ht) = 0; stack(ht++) = xPtr; yPtr = xPtr->link(0); if (!yPtr->link(0)) break; xPtr = yPtr; ) dir(i) = 1; stack(i) = yPtr; if (i> 0) stack(i - 1)->link(dir(i - 1)) = yPtr; yPtr->link(0) = ptr->link(0); xPtr->link(0) = yPtr->link(1); yPtr->link(1) = ptr->link(1); if (ptr == root) ( root = yPtr; ) color = yPtr->color; yPtr->color = ptr->color; ptr->color = color; ) ) if (ht color == BLACK) ( while (1) ( pPtr = stack(ht - 1)->link(dir(ht - 1)); if (pPtr && pPtr->color == RED) ( pPtr->color = BLACK; break; ) if (ht link(1); if (!rPtr) break; if (rPtr->color == RED) ( stack(ht - 1)->color = RED; rPtr->color = BLACK; stack(ht - 1)->link(1) = rPtr->link(0); rPtr->link(0) = stack(ht - 1); if (stack(ht - 1) == root) ( root = rPtr; ) else ( stack(ht - 2)->link(dir(ht - 2)) = rPtr; ) dir(ht) = 0; stack(ht) = stack(ht - 1); stack(ht - 1) = rPtr; ht++; rPtr = stack(ht - 1)->link(1); ) if ((!rPtr->link(0) || rPtr->link(0)->color == BLACK) && (!rPtr->link(1) || rPtr->link(1)->color == BLACK)) ( rPtr->color = RED; ) else ( if (!rPtr->link(1) || rPtr->link(1)->color == BLACK) ( qPtr = rPtr->link(0); rPtr->color = RED; qPtr->color = BLACK; rPtr->link(0) = qPtr->link(1); qPtr->link(1) = rPtr; rPtr = stack(ht - 1)->link(1) = qPtr; ) rPtr->color = stack(ht - 1)->color; stack(ht - 1)->color = BLACK; rPtr->link(1)->color = BLACK; stack(ht - 1)->link(1) = rPtr->link(0); rPtr->link(0) = stack(ht - 1); if (stack(ht - 1) == root) ( root = rPtr; ) else ( stack(ht - 2)->link(dir(ht - 2)) = rPtr; ) break; ) ) else ( rPtr = stack(ht - 1)->link(0); if (!rPtr) break; if (rPtr->color == RED) ( stack(ht - 1)->color = RED; rPtr->color = BLACK; stack(ht - 1)->link(0) = rPtr->link(1); rPtr->link(1) = stack(ht - 1); if (stack(ht - 1) == root) ( root = rPtr; ) else ( stack(ht - 2)->link(dir(ht - 2)) = rPtr; ) dir(ht) = 1; stack(ht) = stack(ht - 1); stack(ht - 1) = rPtr; ht++; rPtr = stack(ht - 1)->link(0); ) if ((!rPtr->link(0) || rPtr->link(0)->color == BLACK) && (!rPtr->link(1) || rPtr->link(1)->color == BLACK)) ( rPtr->color = RED; ) else ( if (!rPtr->link(0) || rPtr->link(0)->color == BLACK) ( qPtr = rPtr->link(1); rPtr->color = RED; qPtr->color = BLACK; rPtr->link(1) = qPtr->link(0); qPtr->link(0) = rPtr; rPtr = stack(ht - 1)->link(0) = qPtr; ) rPtr->color = stack(ht - 1)->color; stack(ht - 1)->color = BLACK; rPtr->link(0)->color = BLACK; stack(ht - 1)->link(0) = rPtr->link(1); rPtr->link(1) = stack(ht - 1); if (stack(ht - 1) == root) ( root = rPtr; ) else ( stack(ht - 2)->link(dir(ht - 2)) = rPtr; ) break; ) ) ht--; ) ) ) // Print the inorder traversal of the tree void inorderTraversal(struct rbNode *node) ( if (node) ( inorderTraversal(node->link(0)); printf("%d ", node->data); inorderTraversal(node->link(1)); ) return; ) // Driver code int main() ( int ch, data; while (1) ( printf("1. Insertion 2. Deletion"); printf("3. Traverse 4. Exit"); printf("Enter your choice:"); scanf("%d", &ch); switch (ch) ( case 1: printf("Enter the element to insert:"); scanf("%d", &data); insertion(data); break; case 2: printf("Enter the element to delete:"); scanf("%d", &data); deletion(data); break; case 3: inorderTraversal(root); printf(""); break; case 4: exit(0); default: printf("Not available"); break; ) printf(""); ) return 0; )
