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.sh 
#!/usr/bin/env bash
set -euo pipefail

render() {
  local idx="$1"
  local out=""
  while [[ "$idx" != "-1" ]]; do
    if [[ -n "$out" ]]; then out+=" -> "; fi
    out+="${value[$idx]}"
    idx="${next[$idx]}"
  done
  printf '%s -> null\n' "$out"
}

declare -A value
declare -A next
value[2]=20; next[2]=3
value[3]=30; next[3]=-1
head=2
value[1]=10; next[1]="$head"
head=1
render "$head"

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.