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

Swift DSA Implementation

basic.swift

func listString(_ values: [Int]) -> String { "[" + values.map(String.init).joined(separator: ", ") + "]" }
func heapInsert(_ heap: inout [Int], _ value: Int) {
    heap.append(value)
    var child = heap.count - 1
    while child > 0 {
        let parent = (child - 1) / 2
        if heap[parent] <= heap[child] { break }
        heap.swapAt(parent, child)
        child = parent
    }
}
func heapPop(_ heap: inout [Int]) -> Int {
    let smallest = heap[0]
    heap[0] = heap.removeLast()
    var parent = 0
    while true {
        let left = parent * 2 + 1
        let right = left + 1
        if left >= heap.count { break }
        var child = left
        if right < heap.count && heap[right] < heap[left] { child = right }
        if heap[parent] <= heap[child] { break }
        heap.swapAt(parent, child)
        parent = child
    }
    return smallest
}
var heap = [1, 4, 2, 9, 6, 7]
let popped = heapPop(&heap)
print("\(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].

Implementation notes

var heap = [1, 4, 2, 9, 6, 7] is a mutable Swift [Int] representing a min-heap in array layout.
heapPop(_ heap: inout [Int]) -> Int mutates the caller's array and returns the removed minimum.
let smallest = heap[0] saves the root value, then heap[0] = heap.removeLast() moves the last element into the root slot while shrinking the array.
Sift-down starts with var parent = 0 and computes children as left = parent * 2 + 1 and right = left + 1.
The loop breaks when left >= heap.count, meaning the parent has no children.
var child = left picks the left child first; if the right child exists and heap[right] < heap[left], the right child becomes the smaller child.
The min-heap condition heap[parent] <= heap[child] stops the loop; otherwise heap.swapAt(parent, child) restores one level and moves parent = child.
The trace starts at [1, 4, 2, 9, 6, 7], removes 1, moves 7 to get [7, 4, 2, 9, 6], then swaps 7 with smaller child 2 for [2, 4, 7, 9, 6].
let popped = heapPop(&heap) is printed with listString(heap), producing 1 -> [2, 4, 7, 9, 6].

Output

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