Insertion in a Red-Black Tree

Insertion in a Red-Black Tree

In this tutorial, you will learn how a new node can be inserted into a red-black tree is. Also, you will find working examples of insertions performed on a red-black tree in C, C++, Java and Python.

Red-Black tree is a self-balancing binary search tree in which each node contains an extra bit for denoting the color of the node, either red or black.

Before reading this article, please refer to the article on red-black tree.

While inserting a new node, the new node is always inserted as a RED node. After insertion of a new node, if the tree is violating the properties of the red-black tree then, we do the following operations.

  1. Recolor
  2. Rotation

Algorithm to Insert a New Node

Following steps are followed for inserting a new element into a red-black tree:

  1. The newNode be:
    New Node
    New node
  2. Let y be the leaf (ie. NIL) and x be the root of the tree. The new node is inserted in the following tree.
    insertion in red black tree
    Initial tree
  3. Check if the tree is empty (ie. whether x is NIL). If yes, insert newNode as a root node and color it black.
  4. Else, repeat steps following steps until leaf (NIL) is reached.
    1. Compare newKey with rootKey.
    2. If newKey is greater than rootKey, traverse through the right subtree.
    3. Else traverse through the left subtree.
      insertion in red black tree
      Path leading to the node where newNode is to be inserted
  5. Assign the parent of the leaf as parent of newNode.
  6. If leafKey is greater than newKey, make newNode as rightChild.
  7. Else, make newNode as leftChild.
    insertion in red black tree
    New node inserted
  8. Assign NULL to the left and rightChild of newNode.
  9. Assign RED color to newNode.
    insertion in red black tree
    Set the color of the newNode red and assign null to the children
  10. Call InsertFix-algorithm to maintain the property of red-black tree if violated.

Why newly inserted nodes are always red in a red-black tree?

This is because inserting a red node does not violate the depth property of a red-black tree.

If you attach a red node to a red node, then the rule is violated but it is easier to fix this problem than the problem introduced by violating the depth property.


Algorithm to Maintain Red-Black Property After Insertion

This algorithm is used for maintaining the property of a red-black tree if insertion of a newNode violates this property.

  1. Do the following until the parent of newNode p is RED.
  2. If p is the left child of grandParent gP of newNode, do the following.
    Case-I:
    1. If the color of the right child of gP of newNode is RED, set the color of both the children of gP as BLACK and the color of gP as RED.
      insertion in a red-black tree
      Color change
    2. Assign gP to newNode.
      insertion in a red-black tree
      Reassigning newNode

      Case-II:
    3. (Before moving on to this step, while loop is checked. If conditions are not satisfied, it the loop is broken.)
      Else if newNode is the right child of p then, assign p to newNode.
      insertion in a red-black tree
      Assigning parent of newNode as newNode
    4. Left-Rotate newNode.
      Insertion in a red-black tree
      Left Rotate

      Case-III:
    5. (Before moving on to this step, while loop is checked. If conditions are not satisfied, it the loop is broken.)
      Set color of p as BLACK and color of gP as RED.
      insertion in a redblack tree
      Color change
    6. Right-Rotate gP.
      insertion in a red-black tree
      Right Rotate
  3. Else, do the following.
    1. If the color of the left child of gP of z is RED, set the color of both the children of gP as BLACK and the color of gP as RED.
    2. Assign gP to newNode.
    3. Else if newNode is the left child of p then, assign p to newNode and Right-Rotate newNode.
    4. Set color of p as BLACK and color of gP as RED.
    5. Left-Rotate gP.
  4. (This step is performed after coming out of the while loop.)
    Set the root of the tree as BLACK.
    insertion in a red-black tree
    Set root's color black

The final tree look like this:

insertion in a red-black tree
Final tree

Python, Java and C/C++ Examples

# 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 <stdio.h>
#include <stdlib.h>

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!!\n");
      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\n");
    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 < 1)
    return;

  if (ptr->color == BLACK) {
    while (1) {
      pPtr = stack[ht - 1]->link[dir[ht - 1]];
      if (pPtr && pPtr->color == RED) {
        pPtr->color = BLACK;
        break;
      }

      if (ht < 2)
        break;

      if (dir[ht - 2] == 0) {
        rPtr = stack[ht - 1]->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\t2. Deletion\n");
    printf("3. Traverse\t4. Exit");
    printf("\nEnter 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("\n");
        break;
      case 4:
        exit(0);
      default:
        printf("Not available\n");
        break;
    }
    printf("\n");
  }
  return 0;
}
// Implementing Red-Black Tree in C++

#include <iostream>
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 << node->data << " ";
      preOrderHelper(node->left);
      preOrderHelper(node->right);
    }
  }

  // Inorder
  void inOrderHelper(NodePtr node) {
    if (node != TNULL) {
      inOrderHelper(node->left);
      cout << node->data << " ";
      inOrderHelper(node->right);
    }
  }

  // Post order
  void postOrderHelper(NodePtr node) {
    if (node != TNULL) {
      postOrderHelper(node->left);
      postOrderHelper(node->right);
      cout << node->data << " ";
    }
  }

  NodePtr searchTreeHelper(NodePtr 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);
  }

  // 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 <= key) {
        node = node->right;
      } else {
        node = node->left;
      }
    }

    if (z == TNULL) {
      cout << "Key not found in the tree" << endl;
      return;
    }

    y = z;
    int y_original_color = 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);
      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 << "L----";
        indent += "|  ";
      }

      string sColor = root->color ? "RED" : "BLACK";
      cout << root->data << "(" << sColor << ")" << endl;
      printHelper(root->left, indent, false);
      printHelper(root->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 < x->data) {
        x = x->left;
      } else {
        x = x->right;
      }
    }

    node->parent = y;
    if (y == nullptr) {
      root = node;
    } else if (node->data < y->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();
}