## Problem statement

Given the `head`

of a singly linked list, group all the nodes with odd indices together followed by the nodes with even indices, and return *the reordered list*.

The **first** node is considered **odd**, and the **second** node is **even**, and so on.

Note that the relative order inside both the even and odd groups should remain as it was in the input.

You must solve the problem in O(1) extra space complexity and O(n) time complexity.

Problem statement taken from: https://leetcode.com/problems/odd-even-linked-list.

**Example 1:**

```
Input: head = [1, 2, 3, 4, 5]
Output: [1, 3, 5, 2, 4]
```

**Example 2:**

```
Input: head = [2, 1, 3, 5, 6, 4, 7]
Output: [2, 3, 6, 7, 1, 5, 4]
```

**Constraints:**

```
- The number of nodes in the linked list is in the range [0, 10^4].
- -10^6 <= Node.val <= 10^6
```

### Solution

#### Approach 1: Using additional

The naive approach is to create two separate linked lists, one for the odd-indices nodes and the other for the even-indices nodes. We iterate the original linked list, and for each node, we will check the node's position using a counter. If the linked list position node is odd, we append it to the odd-indices linked list, or if the position is even, we append it to the even-indices linked list. Once the complete linked list is traversed, we append the even-indices linked list at the end of the odd-indices linked list.

A C++ snippet of this approach is as follows:

```
ListNode* oddEvenList(ListNode* head) {
// initialize oddHead and evenHead pointers
ListNode* oddHead = new ListNode(0);
ListNode* odd = oddHead;
ListNode* evenHead = new ListNode(0);
ListNode* even = evenHead;
ListNode* currend = head;
int counter = 1;
// traverse the linked list till the end
while(current) {
// odd-indices node
if(counter % 2 == 1) {
odd->next = current;
odd = odd->next;
} else {
// even-indices node
even->next = current;
even = even->next;
}
current = current->next;
counter++;
}
// append even-indices linked list
// at the end of the odd-indices linked list
odd->next = evenHead->next;
even->next = NULL;
return oddHead->next;
};
```

The time complexity of the above algorithm is **O(n)**, and the space complexity is **O(1)**.

#### Approach 2: Sorting in-place

We can tweak the above algorithm to solve the odd-even linked list problem. The `counter`

variable can be eliminated, and instead of pointing the `oddHead`

and `evenHead`

to a new node, we can point them to `head`

and `head->next`

, respectively.

When working on the solution, itβs important to ensure we are covering all the edge cases.

- Empty linked list or a linked list with a single node.
- A linked list with only two nodes.
- A linked list with odd numbers of nodes.
- A linked list with an even number of nodes.

Let's check the algorithm first.

#### Algorithm

```
// if the list is empty or has only one node
- if head == NULL || head->next == NULL
- return head
- end if
// initialize the odd and even pointers
- oddPointer = head
evenPointer = head->next
evenHead = head->next
// loop while even pointer is not NULL
// or even pointer next is not NULL
- loop while evenPointer != NULL && evenPointer->next != NULL
// skip the next node and point the current odd index node to
// the next odd index node
- oddPointer->next = oddPointer->next->next
- oddPointer = oddPointer->next
// skip the next node and point the current even index node to
// the even odd index node
- evenPointer->next = evenPointer->next->next
- evenPointer = evenPointer->next
- while end
- oddPointer->next = evenHead
- return head
```

We initialized three-pointers `oddPointer`

, `evenPointer`

and `evenHead`

. `oddPointer`

will point to the head and the `evenPointer`

will point to the head's next node. In each iteration, the oddPointer and evenPointer will skip the next node point to the next odd and even index node. Once the iteration over the linked list is done, we point the oddPointer next to the start of evenHead.

The time complexity of the above algorithm is **O(n)**, and the space complexity is **O(1)**.

Let's check out our solutions in **C++**, **Golang**, and **Javascript**.

