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// 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. 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 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 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 Interface interface {
sort.Interface
Push(x interface{}) // add x as element Len()
Pop() interface{} // remove and return element Len() - 1.
}
// 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().
// It is equivalent to 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()
}
// Fix re-establishes the heap ordering after the element at index i has changed its value.
// Changing the value of the element at index i and then calling Fix is equivalent to,
// but less expensive than, calling Remove(h, i) followed by a Push of the new value.
// The complexity is O(log(n)) where n = h.Len().
func Fix(h Interface, i int) {
down(h, i, h.Len())
up(h, i)
}
func up(h Interface, j int) {
for {
i := (j - 1) / 2 // parent
if i == j || !h.Less(j, i) {
break
}
h.Swap(i, j)
j = i
}
}
func down(h Interface, i, n int) {
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(j1, j2) {
j = j2 // = 2*i + 2 // right child
}
if !h.Less(j, i) {
break
}
h.Swap(i, j)
i = j
}
}
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