// Package heap provides heap operations for any type that implements
// heap.Interface. A heap is a tree with the property that each node is the
// minimum-valued node in its subtree.
//
// The minimum element in the tree is the root, at index 0.
//
// A heap is a common way to implement a priority queue. To build a priority
// queue, implement the Heap interface with the (negative) priority as the
// ordering for the Less method, so Push adds items while Pop removes the
// highest-priority item from the queue. The Examples include such an
// implementation; the file example_pq_test.go has the complete source.
//

package tinykv

type tohVal = *timeout

// Any type that implements heap.Interface may be used as a
// min-heap with the following invariants (established after
// Init has been called or if the data is empty or sorted):
//
//	!h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()
//
// Note that Push and Pop in this interface are for package heap's
// implementation to call. To add and remove things from the heap,
// use heap.Push and heap.Pop.
type timeheapInterface interface {
	Len() int
	Less(i, j int) bool
	Swap(i, j int)
	Push(x tohVal) // add x as element Len()
	Pop() tohVal   // remove and return element Len() - 1.
}

// Push pushes the element x onto the heap. The complexity is
// O(log(n)) where n = h.Len().
func timeheapPush(h timeheapInterface, x tohVal) {
	h.Push(x)
	timeheapup(h, h.Len()-1)
}

// Pop removes the minimum element (according to Less) from the heap
// and returns it. The complexity is O(log(n)) where n = h.Len().
// It is equivalent to Remove(h, 0).
func timeheapPop(h timeheapInterface) tohVal {
	n := h.Len() - 1
	h.Swap(0, n)
	timeheapdown(h, 0, n)
	return h.Pop()
}

func timeheapup(h timeheapInterface, j int) {
	for {
		i := (j - 1) / 2 // parent
		if i == j || !h.Less(j, i) {
			break
		}
		h.Swap(i, j)
		j = i
	}
}

func timeheapdown(h timeheapInterface, i0, n int) bool {
	i := i0
	for {
		j1 := 2*i + 1
		if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
			break
		}
		j := j1 // left child
		if j2 := j1 + 1; j2 < n && h.Less(j2, j1) {
			j = j2 // = 2*i + 2  // right child
		}
		if !h.Less(j, i) {
			break
		}
		h.Swap(i, j)
		i = j
	}
	return i > i0
}