# Delete the last leaf node in a Binary Tree

Given a Binary Tree, the task is to find and DELETE the last leaf node.

The leaf node is a node with no children. The last leaf node would be the node that is traversed last in sequence during Level Order Traversal. The problem statement is to identify this last visited node and delete this particular node.

Examples:

```
Input:
Given Tree is:
6
/     \
5       4
/   \       \
1     2       5

Level Order Traversal is: 6 5 4 1 2 5
Output:
After deleting the last node (5),
the tree would look like as follows.

6
/     \
5       4
/   \
1     2
Level Order Traversal is: 6 5 4 1 2

Input:
Given tree is:
1
/     \
3        10
/   \     /   \
2     15   4     5
/
1
Level Order Traversal is: 1 3 10 2 15 4 5 1
Output:
After deleting the last node (1),
the tree would look like as follows.

1
/     \
3        10
/   \     /   \
2     15   4     5

Level Order Traversal is: 1 3 10 2 15 4 5
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

This problem is slightly different from Delete leaf node with value as X wherein we are right away given the value of last leaf node (X) to be deleted, based on which we perform checks and mark the parent node as null to delete it.

This approach would identify the last present leaf node on last level of the tree and would delete it.

Approach 1: Traversing last level nodes and keeping track of Parent and traversed node.

This approach would traverse each node until we reach the last level of the given binary tree. While traversing, we keep track of the last traversed node and its Parent.

Once done with traversal, Check if the parent has Right Child, if yes, set it to NULL. If no, set the left pointer to NULL

Below is the implementation of the approach:

## C++

 `// CPP implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Tree Node ` `class` `Node ` `{ ` `public``: ` `    ``int` `data; ` `    ``Node *left, *right; ` ` `  `    ``Node(``int` `data) : data(data) {} ` `}; ` ` `  `// Method to perform inorder traversal ` `void` `inorder(Node *root) ` `{ ` `    ``if` `(root == NULL) ` `        ``return``; ` ` `  `    ``inorder(root->left); ` `    ``cout << root->data << ``" "``; ` `    ``inorder(root->right); ` `} ` ` `  `// To keep track of last processed ` `// nodes parent and node itself. ` `Node *lastNode, *parentOfLastNode; ` ` `  `// Method to get the height of the tree ` `int` `height(Node *root) ` `{ ` `    ``if` `(root == NULL) ` `        ``return` `0; ` ` `  `    ``int` `lheight = height(root->left) + 1; ` `    ``int` `rheight = height(root->right) + 1; ` ` `  `    ``return` `max(lheight, rheight); ` `} ` ` `  `// Method to keep track of parents ` `// of every node ` `void` `getLastNodeAndItsParent(Node *root, ``int` `level, Node *parent) ` `{ ` `    ``if` `(root == NULL) ` `        ``return``; ` ` `  `    ``// The last processed node in ` `    ``// Level Order Traversal has to ` `    ``// be the node to be deleted. ` `    ``// This will store the last ` `    ``// processed node and its parent. ` `    ``if` `(level == 1) ` `    ``{ ` `        ``lastNode = root; ` `        ``parentOfLastNode = parent; ` `    ``} ` `    ``getLastNodeAndItsParent(root->left, level - 1, root); ` `    ``getLastNodeAndItsParent(root->right, level - 1, root); ` `} ` ` `  `// Method to delete last leaf node ` `void` `deleteLastNode(Node *root) ` `{ ` `    ``int` `levelOfLastNode = height(root); ` `    ``getLastNodeAndItsParent(root, levelOfLastNode, NULL); ` ` `  `    ``if` `(lastNode and parentOfLastNode) ` `    ``{ ` `        ``if` `(parentOfLastNode->right) ` `            ``parentOfLastNode->right = NULL; ` `        ``else` `            ``parentOfLastNode->left = NULL; ` `    ``} ` `    ``else` `        ``cout << ``"Empty Tree\n"``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``Node *root = ``new` `Node(6); ` `    ``root->left = ``new` `Node(5); ` `    ``root->right = ``new` `Node(4); ` `    ``root->left->left = ``new` `Node(1); ` `    ``root->left->right = ``new` `Node(2); ` `    ``root->right->right = ``new` `Node(5); ` ` `  `    ``cout << ``"Inorder traversal before deletion of last node :\n"``; ` `    ``inorder(root); ` ` `  `    ``deleteLastNode(root); ` ` `  `    ``cout << ``"\nInorder traversal after deletion of last node :\n"``; ` `    ``inorder(root); ` ` `  `    ``return` `0; ` `} ` ` `  `// This code is contributed by ` `// sanjeev2552 `

