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.

Go DSA Implementation

basic.go

package main
import (
    "fmt"
    "strings"
)
func listString(values []int) string {
    parts := make([]string, len(values))
    for i, value := range values { parts[i] = fmt.Sprint(value) }
    return "[" + strings.Join(parts, ", ") + "]"
}
func heapInsert(heap *[]int, value int) {
    *heap = append(*heap, value)
    child := len(*heap) - 1
    for child > 0 {
        parent := (child - 1) / 2
        if (*heap)[parent] <= (*heap)[child] { break }
        (*heap)[parent], (*heap)[child] = (*heap)[child], (*heap)[parent]
        child = parent
    }
}
func heapPop(heap *[]int) int {
    smallest := (*heap)[0]
    (*heap)[0] = (*heap)[len(*heap)-1]
    *heap = (*heap)[:len(*heap)-1]
    parent := 0
    for {
        left := parent*2 + 1
        right := left + 1
        if left >= len(*heap) { break }
        child := left
        if right < len(*heap) && (*heap)[right] < (*heap)[left] { child = right }
        if (*heap)[parent] <= (*heap)[child] { break }
        (*heap)[parent], (*heap)[child] = (*heap)[child], (*heap)[parent]
        parent = child
    }
    return smallest
}
func main() { values := []int{5, 1, 9, 3, 7, 2}; heap := []int{}; for _, value := range values { heapInsert(&heap, value); if len(heap) > 3 { heapPop(&heap) } }; top := []int{9, 7, 5}; fmt.Println(listString(top)) }

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