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. @end @complexity

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

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

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 = [2, 4, 7, 9, 6]
heapInsert(&heap, 1)
print(listString(heap))

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