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

Rust DSA Implementation

basic.rs

fn list_string(values: &[i32]) -> String {
    format!("[{}]", values.iter().map(|v| v.to_string()).collect::<Vec<_>>().join(", "))
}
fn heap_insert(heap: &mut Vec<i32>, value: i32) {
    heap.push(value);
    let mut child = heap.len() - 1;
    while child > 0 {
        let parent = (child - 1) / 2;
        if heap[parent] <= heap[child] { break; }
        heap.swap(parent, child);
        child = parent;
    }
}
fn heap_pop(heap: &mut Vec<i32>) -> i32 {
    let smallest = heap[0];
    let last = heap.pop().unwrap();
    heap[0] = last;
    let mut parent = 0;
    loop {
        let left = parent * 2 + 1;
        let right = left + 1;
        if left >= heap.len() { break; }
        let mut child = left;
        if right < heap.len() && heap[right] < heap[left] { child = right; }
        if heap[parent] <= heap[child] { break; }
        heap.swap(parent, child);
        parent = child;
    }
    smallest
}
fn main() { let mut heap = vec![1, 4, 2, 9, 6, 7]; let popped = heap_pop(&mut heap); println!("{} -> {}", popped, list_string(&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

The heap is a mutable Vec<i32> in main and is passed to heap_pop(heap: &mut Vec<i32>) -> i32, so the helper mutates the caller's vector and returns the removed minimum value.
let smallest = heap[0] copies the root value. heap.pop().unwrap() removes the last slot and assumes the heap is non-empty; the checked example starts with six elements.
The last value is written back with heap[0] = last, producing the traced state [7, 4, 2, 9, 6] after removing 1.
Child indexes are usize values: left = parent * 2 + 1 and right = left + 1. if left >= heap.len() { break; } stops when a parent has no children.
This is a min-heap. The right child is selected only when it exists and is smaller than the left child: heap[right] < heap[left].
if heap[parent] <= heap[child] { break; } stops once the parent is no larger than the selected child; otherwise heap.swap(parent, child) mutates the vector in place.
The trace shows one sift-down swap, changing [7, 4, 2, 9, 6] to [2, 4, 7, 9, 6], then println!("{} -> {}", popped, list_string(&heap)) prints 1 -> [2, 4, 7, 9, 6].