# Deletion in a Binary Tree

Given a binary tree, delete a node from it by making sure that tree shrinks from the bottom (i.e. the deleted node is replaced by bottom most and rightmost node). This different from BST deletion. Here we do not have any order among elements, so we replace with last element.

Examples :

```Delete 10 in below tree
10
/
20     30
Output :
30
/
20

Delete 20 in below tree
10
/
20     30

40
Output :
10
/
40    30
```

Algorithm
1. Starting at root, find the deepest and rightmost node in binary tree and node which we want to delete.
2. Replace the deepest rightmost node’s data with node to be deleted.
3. Then delete the deepest rightmost node. `// C++ program to delete element in binary tree ` `#include ` `using` `namespace` `std; ` ` `  `/* A binary tree node has key, pointer to left ` `   ``child and a pointer to right child */` `struct` `Node ` `{ ` `    ``int` `key; ` `    ``struct` `Node* left, *right; ` `}; ` ` `  `/* function to create a new node of tree and ` `   ``return pointer */` `struct` `Node* newNode(``int` `key) ` `{ ` `    ``struct` `Node* temp = ``new` `Node; ` `    ``temp->key = key; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `}; ` ` `  `/* Inorder traversal of a binary tree*/` `void` `inorder(``struct` `Node* temp) ` `{ ` `    ``if` `(!temp) ` `        ``return``; ` `    ``inorder(temp->left); ` `    ``cout << temp->key << ``" "``; ` `    ``inorder(temp->right); ` `} ` ` `  `/* function to delete the given deepest node ` `   ``(d_node) in binary tree */` `void` `deletDeepest(``struct` `Node *root, ` `                  ``struct` `Node *d_node) ` `{ ` `    ``queue<``struct` `Node*> q; ` `    ``q.push(root); ` ` `  `    ``// Do level order traversal until last node ` `    ``struct` `Node* temp; ` `    ``while``(!q.empty()) ` `    ``{ ` `        ``temp = q.front(); ` `        ``q.pop(); ` `        ``if``(temp == d_node) ` `        ``{ ` `            ``temp = NULL; ` `            ``delete``(d_node); ` `            ``return``; ` `        ``} ` `        ``if` `(temp->right) ` `        ``{ ` `            ``if` `(temp->right == d_node) ` `            ``{ ` `                ``temp->right = NULL; ` `                ``delete``(d_node); ` `                ``return``; ` `            ``} ` `            ``else` `                ``q.push(temp->right); ` `        ``} ` ` `  `        ``if` `(temp->left) ` `        ``{ ` `            ``if` `(temp->left == d_node) ` `            ``{ ` `                ``temp->left=NULL; ` `                ``delete``(d_node); ` `                ``return``; ` `            ``} ` `            ``else` `                ``q.push(temp->left); ` `        ``} ` `    ``} ` `} ` ` `  `/* function to delete element in binary tree */` `void` `deletion(``struct` `Node* root, ``int` `key) ` `{ ` `    ``queue<``struct` `Node*> q; ` `    ``q.push(root); ` ` `  `    ``struct` `Node *temp; ` `    ``struct` `Node *key_node = NULL; ` ` `  `    ``// Do level order traversal to find deepest ` `    ``// node(temp) and node to be deleted (key_node) ` `    ``while` `(!q.empty()) ` `    ``{ ` `        ``temp = q.front(); ` `        ``q.pop(); ` ` `  `        ``if` `(temp->key == key) ` `            ``key_node = temp; ` ` `  `        ``if` `(temp->left) ` `            ``q.push(temp->left); ` ` `  `        ``if` `(temp->right) ` `            ``q.push(temp->right); ` `    ``} ` ` `  `    ``int` `x = temp->key; ` `    ``deletDeepest(root, temp); ` `    ``key_node->key = x; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``struct` `Node* root = newNode(10); ` `    ``root->left = newNode(11); ` `    ``root->left->left = newNode(7); ` `    ``root->left->right = newNode(12); ` `    ``root->right = newNode(9); ` `    ``root->right->left = newNode(15); ` `    ``root->right->right = newNode(8); ` ` `  `    ``cout << ``"Inorder traversal before deletion : "``; ` `    ``inorder(root); ` ` `  `    ``int` `key = 11; ` `    ``deletion(root, key); ` ` `  `    ``cout << endl; ` `    ``cout << ``"Inorder traversal after deletion : "``; ` `    ``inorder(root); ` ` `  `    ``return` `0; ` `} `

Output:

```Inorder traversal before deletion : 7 11 12 10 15 9 8
Inorder traversal after deletion : 7 8 12 10 15 9
```

Note: We can also replace node’s data that is to be deleted with any node whose left and right child points to NULL but we only use deepest node in order to maintain the Balance of a binary tree.

Tree Tree