## Java

 `// Java Implementation of the approach ` `public` `class` `DeleteLastNode { ` ` `  `    ``// Tree Node ` `    ``static` `class` `Node { ` ` `  `        ``Node left, right; ` `        ``int` `data; ` ` `  `        ``Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `        ``} ` `    ``} ` ` `  `    ``// Method to perform inorder traversal ` `    ``public` `void` `inorder(Node root) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``inorder(root.left); ` `        ``System.out.print(root.data + ``" "``); ` `        ``inorder(root.right); ` `    ``} ` ` `  `    ``// To keep track of last processed ` `    ``// nodes parent and node itself. ` `    ``public` `static` `Node lastNode; ` `    ``public` `static` `Node parentOfLastNode; ` ` `  `    ``// Method to get the height of the tree ` `    ``public` `int` `height(Node root) ` `    ``{ ` ` `  `        ``if` `(root == ``null``) ` `            ``return` `0``; ` ` `  `        ``int` `lheight = height(root.left) + ``1``; ` `        ``int` `rheight = height(root.right) + ``1``; ` ` `  `        ``return` `Math.max(lheight, rheight); ` `    ``} ` ` `  `    ``// Method to delete last leaf node ` `    ``public` `void` `deleteLastNode(Node root) ` `    ``{ ` ` `  `        ``int` `levelOfLastNode = height(root); ` ` `  `        ``// Get all nodes at last level ` `        ``getLastNodeAndItsParent(root, ` `                                ``levelOfLastNode, ` `                                ``null``); ` ` `  `        ``if` `(lastNode != ``null` `            ``&& parentOfLastNode != ``null``) { ` ` `  `            ``if` `(parentOfLastNode.right != ``null``) ` `                ``parentOfLastNode.right = ``null``; ` `            ``else` `                ``parentOfLastNode.left = ``null``; ` `        ``} ` `        ``else` `            ``System.out.println(``"Empty Tree"``); ` `    ``} ` ` `  `    ``// Method to keep track of parents ` `    ``// of every node ` `    ``public` `void` `getLastNodeAndItsParent(Node root, ` `                                        ``int` `level, ` `                                        ``Node parent) ` `    ``{ ` ` `  `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``// The last processed node in ` `        ``// Level Order Traversal has to ` `        ``// be the node to be deleted. ` `        ``// This will store the last ` `        ``// processed node and its parent. ` `        ``if` `(level == ``1``) { ` `            ``lastNode = root; ` `            ``parentOfLastNode = parent; ` `        ``} ` `        ``getLastNodeAndItsParent(root.left, ` `                                ``level - ``1``, ` `                                ``root); ` `        ``getLastNodeAndItsParent(root.right, ` `                                ``level - ``1``, ` `                                ``root); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``Node root = ``new` `Node(``6``); ` `        ``root.left = ``new` `Node(``5``); ` `        ``root.right = ``new` `Node(``4``); ` `        ``root.left.left = ``new` `Node(``1``); ` `        ``root.left.right = ``new` `Node(``2``); ` `        ``root.right.right = ``new` `Node(``5``); ` ` `  `        ``DeleteLastNode deleteLastNode = ``new` `DeleteLastNode(); ` ` `  `        ``System.out.println(``"Inorder traversal "` `                           ``+ ``"before deletion "` `                           ``+ ``"of last node : "``); ` ` `  `        ``deleteLastNode.inorder(root); ` ` `  `        ``deleteLastNode.deleteLastNode(root); ` ` `  `        ``System.out.println(``"\nInorder traversal "` `                           ``+ ``"after deletion of "` `                           ``+ ``"last node : "``); ` `        ``deleteLastNode.inorder(root); ` `    ``} ` `} `

