Given a singly linked list, swap every two adjacent nodes of the linked list. After the swap, return the head of the linked list.

Note: Solve the problem without modifying the values in the list’s nodes. In other words, only the nodes themselves can be changed.

Constraints:

• The number of nodes in the list is in the range $[0, 100]$.

• $0 \leq$ Node.value $\leq 100$

The essence of this solution lies in understanding that we need to swap nodes in pairs without altering the values within the nodes. To accomplish this, we use an in-place reversal approach, manipulating pointers to rearrange the nodes while preserving the overall structure of the linked list. By adjusting the pointers of each node, we can efficiently swap the nodes in place in linear time without needing extra space or altering the data. This method ensures that the linked list remains intact and correctly ordered, with each pair of nodes swapped seamlessly as we progress through the list.

The algorithm for this problem is as follows:

• Initialize a dummy node that would reference the first node of the linked list, which is the head of the linked list. We’ll use prev_node to update the pointer of the dummy node.

• Next, we iterate over the linked list and swap the pairs of nodes as we proceed. The two nodes to be swapped can be represented as first_node and second_node.

These steps are represented in the following illustration: