# Remove all the Even Digit Sum Nodes from a Doubly Linked List

Given a Doubly linked list containing N nodes, the task is to remove all the nodes from the list which contains elements whose digit sum is even.

Examples:

Input: DLL = 18 <=> 15 <=> 8 <=> 9 <=> 14
Output: 18 <=> 9 <=> 14
Explanation:
18 -> 1 + 8 = 9
15 -> 1 + 5 = 6
8 -> 8
9 -> 9
14 -> 1 + 4 = 5
Here, digit sum for nodes containing 15 and 8 are even.
Hence, these nodes have been deleted.

Input: DLL = 5 <=> 3 <=> 4 <=> 2 <=> 9
Output: 5 <=> 3 <=> 9
Explanation:
The linked list contains two digit sum values 4 and 2.
Hence, these nodes have been deleted.

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

Approach:
A simple approach is to traverse the nodes of the doubly linked list one by one and for each node first, find the digit sum for the value present in the node by iterating through each digit and then finally remove the nodes whose digit sum is even.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to remove all ` `// the Even Digit Sum Nodes from a ` `// doubly linked list ` ` `  `#include ` ` `  `using` `namespace` `std; ` ` `  `// Node of the doubly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``Node *prev, *next; ` `}; ` ` `  `// Function to insert a node at the beginning ` `// of the Doubly Linked List ` `void` `push(Node** head_ref, ``int` `new_data) ` `{ ` `    ``// Allocate the node ` `    ``Node* new_node ` `        ``= (Node*)``malloc``(``sizeof``(``struct` `Node)); ` ` `  `    ``// Insert the data ` `    ``new_node->data = new_data; ` ` `  `    ``// Since we are adding at the beginning, ` `    ``// prev is always NULL ` `    ``new_node->prev = NULL; ` ` `  `    ``// Link the old list off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// Change the prev of head node to new node ` `    ``if` `((*head_ref) != NULL) ` `        ``(*head_ref)->prev = new_node; ` ` `  `    ``// Move the head to point to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Function to find the digit sum ` `// for a number ` `int` `digitSum(``int` `num) ` `{ ` `    ``int` `sum = 0; ` `    ``while` `(num) { ` `        ``sum += (num % 10); ` `        ``num /= 10; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Function to delete a node ` `// in a Doubly Linked List. ` `// head_ref --> pointer to head node pointer. ` `// del --> pointer to node to be deleted ` `void` `deleteNode(Node** head_ref, Node* del) ` `{ ` `    ``// Base case ` `    ``if` `(*head_ref == NULL || del == NULL) ` `        ``return``; ` ` `  `    ``// If the node to be deleted is head node ` `    ``if` `(*head_ref == del) ` `        ``*head_ref = del->next; ` ` `  `    ``// Change next only if node to be ` `    ``// deleted is not the last node ` `    ``if` `(del->next != NULL) ` `        ``del->next->prev = del->prev; ` ` `  `    ``// Change prev only if node to be ` `    ``// deleted is not the first node ` `    ``if` `(del->prev != NULL) ` `        ``del->prev->next = del->next; ` ` `  `    ``// Finally, free the memory ` `    ``// occupied by del ` `    ``free``(del); ` ` `  `    ``return``; ` `} ` ` `  `// Function to to remove all ` `// the Even Digit Sum Nodes from a ` `// doubly linked list ` `void` `deleteEvenDigitSumNodes(Node** head_ref) ` `{ ` `    ``Node* ptr = *head_ref; ` `    ``Node* next; ` ` `  `    ``// Iterating through the linked list ` `    ``while` `(ptr != NULL) { ` `        ``next = ptr->next; ` ` `  `        ``// If node's data's digit sum ` `        ``// is even ` `        ``if` `(!(digitSum(ptr->data) & 1)) ` `            ``deleteNode(head_ref, ptr); ` ` `  `        ``ptr = next; ` `    ``} ` `} ` ` `  `// Function to print nodes in a ` `// given doubly linked list ` `void` `printList(Node* head) ` `{ ` `    ``while` `(head != NULL) { ` `        ``cout << head->data << ``" "``; ` `        ``head = head->next; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``Node* head = NULL; ` ` `  `    ``// Create the doubly linked list ` `    ``// 18 <-> 15 <-> 8 <-> 9 <-> 14 ` `    ``push(&head, 14); ` `    ``push(&head, 9); ` `    ``push(&head, 8); ` `    ``push(&head, 15); ` `    ``push(&head, 18); ` ` `  `    ``cout << ``"Original List: "``; ` `    ``printList(head); ` ` `  `    ``deleteEvenDigitSumNodes(&head); ` ` `  `    ``cout << ``"\nModified List: "``; ` `    ``printList(head); ` `} `

Output:

```Original List: 18 15 8 9 14
Modified List: 18 9 14
```

Time Complexity: O(N), where N is the total number of nodes.

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