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. @end @complexity

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

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

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))")

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