// Implementing Red-Black Tree in C++ #include using namespace std; struct Node ( int data; Node *parent; Node *left; Node *right; int color; ); typedef Node *NodePtr; class RedBlackTree ( private: NodePtr root; NodePtr TNULL; void initializeNULLNode(NodePtr node, NodePtr parent) ( node->data = 0; node->parent = parent; node->left = nullptr; node->right = nullptr; node->color = 0; ) // Preorder void preOrderHelper(NodePtr node) ( if (node != TNULL) ( cout right); ) ) // Inorder void inOrderHelper(NodePtr node) ( if (node != TNULL) ( inOrderHelper(node->left); cout left); postOrderHelper(node->right); cout left, key); ) return searchTreeHelper(node->right, key); ) // For balancing the tree after deletion void deleteFix(NodePtr x) ( NodePtr s; while (x != root && x->color == 0) ( if (x == x->parent->left) ( s = x->parent->right; if (s->color == 1) ( s->color = 0; x->parent->color = 1; leftRotate(x->parent); s = x->parent->right; ) if (s->left->color == 0 && s->right->color == 0) ( s->color = 1; x = x->parent; ) else ( if (s->right->color == 0) ( s->left->color = 0; s->color = 1; rightRotate(s); s = x->parent->right; ) s->color = x->parent->color; x->parent->color = 0; s->right->color = 0; leftRotate(x->parent); x = root; ) ) else ( s = x->parent->left; if (s->color == 1) ( s->color = 0; x->parent->color = 1; rightRotate(x->parent); s = x->parent->left; ) if (s->right->color == 0 && s->right->color == 0) ( s->color = 1; x = x->parent; ) else ( if (s->left->color == 0) ( s->right->color = 0; s->color = 1; leftRotate(s); s = x->parent->left; ) s->color = x->parent->color; x->parent->color = 0; s->left->color = 0; rightRotate(x->parent); x = root; ) ) ) x->color = 0; ) void rbTransplant(NodePtr u, NodePtr v) ( if (u->parent == nullptr) ( root = v; ) else if (u == u->parent->left) ( u->parent->left = v; ) else ( u->parent->right = v; ) v->parent = u->parent; ) void deleteNodeHelper(NodePtr node, int key) ( NodePtr z = TNULL; NodePtr x, y; while (node != TNULL) ( if (node->data == key) ( z = node; ) if (node->data right; ) else ( node = node->left; ) ) if (z == TNULL) ( cout << "Key not found in the tree"  left == TNULL) ( x = z->right; rbTransplant(z, z->right); ) else if (z->right == TNULL) ( x = z->left; rbTransplant(z, z->left); ) else ( y = minimum(z->right); y_original_color = y->color; x = y->right; if (y->parent == z) ( x->parent = y; ) else ( rbTransplant(y, y->right); y->right = z->right; y->right->parent = y; ) rbTransplant(z, y); y->left = z->left; y->left->parent = y; y->color = z->color; ) delete z; if (y_original_color == 0) ( deleteFix(x); ) ) // For balancing the tree after insertion void insertFix(NodePtr k) ( NodePtr u; while (k->parent->color == 1) ( if (k->parent == k->parent->parent->right) ( u = k->parent->parent->left; if (u->color == 1) ( u->color = 0; k->parent->color = 0; k->parent->parent->color = 1; k = k->parent->parent; ) else ( if (k == k->parent->left) ( k = k->parent; rightRotate(k); ) k->parent->color = 