# Python Program To Find The Sum Of Last N Nodes Of The Given Linked List

• Last Updated : 18 May, 2022

Given a linked list and a number n. Find the sum of the last n nodes of the linked list.
Constraints: 0 <= n <= number of nodes in the linked list.

Examples:

```Input: 10->6->8->4->12, n = 2
Output: 16
Sum of last two nodes:
12 + 4 = 16

Input: 15->7->9->5->16->14, n = 4
Output: 44```

Method 1: (Recursive approach using system call stack)
Recursively traverse the linked list up to the end. Now during the return from the function calls, add up the last n nodes. The sum can be accumulated in some variable passed by reference to the function or to some global variable.

## Python3

 `# Python3 implementation to find the sum of``# last 'n' nodes of the Linked List`` ` `# Linked List node ``class` `Node: ``    ``def` `__init__(``self``, data): ``        ``self``.data ``=` `data ``        ``self``.``next` `=` `None`` ` `head ``=` `None``n ``=` `0``sum` `=` `0`` ` `# Function to insert a node at the``# beginning of the linked list``def` `push(head_ref, new_data):``    ``global` `head``     ` `    ``# Allocate node ``    ``new_node ``=` `Node(``0``)``     ` `    ``# Put in the data ``    ``new_node.data ``=` `new_data``     ` `    ``# Link the old list to the new node ``    ``new_node.``next` `=` `head_ref``     ` `    ``# Move the head to point to the ``    ``# new node ``    ``head_ref ``=` `new_node``    ``head ``=` `head_ref`` ` `# Function to recursively find the sum of ``# last 'n' nodes of the given linked list``def` `sumOfLastN_Nodes(head):`` ` `    ``global` `sum``    ``global` `n`` ` `    ``# if head = None``    ``if` `(head ``=``=` `None``):``        ``return`` ` `    ``# Recursively traverse the remaining ``    ``# nodes``    ``sumOfLastN_Nodes(head.``next``)`` ` `    ``# if node count 'n' is greater than 0``    ``if` `(n > ``0``) :``     ` `        ``# Accumulate sum``        ``sum` `=` `sum` `+` `head.data`` ` `        ``# Reduce node count 'n' by 1``        ``n ``=` `n ``-` `1``     ` `# Utility function to find the sum of ``# last 'n' nodes``def` `sumOfLastN_NodesUtil(head, n):``     ` `    ``global` `sum``     ` `    ``# if n == 0``    ``if` `(n <``=` `0``):``        ``return` `0`` ` `    ``sum` `=` `0`` ` `    ``# Find the sum of last 'n' nodes``    ``sumOfLastN_Nodes(head)`` ` `    ``# Required sum``    ``return` `sum`` ` `# Driver Code``head ``=` `None`` ` `# Create linked list 10.6.8.4.12``push(head, ``12``)``push(head, ``4``)``push(head, ``8``)``push(head, ``6``)``push(head, ``10``)`` ` `n ``=` `2``print``(``"Sum of last "` `, n , ``      ``" nodes = "``, ``      ``sumOfLastN_NodesUtil(head, n))`` ` `# This code is contributed by Arnab Kundu`

Output:

`Sum of last 2 nodes = 16`

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(n), if system call stack is being considered.

Method 2: (Iterative approach using user-defined stack)
It is an iterative procedure to the recursive approach explained in Method 1 of this post. Traverses the nodes from left to right. While traversing pushes the nodes to a user-defined stack. Then pops the top n values from the stack and adds them.

## Python3

 `# Python3 implementation to find the sum of ``# last 'n' nodes of the Linked List `` ` `# Linked List node ``class` `Node: ``    ``def` `__init__(``self``, data): ``        ``self``.data ``=` `data ``        ``self``.``next` `=` `None`` ` `head ``=` `None``n ``=` `0``sum` `=` `0`` ` `# Function to insert a node at the ``# beginning of the linked list ``def` `push(head_ref, new_data): ``    ``global` `head ``     ` `    ``# Allocate node ``    ``new_node ``=` `Node(``0``) ``     ` `    ``# Put in the data ``    ``new_node.data ``=` `new_data ``     ` `    ``# Link the old list to the new node ``    ``new_node.``next` `=` `head_ref ``     ` `    ``# Move the head to point to the ``    ``# new node ``    ``head_ref ``=` `new_node ``    ``head ``=` `head_ref ``     ` `# Utility function to find the sum of ``# last 'n' nodes ``def` `sumOfLastN_NodesUtil(head, n):``     ` `    ``global` `sum``     ` `    ``# if n == 0 ``    ``if` `(n <``=` `0``):``        ``return` `0``     ` `    ``st ``=` `[]``    ``sum` `=` `0``     ` `    ``# Traverses the list from left to right ``    ``while` `(head !``=` `None``):``         ` `        ``# Push the node's data onto the ``        ``# stack 'st' ``        ``st.append(head.data) ``         ` `        ``# Move to next node ``        ``head ``=` `head.``next``     ` `    ``# Pop 'n' nodes from 'st' and ``    ``# add them ``    ``while` `(n):``        ``n ``-``=` `1``        ``sum` `+``=` `st[``0``]``        ``st.pop(``0``) ``         ` `    ``# Required sum ``    ``return` `sum`` ` `# Driver Code ``head ``=` `None`` ` `# Create linked list 10.6.8.4.12 ``push(head, ``12``) ``push(head, ``4``) ``push(head, ``8``) ``push(head, ``6``) ``push(head, ``10``) `` ` `n ``=` `2``print``(``"Sum of last"` `, n , ``      ``"nodes ="``, ``      ``sumOfLastN_NodesUtil(head, n)) ``# This code is contributed by shubhamsingh10 `

Output:

`Sum of last 2 nodes = 16`

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(n), stack size

Method 3: (Reversing the linked list)
Following are the steps:

