Min-Heap Insert (Sift Up)

Insert one value into a min-heap and restore the parent-child order by sifting upward.

Algorithm

@steps

Store the heap in an array.
Compare parent and child indexes instead of building explicit tree nodes.
Swap only when the heap order is violated.
Print the deterministic final heap state for replay comparison. @end @complexity

Time: O(log n)
Space: O(1) extra @end

sift up A new value starts at the end of the array and swaps with its parent while it is smaller.

Bash DSA Implementation

basic.sh

#!/usr/bin/env bash
list_string() {
  local joined=""
  for value in "$@"; do [[ -n "$joined" ]] && joined+=", "; joined+="$value"; done
  printf '[%s]' "$joined"
}
heap_insert() {
  local value=$1 child parent tmp
  heap+=("$value")
  child=$((${#heap[@]} - 1))
  while (( child > 0 )); do
    parent=$(((child - 1) / 2))
    (( heap[parent] <= heap[child] )) && break
    tmp=${heap[$parent]}; heap[$parent]=${heap[$child]}; heap[$child]=$tmp
    child=$parent
  done
}
heap_pop() {
  popped=${heap[0]}
  heap[0]=${heap[-1]}
  unset 'heap[-1]'
  local parent=0 left right child tmp
  while true; do
    left=$((parent * 2 + 1)); right=$((left + 1))
    (( left >= ${#heap[@]} )) && break
    child=$left
    if (( right < ${#heap[@]} && heap[right] < heap[left] )); then child=$right; fi
    (( heap[parent] <= heap[child] )) && break
    tmp=${heap[$parent]}; heap[$parent]=${heap[$child]}; heap[$child]=$tmp
    parent=$child
  done
}
heap=(2 4 7 9 6)
heap_insert 1
list_string "${heap[@]}"; echo

@end @output [1, 4, 2, 9, 6, 7] @end