## C#

 `// C# implementation of the above approach ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `    ``// Tree Node ` `    ``public` `class` `Node ` `    ``{ ` `        ``public` `Node left, right; ` `        ``public` `int` `data; ` ` `  `        ``public` `Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `        ``} ` `    ``} ` ` `  `    ``// Method to perform inorder traversal ` `    ``public` `void` `inorder(Node root) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``inorder(root.left); ` `        ``Console.Write(root.data + ``" "``); ` `        ``inorder(root.right); ` `    ``} ` ` `  `    ``// To keep track of last processed ` `    ``// nodes parent and node itself. ` `    ``public` `static` `Node lastNode; ` `    ``public` `static` `Node parentOfLastNode; ` ` `  `    ``// Method to get the height of the tree ` `    ``public` `int` `height(Node root) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return` `0; ` ` `  `        ``int` `lheight = height(root.left) + 1; ` `        ``int` `rheight = height(root.right) + 1; ` ` `  `        ``return` `Math.Max(lheight, rheight); ` `    ``} ` ` `  `    ``// Method to delete last leaf node ` `    ``public` `void` `deleteLastNode(Node root) ` `    ``{ ` `        ``int` `levelOfLastNode = height(root); ` ` `  `        ``// Get all nodes at last level ` `        ``getLastNodeAndItsParent(root, ` `                                ``levelOfLastNode, ` `                                ``null``); ` ` `  `        ``if` `(lastNode != ``null` `&&  ` `            ``parentOfLastNode != ``null``) ` `        ``{ ` `            ``if` `(parentOfLastNode.right != ``null``) ` `                ``parentOfLastNode.right = ``null``; ` `            ``else` `                ``parentOfLastNode.left = ``null``; ` `        ``} ` `        ``else` `            ``Console.WriteLine(``"Empty Tree"``); ` `    ``} ` ` `  `    ``// Method to keep track of parents ` `    ``// of every node ` `    ``public` `void` `getLastNodeAndItsParent(Node root, ` `                                        ``int` `level, ` `                                        ``Node parent) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``// The last processed node in ` `        ``// Level Order Traversal has to ` `        ``// be the node to be deleted. ` `        ``// This will store the last ` `        ``// processed node and its parent. ` `        ``if` `(level == 1) ` `        ``{ ` `            ``lastNode = root; ` `            ``parentOfLastNode = parent; ` `        ``} ` `        ``getLastNodeAndItsParent(root.left, ` `                                ``level - 1, ` `                                ``root); ` `        ``getLastNodeAndItsParent(root.right, ` `                                ``level - 1, ` `                                ``root); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``Node root = ``new` `Node(6); ` `        ``root.left = ``new` `Node(5); ` `        ``root.right = ``new` `Node(4); ` `        ``root.left.left = ``new` `Node(1); ` `        ``root.left.right = ``new` `Node(2); ` `        ``root.right.right = ``new` `Node(5); ` ` `  `        ``GFG deleteLastNode = ``new` `GFG(); ` ` `  `        ``Console.WriteLine(``"Inorder traversal "` `+  ` `                            ``"before deletion "` `+  ` `                             ``"of last node : "``); ` ` `  `        ``deleteLastNode.inorder(root); ` ` `  `        ``deleteLastNode.deleteLastNode(root); ` ` `  `        ``Console.WriteLine(``"\nInorder traversal "` `+  ` `                            ``"after deletion of "` `+  ` `                                  ``"last node : "``); ` `        ``deleteLastNode.inorder(root); ` `    ``} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```Inorder traversal before deletion of last node :
1 5 2 6 4 5
Inorder traversal after deletion of last node :
1 5 2 6 4
```