1. Reverse the given linked list.
2. Traverse the first n nodes of the reversed linked list.
4. Reverse the linked list back to its original order.

## Python3

 `# Python implementation to find the sum of last``# 'n' Nodes of the Linked List``''' A Linked list Node '''`` ` `# A Linked list Node``class` `Node:`` ` `    ``def` `__init__(``self``, x):``        ``self``.data ``=` `x``        ``self``.``next` `=` `None`` ` `head ``=` `None`` ` `# Function to insert a Node at the``# beginning of the linked list``def` `push(head_ref, new_data):``   ` `    ``# Allocate Node``    ``new_Node ``=` `Node(new_data)`` ` `    ``# Put in the data``    ``new_Node.data ``=` `new_data`` ` `    ``# Link the old list to the new Node``    ``new_Node.``next` `=` `head_ref`` ` `    ``# Move the head to point the new Node``    ``head_ref ``=` `new_Node``    ``head ``=` `head_ref``    ``return` `head`` ` `def` `reverseList():``    ``global` `head;``    ``current, prev, ``next` `=` `None``, ``    ``None``, ``None``;``    ``current ``=` `head;``    ``prev ``=` `None``;`` ` `    ``while` `(current !``=` `None``):``        ``next` `=` `current.``next``;``        ``current.``next` `=` `prev;``        ``prev ``=` `current;``        ``current ``=` `next``;`` ` `    ``head ``=` `prev;`` ` `# Utility function to find the sum ``# of last 'n' Nodes``def` `sumOfLastN_NodesUtil(n):``   ` `    ``# if n == 0``    ``if` `(n <``=` `0``):``        ``return` `0``;`` ` `    ``# Reverse the linked list``    ``reverseList();`` ` `    ``sum` `=` `0``;``    ``current ``=` `head;`` ` `    ``# Traverse the 1st 'n' Nodes of the ``    ``# reversed linked list and add them``    ``while` `(current !``=` `None` `and` `n > ``0``):``       ` `        ``# Accumulate Node's data to 'sum'``        ``sum` `+``=` `current.data;`` ` `        ``# Move to next Node``        ``current ``=` `current.``next``;``        ``n ``-``=` `1``;`` ` `    ``# Reverse back the linked list``    ``reverseList();`` ` `    ``# Required sum``    ``return` `sum``;`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:`` ` `    ``# Create linked list 10.6.8.4.12``    ``head ``=` `push(head, ``12``)``    ``head ``=` `push(head, ``4``)``    ``head ``=` `push(head, ``8``)``    ``head ``=` `push(head, ``6``)``    ``head ``=` `push(head, ``10``)`` ` `    ``n ``=` `2``;``    ``print``(``"Sum of last "``, n, ``          ``" Nodes = "``, ``          ``sumOfLastN_NodesUtil(n));``# This code is contributed by Princi Singh`

Output:

`Sum of last 2 nodes = 16`

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(1)

Method 4: (Using the length of linked list)
Following are the steps:

