Dzēšana sarkan-melnā kokā

Šajā apmācībā jūs uzzināsiet, kā mezgls tiek izdzēsts no sarkanmelna koka. Jūs atradīsit arī piemērus dzēšanai, kas veikta sarkanā-melnā kokā C, C ++, Java un Python.

Sarkanmelns koks ir pašbalansējošs binārs meklēšanas koks, kurā katrā mezglā ir papildu bits, lai apzīmētu mezgla krāsu - vai nu sarkanu, vai melnu.

Pirms lasāt šo rakstu, lūdzu, skatiet rakstu par sarkanmelnu koku.

Dzēšot mezglu, var tikt traucēta sarkanmelnā koka sarkanmelnās īpašības. Ja šī darbība pārkāpj sarkanmelnās īpašības, tad sarkano-melno īpašību atgūšanai tiek izmantots fiksēšanas algoritms.

Elementa dzēšana no sarkan-melna koka

Šī darbība noņem koku no mezgla. Pēc mezgla dzēšanas sarkanmelnā īpašība atkal tiek saglabāta.

Ļaujiet dzēst mezglu nodeToBeDeletedbe:
Saglabājiet nodeToBeDeleted krāsu origrinalColor. Sākotnējās krāsas saglabāšana
Ja mezglaToBeDeleted kreisais bērns ir NULL
1. Piešķiriet nodeToBeDeleted labo bērnu x. Piešķirt x labajamBērns
2. Pārstādīšanas mezglsToBeDeleted ar x. Pārstādīšanas mezglsToBeDeleted ar x
Citādi, ja nodeToBeDeleted pareizais bērns ir NULL
1. Piešķiriet nodeToBeDeleted kreiso bērnu x.
2. Pārstādīšanas mezglsToBeDeleted ar x.
Cits
1. Piešķiriet minimālo labo apakškopa noteToBeDeleted apakšgrupā y.
2. Saglabājiet y krāsu oriģinālajā krāsā.
3. Piešķiriet y labo bērnu ar x.
4. Ja y ir nodeToBeDeleted bērns, tad iestatiet x vecāku kā y.
5. Pārējā gadījumā pārstādiet y ar labo bērnu.
6. Pārstādīšanas mezglsToBeDeleted ar y.
7. Iestatiet y krāsu ar oriģinālo krāsu.
Ja originalColor ir MELNA, izsauciet DeleteFix (x).

Algoritms, lai pēc dzēšanas saglabātu sarkano-melno īpašību

Šis algoritms tiek ieviests, kad melnais mezgls tiek dzēsts, jo tas pārkāpj sarkanmelnā koka melnā dziļuma īpašību.

Šis pārkāpums tiek labots, pieņemot, ka mezglā x (kas aizņem y sākotnējo stāvokli) ir īpaši melns. Tas padara mezglu x ne sarkanu, ne melnu. Tas ir vai nu divreiz melns, vai melnbalts. Tas pārkāpj sarkanmelnās īpašības.

Tomēr x krāsas atribūts netiek mainīts, bet papildu melnais ir attēlots x norādot uz mezglu.

Papildu melno var noņemt, ja

Tas sasniedz saknes mezglu.
Ja x norāda uz sarkanu-melnu mezglu. Šajā gadījumā x ir melnā krāsā.
Tiek veiktas piemērotas rotācijas un pārkrāsošana.

Sekojošais algoritms saglabā sarkanmelnā koka īpašības.

