// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Package heap provides heap operations for any type that implements
// heap.Interface.
//
package heap

import "sort"

// Any type that implements heap.Interface may be used as a
// min-heap with the following invariants (established after
// Init has been called):
//
//	!h.Less(j, i) for 0 <= i < h.Len() and j = 2*i+1 or 2*i+2 and j < h.Len()
//
type Interface interface {
	sort.Interface
	Push(x interface{})
	Pop() interface{}
}


// A heap must be initialized before any of the heap operations
// can be used. Init is idempotent with respect to the heap invariants
// and may be called whenever the heap invariants may have been invalidated.
// Its complexity is O(n) where n = h.Len().
//
func Init(h Interface) {
	// heapify
	n := h.Len()
	for i := n/2 - 1; i >= 0; i-- {
		down(h, i, n)
	}
}


// Push pushes the element x onto the heap. The complexity is
// O(log(n)) where n = h.Len().
//
func Push(h Interface, x interface{}) {
	h.Push(x)
	up(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().
// Same as Remove(h, 0).
//
func Pop(h Interface) interface{} {
	n := h.Len() - 1
	h.Swap(0, n)
	down(h, 0, n)
	return h.Pop()
}


// Remove removes the element at index i from the heap.
// The complexity is O(log(n)) where n = h.Len().
//
func Remove(h Interface, i int) interface{} {
	n := h.Len() - 1
	if n != i {
		h.Swap(i, n)
		down(h, i, n)
		up(h, i)
	}
	return h.Pop()
}


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


func down(h Interface, i, n int) {
	for {
		j1 := 2*i + 1
		if j1 >= n {
			break
		}
		j := j1 // left child
		if j2 := j1 + 1; j2 < n && !h.Less(j1, j2) {
			j = j2 // = 2*i + 2  // right child
		}
		if h.Less(i, j) {
			break
		}
		h.Swap(i, j)
		i = j
	}
}