Time Complexity: Since each node would be traversed once, the time taken would be linear to the number of nodes in a given tree.

Approach 2: Performing Level Order Traversal on given Binary Tree using Queue and tracking Parent and last traversed node.

This is a Non-Recursive way of achieving above Approach 1. We perform the Level Order Traversal using Queue and keeping track of every visited node and its parent. The last visited node would be the last node that is to be deleted.

Below is the implementation of the approach:

## Java

 `// Java implementation ` `import` `java.util.LinkedList; ` `import` `java.util.Queue; ` ` `  ` `  `public` `class` `DeleteLastNode { ` `     `  `    ``// Tree Node ` `    ``static` `class` `Node { ` ` `  `        ``Node left, right; ` `        ``int` `data; ` ` `  `        ``Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `        ``} ` `    ``}  ` ` `  `    ``// Function to perform the inorder traversal of the tree ` `    ``public` `void` `inorder(Node root) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``inorder(root.left); ` `        ``System.out.print(root.data + ``" "``); ` `        ``inorder(root.right); ` `    ``} ` ` `  `    ``// To keep track of last ` `    ``// processed nodes parent ` `    ``// and node itself. ` `    ``public` `static` `Node lastLevelLevelOrder; ` `    ``public` `static` `Node parentOfLastNode; ` ` `  `    ``// Method to delete the last node ` `    ``// from the tree ` `    ``public` `void` `deleteLastNode(Node root) ` `    ``{ ` ` `  `        ``// If tree is empty, it ` `        ``// would return without ` `        ``// any deletion ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``// The queue would be needed ` `        ``// to maintain the level order ` `        ``// traversal of nodes ` `        ``Queue queue = ``new` `LinkedList<>(); ` ` `  `        ``queue.offer(root); ` ` `  `        ``// The traversing would ` `        ``// continue untill all ` `        ``// nodes are traversed once ` `        ``while` `(!queue.isEmpty()) { ` ` `  `            ``Node temp = queue.poll(); ` ` `  `            ``// If there is left child ` `            ``if` `(temp.left != ``null``) { ` `                ``queue.offer(temp.left); ` ` `  `                ``// For every traverssed node, ` `                ``// we would check if it is a ` `                ``// leaf node by checking if ` `                ``// current node has children to it ` `                ``if` `(temp.left.left == ``null` `                    ``&& temp.left.right == ``null``) { ` ` `  `                    ``// For every leaf node ` `                    ``// encountered, we would ` `                    ``// keep not of it as ` `                    ``// "Previously Visided Leaf node. ` `                    ``lastLevelLevelOrder = temp.left; ` `                    ``parentOfLastNode = temp; ` `                ``} ` `            ``} ` ` `  `            ``if` `(temp.right != ``null``) { ` `                ``queue.offer(temp.right); ` ` `  `                ``if` `(temp.right.left == ``null` `                    ``&& temp.right.right == ``null``) { ` ` `  `                    ``// For every leaf node ` `                    ``// encountered, we would ` `                    ``// keep not of it as ` `                    ``// "Previously Visided Leaf node. ` `                    ``lastLevelLevelOrder = temp.right; ` `                    ``parentOfLastNode = temp; ` `                ``} ` `            ``} ` `        ``} ` ` `  `        ``// Once out of above loop. ` `        ``// we would certainly have ` `        ``// last visited node, which ` `        ``// is to be deleted and its ` `        ``// parent node. ` ` `  `        ``if` `(lastLevelLevelOrder != ``null` `            ``&& parentOfLastNode != ``null``) { ` ` `  `            ``// If last node is right child ` `            ``// of parent, make right node ` `            ``// of its parent as NULL or ` `            ``// make left node as NULL ` `            ``if` `(parentOfLastNode.right != ``null``) ` `                ``parentOfLastNode.right = ``null``; ` `            ``else` `                ``parentOfLastNode.left = ``null``; ` `        ``} ` `        ``else` `            ``System.out.println(``"Empty Tree"``); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``Node root = ``new` `Node(``6``); ` `        ``root.left = ``new` `Node(``5``); ` `        ``root.right = ``new` `Node(``4``); ` `        ``root.left.left = ``new` `Node(``1``); ` `        ``root.left.right = ``new` `Node(``2``); ` `        ``root.right.right = ``new` `Node(``5``); ` ` `  `        ``DeleteLastNode deleteLastNode ` `            ``= ``new` `DeleteLastNode(); ` ` `  `        ``System.out.println(``"Inorder traversal "` `                           ``+ ``"before deletion of "` `                           ``+ ``"last node : "``); ` `        ``deleteLastNode.inorder(root); ` ` `  `        ``deleteLastNode.deleteLastNode(root); ` ` `  `        ``System.out.println(``"\nInorder traversal "` `                           ``+ ``"after deletion "` `                           ``+ ``"of last node : "``); ` ` `  `        ``deleteLastNode.inorder(root); ` `    ``} ` `} `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` `public` `class` `DeleteLastNode { ` `      `  `    ``// Tree Node ` `    ``public` `class` `Node { ` `  `  `        ``public` `Node left, right; ` `        ``public` `int` `data; ` `  `  `        ``public` `Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `        ``} ` `    ``}  ` `  `  `    ``// Function to perform the inorder traversal of the tree ` `    ``public` `void` `inorder(Node root) ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` `  `  `        ``inorder(root.left); ` `        ``Console.Write(root.data + ``" "``); ` `        ``inorder(root.right); ` `    ``} ` `  `  `    ``// To keep track of last ` `    ``// processed nodes parent ` `    ``// and node itself. ` `    ``public` `static` `Node lastLevelLevelOrder; ` `    ``public` `static` `Node parentOfLastNode; ` `  `  `    ``// Method to delete the last node ` `    ``// from the tree ` `    ``public` `void` `deleteLastNode(Node root) ` `    ``{ ` `  `  `        ``// If tree is empty, it ` `        ``// would return without ` `        ``// any deletion ` `        ``if` `(root == ``null``) ` `            ``return``; ` `  `  `        ``// The queue would be needed ` `        ``// to maintain the level order ` `        ``// traversal of nodes ` `        ``Queue queue = ``new` `Queue(); ` `  `  `        ``queue.Enqueue(root); ` `  `  `        ``// The traversing would ` `        ``// continue untill all ` `        ``// nodes are traversed once ` `        ``while` `(queue.Count!=0) { ` `  `  `            ``Node temp = queue.Dequeue(); ` `  `  `            ``// If there is left child ` `            ``if` `(temp.left != ``null``) { ` `                ``queue.Enqueue(temp.left); ` `  `  `                ``// For every traverssed node, ` `                ``// we would check if it is a ` `                ``// leaf node by checking if ` `                ``// current node has children to it ` `                ``if` `(temp.left.left == ``null` `                    ``&& temp.left.right == ``null``) { ` `  `  `                    ``// For every leaf node ` `                    ``// encountered, we would ` `                    ``// keep not of it as ` `                    ``// "Previously Visided Leaf node. ` `                    ``lastLevelLevelOrder = temp.left; ` `                    ``parentOfLastNode = temp; ` `                ``} ` `            ``} ` `  `  `            ``if` `(temp.right != ``null``) { ` `                ``queue.Enqueue(temp.right); ` `  `  `                ``if` `(temp.right.left == ``null` `                    ``&& temp.right.right == ``null``) { ` `  `  `                    ``// For every leaf node ` `                    ``// encountered, we would ` `                    ``// keep not of it as ` `                    ``// "Previously Visided Leaf node. ` `                    ``lastLevelLevelOrder = temp.right; ` `                    ``parentOfLastNode = temp; ` `                ``} ` `            ``} ` `        ``} ` `  `  `        ``// Once out of above loop. ` `        ``// we would certainly have ` `        ``// last visited node, which ` `        ``// is to be deleted and its ` `        ``// parent node. ` `  `  `        ``if` `(lastLevelLevelOrder != ``null` `            ``&& parentOfLastNode != ``null``) { ` `  `  `            ``// If last node is right child ` `            ``// of parent, make right node ` `            ``// of its parent as NULL or ` `            ``// make left node as NULL ` `            ``if` `(parentOfLastNode.right != ``null``) ` `                ``parentOfLastNode.right = ``null``; ` `            ``else` `                ``parentOfLastNode.left = ``null``; ` `        ``} ` `        ``else` `            ``Console.WriteLine(``"Empty Tree"``); ` `    ``} ` `  `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `  `  `        ``Node root = ``new` `Node(6); ` `        ``root.left = ``new` `Node(5); ` `        ``root.right = ``new` `Node(4); ` `        ``root.left.left = ``new` `Node(1); ` `        ``root.left.right = ``new` `Node(2); ` `        ``root.right.right = ``new` `Node(5); ` `  `  `        ``DeleteLastNode deleteLastNode ` `            ``= ``new` `DeleteLastNode(); ` `  `  `        ``Console.WriteLine(``"Inorder traversal "` `                           ``+ ``"before deletion of "` `                           ``+ ``"last node : "``); ` `        ``deleteLastNode.inorder(root); ` `  `  `        ``deleteLastNode.deleteLastNode(root); ` `  `  `        ``Console.WriteLine(``"\nInorder traversal "` `                           ``+ ``"after deletion "` `                           ``+ ``"of last node : "``); ` `  `  `        ``deleteLastNode.inorder(root); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```Inorder traversal before deletion of last node :
1 5 2 6 4 5
Inorder traversal after deletion of last node :
1 5 2 6 4
```

Time Complexity: Since every node would be visited once, the time taken would be linear to the number of nodes present in the tree.
Auxilary Space: Since we would be maintaining a queue to do the level order traversal, the space consumed would be .

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