#### C++ solution

```
/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode() : val(0), next(nullptr) {}
* ListNode(int x) : val(x), next(nullptr) {}
* ListNode(int x, ListNode *next) : val(x), next(next) {}
* };
*/
class Solution {
public:
ListNode* oddEvenList(ListNode* head) {
// if the list is empty or has only one node
if(head == NULL || head->next == NULL) {
return head;
}
// initialize the odd and even pointers
ListNode* oddPointer = head;
ListNode* evenPointer = head->next;
ListNode* evenHead = head->next;
// loop while even pointer is not NULL
// or even pointer next is not NULL
while(evenPointer != NULL && evenPointer->next != NULL) {
// skip the next node and point the current odd index node to
// the next odd index node
oddPointer->next = oddPointer->next->next;
oddPointer = oddPointer->next;
// skip the next node and point the current even index node to
// the even odd index node
evenPointer->next = evenPointer->next->next;
evenPointer = evenPointer->next;
}
oddPointer->next = evenHead;
return head;
}
};
```

#### Go solution

```
/**
* Definition for singly-linked list.
* type ListNode struct {
* Val int
* Next *ListNode
* }
*/
func oddEvenList(head *ListNode) *ListNode {
// if the list is empty or has only one node
if head == nil || head.Next == nil {
return head
}
// initialize the odd and even pointers
oddPointer, evenPointer, evenHead := head, head.Next, head.Next
// loop while even pointer is not NULL
// or even pointer next is not NULL
for evenPointer != nil && evenPointer.Next != nil {
// skip the next node and point the current odd index node to
// the next odd index node
oddPointer.Next = oddPointer.Next.Next
oddPointer = oddPointer.Next
// skip the next node and point the current even index node to
// the even odd index node
evenPointer.Next = evenPointer.Next.Next
evenPointer = evenPointer.Next
}
oddPointer.Next = evenHead
return head
}
```

#### JavaScript solution

```
/**
* Definition for singly-linked list.
* function ListNode(val, next) {
* this.val = (val===undefined ? 0 : val)
* this.next = (next===undefined ? null : next)
* }
*/
/**
* @param {ListNode} head
* @return {ListNode}
*/
var oddEvenList = function(head) {
// if the list is empty or has only one node
if(head == null || head.next == null) {
return head;
}
// initialize the odd and even pointers
let oddPointer = head;
let evenPointer = head.next;
let evenHead = head.next;
// loop while even pointer is not NULL
// or even pointer next is not NULL
while(evenPointer != null && evenPointer.next != null) {
// skip the next node and point the current odd index node to
// the next odd index node
oddPointer.next = oddPointer.next.next;
oddPointer = oddPointer.next;
// skip the next node and point the current even index node to
// the even odd index node
evenPointer.next = evenPointer.next.next;
evenPointer = evenPointer.next;
}
oddPointer.next = evenHead;
return head;
};
```

#### Dry Run

Let's dry-run our algorithm to see how the solution works.

```
Input: head = [1, 2, 3, 4, 5]
Step 1: if head == NULL || head->next == NULL
head -> 1
head->next -> 2
false
Step 2: ListNode* oddPointer = head
oddPointer -> 1
ListNode* evenPointer = head->next
evenPointer -> 2
ListNode* evenHead = head->next
evenHead -> 2
Step 3: loop while evenPointer != NULL && evenPointer->next != NULL
evenPointer -> 2
evenPointer->next -> 4
2 != NULL && 4 != NULL
true
oddPointer->next = oddPointer->next->next
oddPointer->next -> 2
oddPointer->next->next -> 3
oddPointer -> 1 -> 3
oddPointer = oddPointer->next
oddPointer -> 3
evenPointer->next = evenPointer->next->next
evenPointer->next -> 3
evenPointer->next->next -> 4
evenPointer -> 2 -> 4
evenPointer = evenPointer->next
evenPointer -> 4
Step 4: loop while evenPointer != NULL && evenPointer->next != NULL
evenPointer -> 4
evenPointer->next -> 5
2 != NULL && 5 != NULL
true
oddPointer->next = oddPointer->next->next
oddPointer->next -> 4
oddPointer->next->next -> 5
oddPointer -> 1 -> 3 -> 5
oddPointer = oddPointer->next
oddPointer -> 5
evenPointer->next = evenPointer->next->next
evenPointer->next -> 5
evenPointer->next->next -> NULL
evenPointer -> 2 -> 4 -> NULL
evenPointer = evenPointer->next
evenPointer -> NULL
Step 5: loop while evenPointer != NULL && evenPointer->next != NULL
evenPointer -> NULL
NULL != NULL
false
Step 6: oddPointer->next = evenHead
1 -> 3 -> 5 -> 2 -> 4
Step 7: return head
We return the answer as 1 -> 3 -> 5 -> 2 -> 4.
```

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