0; k->parent->parent->color = 1; leftRotate(k->parent->parent); ) ) else ( u = k->parent->parent->right; if (u->color == 1) ( u->color = 0; k->parent->color = 0; k->parent->parent->color = 1; k = k->parent->parent; ) else ( if (k == k->parent->right) ( k = k->parent; leftRotate(k); ) k->parent->color = 0; k->parent->parent->color = 1; rightRotate(k->parent->parent); ) ) if (k == root) ( break; ) ) root->color = 0; ) void printHelper(NodePtr root, string indent, bool last) ( if (root != TNULL) ( cout << indent; if (last) ( cout << "R----"; indent += " "; ) else ( cout  right, indent, true); ) ) public: RedBlackTree() ( TNULL = new Node; TNULL->color = 0; TNULL->left = nullptr; TNULL->right = nullptr; root = TNULL; ) void preorder() ( preOrderHelper(this->root); ) void inorder() ( inOrderHelper(this->root); ) void postorder() ( postOrderHelper(this->root); ) NodePtr searchTree(int k) ( return searchTreeHelper(this->root, k); ) NodePtr minimum(NodePtr node) ( while (node->left != TNULL) ( node = node->left; ) return node; ) NodePtr maximum(NodePtr node) ( while (node->right != TNULL) ( node = node->right; ) return node; ) NodePtr successor(NodePtr x) ( if (x->right != TNULL) ( return minimum(x->right); ) NodePtr y = x->parent; while (y != TNULL && x == y->right) ( x = y; y = y->parent; ) return y; ) NodePtr predecessor(NodePtr x) ( if (x->left != TNULL) ( return maximum(x->left); ) NodePtr y = x->parent; while (y != TNULL && x == y->left) ( x = y; y = y->parent; ) return y; ) void leftRotate(NodePtr x) ( NodePtr y = x->right; x->right = y->left; if (y->left != TNULL) ( y->left->parent = x; ) y->parent = x->parent; if (x->parent == nullptr) ( this->root = y; ) else if (x == x->parent->left) ( x->parent->left = y; ) else ( x->parent->right = y; ) y->left = x; x->parent = y; ) void rightRotate(NodePtr x) ( NodePtr y = x->left; x->left = y->right; if (y->right != TNULL) ( y->right->parent = x; ) y->parent = x->parent; if (x->parent == nullptr) ( this->root = y; ) else if (x == x->parent->right) ( x->parent->right = y; ) else ( x->parent->left = y; ) y->right = x; x->parent = y; ) // Inserting a node void insert(int key) ( NodePtr node = new Node; node->parent = nullptr; node->data = key; node->left = TNULL; node->right = TNULL; node->color = 1; NodePtr y = nullptr; NodePtr x = this->root; while (x != TNULL) ( y = x; if (node->data data) ( x = x->left; ) else ( x = x->right; ) ) node->parent = y; if (y == nullptr) ( root = node; ) else if (node->data data) ( y->left = node; ) else ( y->right = node; ) if (node->parent == nullptr) ( node->color = 0; return; ) if (node->parent->parent == nullptr) ( return; ) insertFix(node); ) NodePtr getRoot() ( return this->root; ) void deleteNode(int data) ( deleteNodeHelper(this->root, data); ) void printTree() ( if (root) ( printHelper(this->root, "", true); ) ) ); int main() ( RedBlackTree bst; bst.insert(55); bst.insert(40); bst.insert(65); bst.insert(60); bst.insert(75); bst.insert(57); bst.printTree(); cout << endl << "After deleting" << endl; bst.deleteNode(40); bst.printTree(); )

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