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. @end @complexity

Time: O(n log k)
Space: O(k) @end

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)); }

@end @output [9, 7, 5] @end