1. Calculate the length of the given Linked List. Let it be len.
2. First, traverse the (len – n) nodes from the beginning.
3. Then traverse the remaining n nodes and while traversing add them.

## Python3

 `# Python3 implementation to find the sum ``# of last 'n' Nodes of the Linked List`` ` `# A Linked list Node ``class` `Node:``     ` `    ``def` `__init__(``self``, x):        ``        ``self``.data ``=` `x``        ``self``.``next` `=` `None``         ` `head ``=` `None`` ` `# Function to insert a Node at the``# beginning of the linked list``def` `push(head_ref, new_data):``     ` `    ``# Allocate Node ``    ``new_Node ``=` `Node(new_data)`` ` `    ``# Put in the data ``    ``new_Node.data ``=` `new_data`` ` `    ``# Link the old list to the new Node``    ``new_Node.``next` `=` `head_ref`` ` `    ``# Move the head to point to the new Node ``    ``head_ref ``=` `new_Node``    ``head ``=` `head_ref``    ``return` `head`` ` `# Utility function to find the sum of ``# last 'n' Nodes``def` `sumOfLastN_NodesUtil(head, n):``     ` `    ``# If n == 0``    ``if` `(n <``=` `0``):``        ``return` `0`` ` `    ``sum` `=` `0``    ``len` `=` `0``    ``temp ``=` `head``     ` `    ``# Calculate the length of the ``    ``# linked list``    ``while` `(temp !``=` `None``):``        ``len` `+``=` `1``        ``temp ``=` `temp.``next`` ` `    ``# Count of first (len - n) Nodes``    ``c ``=` `len` `-` `n``    ``temp ``=` `head`` ` `    ``# Just traverse the 1st 'c' Nodes``    ``while` `(temp !``=` `None` `and` `c > ``0``):``         ` `        ``# Move to next Node``        ``temp ``=` `temp.``next``        ``c ``-``=` `1`` ` `    ``# Now traverse the last 'n' Nodes ``    ``# and add them``    ``while` `(temp !``=` `None``):``         ` `        ``# Accumulate Node's data to sum``        ``sum` `+``=` `temp.data`` ` `        ``# Move to next Node``        ``temp ``=` `temp.``next`` ` `    ``# Required sum``    ``return` `sum`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``     ` `    ``# Create linked list 10->6->8->4->12``    ``head ``=` `push(head, ``12``)``    ``head ``=` `push(head, ``4``)``    ``head ``=` `push(head, ``8``)``    ``head ``=` `push(head, ``6``)``    ``head ``=` `push(head, ``10``)`` ` `    ``n ``=` `2``     ` `    ``print``(``"Sum of last "``, n, ``" Nodes = "``, ``          ``sumOfLastN_NodesUtil(head, n))`` ` `# This code is contributed by Princi Singh `

Output:

`Sum of last 2 nodes = 16`

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(1)

Method 5: (Use of two pointers requires single traversal)
Maintain two pointers – reference pointer and main pointer. Initialize both reference and main pointers to head. First, move reference pointer to n nodes from head and while traversing accumulate node’s data to some variable, say sum. Now move both pointers simultaneously until the reference pointer reaches the end of the list and while traversing accumulate all node’s data to sum pointed by the reference pointer and accumulate all node’s data to some variable, say, temp, pointed by the main pointer. Now, (sum – temp) is the required sum of the last n nodes.

## Python3

 `# Python3 implementation to find the sum ``# of last 'n' nodes of the Linked List``class` `Node:``    ``def` `__init__(``self``, x):``        ``self``.data ``=` `x``        ``self``.``next` `=` `None`` ` `# Function to insert a node at the``# beginning of the linked list``def` `push(head_ref,new_data):``   ` `    ``# Allocate node ``    ``new_node ``=` `Node(new_data)`` ` `    ``# Link the old list to the new node ``    ``new_node.``next` `=` `head_ref`` ` `    ``# Move the head to point to the ``    ``# new node ``    ``head_ref ``=` `new_node`` ` `    ``return` `head_ref`` ` `# Utility function to find the sum of ``# last 'n' nodes``def` `sumOfLastN_NodesUtil(head, n):``   ` `    ``# if n == 0``    ``if` `(n <``=` `0``):``        ``return` `0`` ` `    ``sum` `=` `0``    ``temp ``=` `0``    ``ref_ptr  ``=` `None``    ``main_ptr ``=` `None``    ``ref_ptr ``=` `main_ptr ``=` `head`` ` `    ``# Traverse 1st 'n' nodes through 'ref_ptr' ``    ``# and accumulate all node's data to 'sum'``    ``while` `(ref_ptr !``=` `None` `and`  `n):``        ``sum` `+``=` `ref_ptr.data`` ` `        ``# Move to next node``        ``ref_ptr ``=` `ref_ptr.``next``        ``n ``-``=` `1`` ` `    ``# Traverse to the end of the linked list``    ``while` `(ref_ptr !``=` `None``):`` ` `        ``# Accumulate all node's data to 'temp' ``        ``# pointed by the 'main_ptr'``        ``temp ``+``=` `main_ptr.data`` ` `        ``# Accumulate all node's data to 'sum' ``        ``# pointed by the 'ref_ptr'``        ``sum` `+``=` `ref_ptr.data`` ` `        ``# Move both the pointers to their ``        ``# respective next nodes``        ``main_ptr ``=` `main_ptr.``next``        ``ref_ptr ``=` `ref_ptr.``next`` ` `    ``# Required sum``    ``return` `(``sum` `-` `temp)`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``head ``=` `None`` ` `    ``# Create linked list 10.6.8.4.12``    ``head ``=` `push(head, ``12``)``    ``head ``=` `push(head, ``4``)``    ``head ``=` `push(head, ``8``)``    ``head ``=` `push(head, ``6``)``    ``head ``=` `push(head, ``10``)`` ` `    ``n ``=` `2``    ``print``(``"Sum of last "``, n, ``" nodes = "``,``          ``sumOfLastN_NodesUtil(head, n))``# This code is contributed by mohit kumar 29`

Output:

`Sum of last 2 nodes = 16`

Time Complexity: O(n), where n is the number of nodes in the linked list.
Auxiliary Space: O(1)

Please refer complete article on Find the sum of last n nodes of the given Linked List for more details!

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