119 lines
3.3 KiB
Go
119 lines
3.3 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package heap provides heap operations for any type that implements
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// heap.Interface. A heap is a tree with the property that each node is the
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// minimum-valued node in its subtree.
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//
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// The minimum element in the tree is the root, at index 0.
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//
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// A heap is a common way to implement a priority queue. To build a priority
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// queue, implement the Heap interface with the (negative) priority as the
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// ordering for the Less method, so Push adds items while Pop removes the
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// highest-priority item from the queue. The Examples include such an
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// implementation; the file example_pq_test.go has the complete source.
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//
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package heap
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import "sort"
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// The Interface type describes the requirements
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// for a type using the routines in this package.
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// Any type that implements it may be used as a
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// min-heap with the following invariants (established after
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// Init has been called or if the data is empty or sorted):
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//
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// !h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()
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//
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// Note that Push and Pop in this interface are for package heap's
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// implementation to call. To add and remove things from the heap,
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// use heap.Push and heap.Pop.
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type Interface interface {
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sort.Interface
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Push(x any) // add x as element Len()
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Pop() any // remove and return element Len() - 1.
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}
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// Init establishes the heap invariants required by the other routines in this package.
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// Init is idempotent with respect to the heap invariants
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// and may be called whenever the heap invariants may have been invalidated.
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// The complexity is O(n) where n = h.Len().
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func Init(h Interface) {
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// heapify
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n := h.Len()
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for i := n/2 - 1; i >= 0; i-- {
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down(h, i, n)
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}
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}
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// Push pushes the element x onto the heap.
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// The complexity is O(log n) where n = h.Len().
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func Push(h Interface, x any) {
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h.Push(x)
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up(h, h.Len()-1)
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}
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// Pop removes and returns the minimum element (according to Less) from the heap.
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// The complexity is O(log n) where n = h.Len().
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// Pop is equivalent to Remove(h, 0).
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func Pop(h Interface) any {
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n := h.Len() - 1
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h.Swap(0, n)
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down(h, 0, n)
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return h.Pop()
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}
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// Remove removes and returns the element at index i from the heap.
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// The complexity is O(log n) where n = h.Len().
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func Remove(h Interface, i int) any {
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n := h.Len() - 1
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if n != i {
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h.Swap(i, n)
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if !down(h, i, n) {
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up(h, i)
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}
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}
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return h.Pop()
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}
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// Fix re-establishes the heap ordering after the element at index i has changed its value.
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// Changing the value of the element at index i and then calling Fix is equivalent to,
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// but less expensive than, calling Remove(h, i) followed by a Push of the new value.
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// The complexity is O(log n) where n = h.Len().
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func Fix(h Interface, i int) {
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if !down(h, i, h.Len()) {
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up(h, i)
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}
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}
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func up(h Interface, j int) {
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for {
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i := (j - 1) / 2 // parent
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if i == j || !h.Less(j, i) {
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break
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}
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h.Swap(i, j)
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j = i
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}
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}
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func down(h Interface, i0, n int) bool {
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i := i0
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for {
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j1 := 2*i + 1
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if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
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break
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}
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j := j1 // left child
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if j2 := j1 + 1; j2 < n && h.Less(j2, j1) {
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j = j2 // = 2*i + 2 // right child
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}
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if !h.Less(j, i) {
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break
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}
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h.Swap(i, j)
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i = j
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}
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return i > i0
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}
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