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.

Complexity

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

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

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{2, 4, 7, 9, 6}; heapInsert(&heap, 1); fmt.Println(listString(heap)) }

The heap is still an array, but the tree view makes parent-child swaps visible. The labels use the pinned replay states from the lesson.

Step 1 - Append 1

The new value 1 starts at index 5 and compares with its parent value 7.

Step 2 - Swap with 7

Because 1 is smaller than 7, those array slots swap.

Step 3 - Swap with 2

1 is also smaller than 2, so it moves to the root and the heap order is restored.

Output

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

Implementation notes

Go stores the min-heap as []int; main starts with heap := []int{2, 4, 7, 9, 6} and passes &heap so heapInsert can update the slice header.
*heap = append(*heap, value) appends 1; append may grow the backing array, so the reassigned slice header is required.
The new child index is len(*heap) - 1. Each sift-up step computes parent := (child - 1) / 2 and stops when child == 0 or (*heap)[parent] <= (*heap)[child].
This is a min-heap: smaller values move upward. Swaps mutate the slice in place with (*heap)[parent], (*heap)[child] = (*heap)[child], (*heap)[parent].
The trace records [2, 4, 7, 9, 6], append to [2, 4, 7, 9, 6, 1], swap 1 with parent 7 to [2, 4, 1, 9, 6, 7], then swap with 2 to [1, 4, 2, 9, 6, 7].
listString builds a []string with fmt.Sprint and strings.Join, so fmt.Println(listString(heap)) prints [1, 4, 2, 9, 6, 7].