Linked Structures

Insert at Head

Insert a new first node by pointing it at the old head and then moving the head pointer.

Algorithm

Basic Implementation

basic.php 
<?php
class Node {
    public int $value;
    public ?Node $next;
    public function __construct(int $value, ?Node $next = null) {
        $this->value = $value;
        $this->next = $next;
    }
}
function render_chain(?Node $head): string {
    $parts = [];
    $cursor = $head;
    while ($cursor !== null) {
        $parts[] = (string)$cursor->value;
        $cursor = $cursor->next;
    }
    return implode(" -> ", $parts) . " -> null";
}
$head = new Node(20, new Node(30));
$newHead = new Node(10);
$newHead->next = $head;
$head = $newHead;
echo render_chain($head) . PHP_EOL;

Head insertion changes only two references: the new node points at the old head, then head moves to the new node.

Step 1 - Old first node

Before insertion, head points at node(20).

Original chain before inserting 10 at the head.headnode(20)node(30)null

Step 2 - New node links to old head

Set new.next to the old first node before moving head.

node(10) is allocated and points at the old head node(20).headnode(10)newnode(20)old headnode(30)null

Step 3 - Head moves to the new node

The final chain has 10 first: 10 -> 20 -> 30 -> null.

After insertion, head points at node(10).headnode(10)node(20)node(30)null

Complexity

  • Time: O(1)
  • Space: O(1)

Implementation notes

  • Keep the explicit node and pointer/reference operations; array shortcuts hide the linked-list state this lesson is meant to replay.
  • The final output prints the chain in a deterministic a -> b -> null form for cross-language comparison.
old head The previous first node becomes the second node.
constant-time insert Only the new node and head pointer change.