Veiciet šādas darbības, līdz x nav koka sakne un x krāsa ir MELNA
Ja x ir vecāka kreisais bērns,
1. Piešķirt wuz brālis x. Piešķirt w
2. Ja x brālis ir RED,
  I gadījums:
  1. Iestatiet x vecāku labā bērna krāsu kā MELNU.
  2. Iestatiet x vecāka krāsu kā RED. Krāsas maiņa
  3. Pagrieziet pa kreisi x vecāku. Pagriezt pa kreisi
  4. Piešķiriet x vecāku tiesībasBērns w. Piešķirt atkārtoti
3. Ja labās un kreisās puses w bērns ir melns,
  II gadījums:
  1. Iestatiet w krāsu kā RED
  2. Piešķiriet x vecāku x.
4. Citādi, ja labā bērna w krāsa ir MELNA,
  III gadījums:
  1. Iestatiet kreisāBērna w krāsu kā MELNU
  2. Iestatiet w krāsu kā RED Color change
  3. Pagriezt pa labi Pagrieziet pa labi
  4. Piešķiriet x vecāku tiesībasBērns w. Piešķirt atkārtoti
5. Ja kāds no iepriekš minētajiem gadījumiem nenotiek, rīkojieties šādi.
  IV gadījums:
  1. Iestatiet w krāsu kā vecāku x krāsu.
  2. Iestatiet vecāku x vecāku krāsu kā MELNU.
  3. Iestatiet w labā bērna krāsu kā MELNU. Krāsas maiņa
  4. Pagrieziet pa kreisi x vecāku. Pagriezt pa kreisi
  5. Iestatiet x kā koka sakni. Iestatiet x kā sakni
Cits tas pats, kas iepriekš, ar labo pusi mainīts uz kreiso un otrādi.
Iestatiet x krāsu kā MELNU.

Iepriekš minēto gadījumu darbplūsmu var saprast ar zemāk esošās blokshēmas palīdzību.

Blokshēma dzēšanai

Python, Java un C / C ++ piemēri

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) # Balancing the tree after deletion def delete_fix(self, x): while x != self.root and x.color == 0: if x == x.parent.left: s = x.parent.right if s.color == 1: s.color = 0 x.parent.color = 1 self.left_rotate(x.parent) s = x.parent.right if s.left.color == 0 and s.right.color == 0: s.color = 1 x = x.parent else: if s.right.color == 0: s.left.color = 0 s.color = 1 self.right_rotate(s) s = x.parent.right s.color = x.parent.color x.parent.color = 0 s.right.color = 0 self.left_rotate(x.parent) x = self.root else: s = x.parent.left if s.color == 1: s.color = 0 x.parent.color = 1 self.right_rotate(x.parent) s = x.parent.left if s.right.color == 0 and s.right.color == 0: s.color = 1 x = x.parent else: if s.left.color == 0: s.right.color = 0 s.color = 1 self.left_rotate(s) s = x.parent.left s.color = x.parent.color x.parent.color = 0 s.left.color = 0 self.right_rotate(x.parent) x = self.root x.color = 0 def __rb_transplant(self, u, v): if u.parent == None: self.root = v elif u == u.parent.left: u.parent.left = v else: u.parent.right = v v.parent = u.parent # Node deletion def delete_node_helper(self, node, key): z = self.TNULL while node != self.TNULL: if node.item == key: z = node if node.item <= key: node = node.right else: node = node.left if z == self.TNULL: print("Cannot find key in the tree") return y = z y_original_color = y.color if z.left == self.TNULL: x = z.right self.__rb_transplant(z, z.right) elif (z.right == self.TNULL): x = z.left self.__rb_transplant(z, z.left) else: y = self.minimum(z.right) y_original_color = y.color x = y.right if y.parent == z: x.parent = y else: self.__rb_transplant(y, y.right) y.right = z.right y.right.parent = y self.__rb_transplant(z, y) y.left = z.left y.left.parent = y y.color = z.color if y_original_color == 0: self.delete_fix(x) # 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 delete_node(self, item): self.delete_node_helper(self.root, item) 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() print("After deleting an element") bst.delete_node(40) 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; ) private void deleteNodeHelper(Node node, int key) ( Node z = TNULL; Node x, y; while (node != TNULL) ( if (node.data == key) ( z = node; ) if (node.data <= key) ( node = node.right; ) else ( node = node.left; ) ) if (z == TNULL) ( System.out.println("Couldn't find key in the tree"); return; ) y = z; int yOriginalColor = y.color; if (z.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); yOriginalColor = 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; ) if (yOriginalColor == 0) ( fixDelete(x); ) ) // 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 deleteNode(int data) ( deleteNodeHelper(this.root, data); ) 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(); System.out.println("After deleting:"); bst.deleteNode(40); 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(); )