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.

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)); }

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