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.

Complexity

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

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

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![2, 4, 7, 9, 6]; heap_insert(&mut heap, 1); println!("{}", list_string(&heap)); }

The heap is still an array, but the tree view makes parent-child swaps visible. The labels use the pinned replay states from the lesson.

Step 1 - Append 1

The new value 1 starts at index 5 and compares with its parent value 7.

Step 2 - Swap with 7

Because 1 is smaller than 7, those array slots swap.

Step 3 - Swap with 2

1 is also smaller than 2, so it moves to the root and the heap order is restored.

Output

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

Implementation notes

The heap is a mutable Vec<i32> created in main and passed to heap_insert(heap: &mut Vec<i32>, value: i32), so the helper mutates the caller's vector in place and returns ().
heap.push(value) appends 1 at the next array slot; child is a usize index initialized from heap.len() - 1.
The parent index is computed as (child - 1) / 2. The while child > 0 guard prevents subtracting from zero before that formula runs.
This is a min-heap: if heap[parent] <= heap[child] { break; } stops when the parent is already no larger than the child.
heap.swap(parent, child) exchanges vector elements in place, then child = parent continues the sift-up from the new position.
The trace shows [2, 4, 7, 9, 6], append to [2, 4, 7, 9, 6, 1], swap with parent 7 to [2, 4, 1, 9, 6, 7], then swap with parent 2 to [1, 4, 2, 9, 6, 7].
list_string(&heap) borrows the vector as a slice, joins display-formatted integers, and println!("{}", ...) prints [1, 4, 2, 9, 6, 7].