08-heaps

Min-Heap Pop (Sift Down)

Remove the minimum value, move the last item to the root, and sift downward.

Algorithm

Steps

  1. Store the heap in an array.
  2. Compare parent and child indexes instead of building explicit tree nodes.
  3. Swap only when the heap order is violated.
  4. Print the deterministic final heap state for replay comparison.
sift down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

Complexity

  • Time: O(log n)
  • Space: O(1) extra

Visual walkthrough

After popping the minimum, the last value moves to the root and sifts down by swapping with the smaller child.

Step 1 - Replace root

The saved minimum is 1; the last value 7 moves to the root before sifting down.

Replacement state [7, 4, 2, 9, 6] with removed value 1.1removed7root4left2smaller9i36i4

Step 2 - Swap with the smaller child

7 swaps with 2, producing the final heap [2, 4, 7, 9, 6].

Final heap after pop and one sift-down swap.2root4i17i29i36i4

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=(1 4 2 9 6 7)
heap_pop
printf '%s -> ' "$popped"; list_string "${heap[@]}"; echo

Output

1 -> [2, 4, 7, 9, 6]