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Linked List

Swap Nodes in Pairs

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DESCRIPTION (inspired by Leetcode.com)

Given a reference head of type ListNode that is the head of a singly linked list, write a function to swap every two adjacent nodes and return its head.

You must solve the problem without modifying the values in the list's nodes (i.e., only nodes themselves may be changed.)

Example 1: input:

output:

Explanation: 5 and 4 are swapped, 3 and 2 are swapped, and 1 is left alone.

Example 2: input:

output:

Explanation: 1 and 2 are swapped, 3 and 4 are swapped.

Solution

Since we can't modify the values in the nodes, our function needs to swap the nodes by traversing the list and updating the next pointers of the nodes.

This question is an example of how using a dummy node simplifies a solution by removing the need for special logic for swapping the first two nodes in the list. To understand why, let's first look at how to swap a pair of nodes in a linked list.

Let's say we want to swap the pair of nodes first and second in the linked list below:

We need to perform 3 operations:

1). Since we need the node before first to point to second instead of first, we need a pointer prev which references the node before first. Then, we can update prev.next to point to second.

2). We need to update first.next to point to second.next.

3). Finally, we need to update second.next to point to first.

Once that is complete, we can move to the next pair of nodes to swap.

Need for a Dummy Node

As we just saw, swapping a pair of nodes requires a pointer to node before the first node in the pair we want to swap. This is not a problem when we are swapping nodes in the middle of the list, but it is when we are swapping the first pair of nodes in the list because there is no node before head!

We fix this by introducing a dummy node that points to the head of the list. This guarantees that each node in the original list has a node before it, meaning we can swap all nodes in the list using the same logic.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

swap nodes in pairs

0 / 1

From there, we can initialize two pointers, prev and first. first will point to the first node in the pair we want to swap, and prev points to the node before first, which is the dummy node to start. We also initialize the pointer second to point to the node after first.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

create dummy node

0 / 2

We then perform the same 3 operations we discussed earlier to swap the pair of nodes:

1). Update prev.next to point to second. 2). Update first.next to point to second.next. 3). Update second.next to point to first.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

identify pair: 5 and 4

0 / 3

Now, with first and second swapped, we move prev and first to prepare for the next iteration. first now points to the node right before the next pair of nodes, so we update prev to point to first and first to point to first.next. After that, we update second to point to first.next, and our pointers are in the same state to perform the same 3 operations to swap the next pair of nodes.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

second.next → 5

0 / 2

Termination

We can stop the loop when first is None, or when first.next is None. When there an even number of nodes in the list, first will be None when all pairs of nodes have been swapped. When there is an odd number of nodes, first.next will be None when first is at the last node in the list, which we can't swap.

After the loop terminates, we return dummy.next, which is the head of the list with all pairs of nodes swapped.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

no more pairs to swap

0 / 1

Implementation

Here's the complete dummy node approach that elegantly handles all edge cases:

Solution

def swapPairs(head):
    # Create dummy node to simplify edge cases
    dummy = ListNode(0)
    dummy.next = head
    prev = dummy
    
    # Process pairs while both nodes exist
    while prev.next and prev.next.next:
        # Identify the two nodes to swap
        first = prev.next
        second = prev.next.next
        
        # Perform the swap by adjusting pointers
        prev.next = second        # Link previous to second node
        first.next = second.next  # Link first to node after second
        second.next = first       # Link second to first (completing swap)
        
        # Move prev to the end of swapped pair for next iteration
        prev = first
    
    return dummy.next  # Return new head

Code

To construct the linked list that is used in the animation below, provide a list of integers nodes. Each integer in nodes is used as the value of a node in the linked list, and the order of the integers in nodes will be the order of the nodes in the linked list.

For example, if nodes = [1, 2, 3], the linked list will be 1 -> 2 -> 3.

Visualization

Try these examples:


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

swap nodes in pairs

0 / 16

Edge Cases

Empty List

When the list is empty, head is None. The while loop never runs, and we return dummy.next, which is equal to None.

Visualization

Try these examples:


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

swap nodes in pairs

0 / 3

`head = []`

One Node

When there is only one node in the list, first is the only node in the list, and first.next is None. The while loop never runs, and we return dummy.next, which is head with the single node.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

swap nodes in pairs

0 / 4

`head = [1]`

Two Nodes

When there are two nodes in the list, first is the first node, and second is the second node. The while loop runs once to swap the two nodes, after which fast is None so the loop terminates. We return dummy.next, which is the head of the list with the two nodes swapped.

Visualization


def swapPairs(head):
    dummy = ListNode(0)
    dummy.next = head
    prev, first = dummy, head
    while first and first.next:
        second = first.next
        # swap nodes
        prev.next = second
        first.next = second.next
        second.next = first
        prev = first
        first = first.next
    return dummy.next

swap nodes in pairs

0 / 10

`head = [1, 2]`

Test Your Knowledge

Complexity Analysis

Time Complexity: O(N) where N is the number of nodes in the list. We visit each node in the list once, and perform the same number of operations at each node.

Space Complexity: O(1) We only use a constant amount of extra space to store the pointers prev, first, and second.

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Linked List

Swap Nodes in Pairs

DESCRIPTION (inspired by Leetcode.com)

Solution

Need for a Dummy Node

Termination

Implementation

Code

Edge Cases

Empty List

One Node

Two Nodes

Test Your Knowledge

Complexity Analysis

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