Top-K with a Heap

Keep only the largest k values by maintaining a small min-heap.

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(n log k)
Space: O(k)

bounded heap For top-k largest values, a min-heap of size k keeps the current cutoff at the root.

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 values = [5, 1, 9, 3, 7, 2]; let mut heap = Vec::new(); for value in values { heap_insert(&mut heap, value); if heap.len() > 3 { heap_pop(&mut heap); } } heap.sort_by(|a, b| b.cmp(a)); println!("{}", list_string(&heap)); }

Output

[9, 7, 5]

Implementation notes

main stores the input in a fixed [i32; 6] array and keeps the working heap in let mut heap = Vec::new(), a mutable Vec<i32>.
Each for value in values iteration copies an i32 value into heap_insert(&mut heap, value). The heap helper mutates the same vector with push, parent index (child - 1) / 2, and heap.swap(parent, child).
The heap is a min-heap: helper comparisons use <= to keep the smallest retained top-k value at index 0.
Top-k size is enforced by if heap.len() > 3 { heap_pop(&mut heap); }. heap_pop removes and returns the minimum with heap.pop().unwrap(), root replacement, child indexes parent * 2 + 1 and left + 1, smaller-child selection, and in-place swaps.
The popped value is not collected; only the final bounded heap remains. The trace states are [5], [1, 5], [1, 5, 9], [3, 5, 9], [5, 7, 9], and [5, 7, 9] after considering 2.
Before printing, heap.sort_by(|a, b| b.cmp(a)) mutates the retained values into high-to-low order. list_string(&heap) borrows the vector as a slice and println!("{}", ...) prints [9, 7, 5].