Min-Heap Pop (Sift Down)

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

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.

Complexity

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

sift down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

Visual walkthrough

Go DSA Implementation

basic.go

package main
import (
    "fmt"
    "strings"
)
func listString(values []int) string {
    parts := make([]string, len(values))
    for i, value := range values { parts[i] = fmt.Sprint(value) }
    return "[" + strings.Join(parts, ", ") + "]"
}
func heapInsert(heap *[]int, value int) {
    *heap = append(*heap, value)
    child := len(*heap) - 1
    for child > 0 {
        parent := (child - 1) / 2
        if (*heap)[parent] <= (*heap)[child] { break }
        (*heap)[parent], (*heap)[child] = (*heap)[child], (*heap)[parent]
        child = parent
    }
}
func heapPop(heap *[]int) int {
    smallest := (*heap)[0]
    (*heap)[0] = (*heap)[len(*heap)-1]
    *heap = (*heap)[:len(*heap)-1]
    parent := 0
    for {
        left := parent*2 + 1
        right := left + 1
        if left >= len(*heap) { break }
        child := left
        if right < len(*heap) && (*heap)[right] < (*heap)[left] { child = right }
        if (*heap)[parent] <= (*heap)[child] { break }
        (*heap)[parent], (*heap)[child] = (*heap)[child], (*heap)[parent]
        parent = child
    }
    return smallest
}
func main() { heap := []int{1, 4, 2, 9, 6, 7}; popped := heapPop(&heap); fmt.Printf("%d -> %s\n", popped, listString(heap)) }

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.

Step 2 - Swap with the smaller child

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

Output

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

Implementation notes

Go stores the min-heap as []int; main starts with heap := []int{1, 4, 2, 9, 6, 7} and calls heapPop(&heap) so the helper can mutate the slice header.
heapPop saves smallest := (*heap)[0], replaces the root with the last element using (*heap)[0] = (*heap)[len(*heap)-1], then shrinks the slice with *heap = (*heap)[:len(*heap)-1].
Sift-down starts at parent := 0. For each loop it computes left := parent*2 + 1 and right := left + 1; left >= len(*heap) stops at a leaf.
This is a min-heap, so the selected child is the smaller child: right < len(*heap) && (*heap)[right] < (*heap)[left] switches from left to right when needed.
The loop stops when (*heap)[parent] <= (*heap)[child]; otherwise the tuple swap mutates the slice in place and parent = child continues downward.
The trace records [1, 4, 2, 9, 6, 7], removes 1 and moves 7 to root as [7, 4, 2, 9, 6], then swaps 7 with smaller child 2 to [2, 4, 7, 9, 6].
fmt.Printf("%d -> %s\n", popped, listString(heap)) prints 1 -> [2, 4, 7, 9, 6].