# Flattening a linked list | Set 2

Given a linked list where every node represents a linked list and contains two pointers of its type:

• Pointer to next node in the main list (we call it ‘right’ pointer in below code)
• Pointer to a linked list where this node is head (we call it ‘down’ pointer in below code).

All linked lists are sorted. See the following example

Examples:

```Input:
5 -> 10 -> 19 -> 28
|    |     |     |
V    V     V     V
7    20    22    35
|          |     |
V          V     V
8          50    40
|                |
V                V
30               45

Output: 5->7->8->10->19->20->22->28->30->35->40->45->50

Input:
5 -> 10 -> 19 -> 28
|          |
V          V
7          22
|          |
V          V
8          50
|
V
30

Output: 5->7->8->10->19->20->22->30->50
```

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

In the previous post, we have use the merge() process of merge sort for linked lists to flatten the linked list.
In this post, we will solve it using Heap.

Approach: The idea is to observe that from each top node there are N nodes that are connected in a downward direction but observe that all the downward nodes are in sorted order. So the task is to sort this entire thing in increasing order(or decreasing order).

1. Push the head of all the linked list in the downward list in priority queue.
2. Pop the smallest node from the priority queue.
3. Check the location of node so that next node pointed by the current node can be pushed into the priority queue.
4. Again pop out the smallest element and insert next node pointed by current node till the heap becomes empty.
5. Keep on adding the data of nodes in a new linked list that are pooped out to the new list.
6. Print the linked list formed above.

Below is the implementation of the above approach:

 `// C++ program for Flattening ` `// a linked list using Heaps ` `#include ` `using` `namespace` `std; ` ` `  `// Structure of given Linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* right; ` `    ``struct` `Node* down; ` ` `  `    ``Node(``int` `x) ` `    ``{ ` `        ``data = x; ` `        ``right = NULL; ` `        ``down = NULL; ` `    ``} ` `}; ` ` `  `// Function to print the ` `// linked list ` `void` `printList(Node* Node) ` `{ ` `    ``while` `(Node != NULL) { ` `        ``printf``(``"%d "``, Node->data); ` `        ``Node = Node->down; ` `    ``} ` `} ` ` `  `// Function that compares the value ` `// pointed by node and returns true ` `// if first data is greater ` `struct` `compare { ` `    ``bool` `operator()(Node* a, Node* b) ` `    ``{ ` `        ``return` `a->data > b->data; ` `    ``} ` `}; ` ` `  `// Function which returns the root ` `// of the flattened linked list ` `Node* flatten(Node* root) ` `{ ` `    ``Node* ptr = root; ` `    ``Node* head = NULL; ` ` `  `    ``// Min Heap which will return ` `    ``// smallest element currently ` `    ``// present in heap ` `    ``priority_queue, ` `                   ``compare> ` `        ``pq; ` ` `  `    ``// Push the head nodes of each ` `    ``// downward linked list ` `    ``while` `(ptr != NULL) { ` `        ``pq.push(ptr); ` `        ``ptr = ptr->right; ` `    ``} ` ` `  `    ``// This loop will execute ` `    ``// till the map becomes empty ` `    ``while` `(!pq.empty()) { ` ` `  `        ``// Pop out the node that ` `        ``// contains element ` `        ``// currently in heap ` `        ``Node* temp = pq.top(); ` `        ``pq.pop(); ` ` `  `        ``// Push the next node pointed by ` `        ``// the current node into heap ` `        ``// if it is not null ` `        ``if` `(temp->down != NULL) { ` `            ``pq.push(temp->down); ` `        ``} ` ` `  `        ``// Create new linked list ` `        ``// that is to be returned ` `        ``if` `(head == NULL) { ` `            ``head = temp; ` `            ``ptr = temp; ` `        ``} ` `        ``else` `{ ` `            ``ptr->down = temp; ` `            ``ptr = temp; ` `        ``} ` `    ``} ` ` `  `    ``// Pointer to head node ` `    ``// in the linked list ` `    ``return` `head; ` `} ` ` `  `// Create and push new nodes ` `void` `push(Node** head_ref, ` `          ``int` `new_data) ` `{ ` `    ``Node* new_node = (Node*)``malloc``(``sizeof``(Node)); ` `    ``new_node->right = NULL; ` `    ``new_node->data = new_data; ` `    ``new_node->down = (*head_ref); ` ` `  `    ``(*head_ref) = new_node; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``Node* root = NULL; ` ` `  `    ``// Given Linked List ` `    ``push(&root, 30); ` `    ``push(&root, 8); ` `    ``push(&root, 7); ` `    ``push(&root, 5); ` ` `  `    ``push(&(root->right), 20); ` `    ``push(&(root->right), 10); ` ` `  `    ``push(&(root->right->right), 50); ` `    ``push(&(root->right->right), 22); ` `    ``push(&(root->right->right), 19); ` ` `  `    ``push(&(root->right->right->right), 45); ` `    ``push(&(root->right->right->right), 40); ` `    ``push(&(root->right->right->right), 35); ` `    ``push(&(root->right->right->right), 20); ` ` `  `    ``// Flatten the list ` `    ``root = flatten(root); ` ` `  `    ``// Print the flatened linked list ` `    ``printList(root); ` ` `  `    ``return` `0; ` `} `

Output:

```5 7 8 10 19 20 20 22 30 35 40 45 50
```

Time Complexity: O(N), where N is number of node is the linked list.
Auxiliary Space: O(N), where N is number of node is the linked list.

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