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golang package heap

heap包提供了對任意型別(實現了heap.Interface介面)的堆操作。(最小)堆是具有“每個節點都是以其為根的子樹中最小值”屬性的樹。

樹的最小元素為其根元素,索引0的位置。

heap是常用的實現優先佇列的方法。要建立一個優先佇列,實現一個具有使用(負的)優先順序作為比較的依據的Less方法的Heap介面,如此一來可用Push新增專案而用Pop取出佇列最高優先順序的專案。

type Interface interface {
    sort.Interface
    Push(x interface{}) // 向末尾新增元素
    Pop()
interface{} // 從末尾刪除元素 }

任何實現了本介面的型別都可以用於構建最小堆。最小堆可以通過heap.Init建立,資料是遞增順序或者空的話也是最小堆。最小堆的約束條件是:!h.Less(j, i) for 0 <= i < h.Len() and 2i+1 <= j <= 2i+2 and j < h.Len()
注意介面的Push和Pop方法是供heap包呼叫的,請使用heap.Push和heap.Pop來向一個堆新增或者刪除元素。

func Init(h Interface)

一個堆在使用任何堆操作之前應先初始化。Init函式對於堆的約束性是冪等的(多次執行無意義),並可能在任何時候堆的約束性被破壞時被呼叫。本函式複雜度為O(n),其中n等於h.Len()。

func Push(h Interface, x interface{})

向堆h中插入元素x,並保持堆的約束性。複雜度O(log(n)),其中n等於h.Len()。

func Pop(h Interface) interface{}

刪除並返回堆h中的最小元素(不影響約束性)。複雜度O(log(n)),其中n等於h.Len()。等價於Remove(h, 0)。

func Remove(h Interface, i int) interface{}

刪除堆中的第i個元素,並保持堆的約束性。複雜度O(log(n)),其中n等於h.Len()。

func Fix(
h Interface, i int)

在修改第i個元素後,呼叫本函式修復堆,比刪除第i個元素後插入新元素更有效率。複雜度O(log(n)),其中n等於h.Len()。

// This example demonstrates an integer heap built using the heap interface.
package main

import (
	"container/heap"
	"fmt"
)

// An IntHeap is a min-heap of ints.
type IntHeap []int

func (h IntHeap) Len() int           { return len(h) }
func (h IntHeap) Less(i, j int) bool { return h[i] < h[j] }
func (h IntHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *IntHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}
func (h *IntHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

func main() {
	h := &IntHeap{2, 1, 5}
	heap.Init(h)

	heap.Push(h, 3)	// 插入3

	fmt.Printf("minimum: %d\n", (*h)[0])

	for h.Len() > 0 {
		fmt.Printf("%d ", heap.Pop(h)) 
	}
	
	// Output:
	// minimum: 1
	// 1 2 3 5
}

執行結果:
minimum: 1
1 2 3 5


// This example demonstrates a priority queue built using the heap interface.
package main

import (
	"container/heap"
	"fmt"
)

// An Item is something we manage in a priority queue.
type Item struct {
	value    string // The value of the item; arbitrary.
	priority int    // The priority of the item in the queue.
	// The index is needed by update and is maintained by the heap.Interface methods.
	index int // The index of the item in the heap.
}

// A PriorityQueue implements heap.Interface and holds Items.
type PriorityQueue []*Item

func (pq PriorityQueue) Len() int { return len(pq) }
func (pq PriorityQueue) Less(i, j int) bool {
	// We want Pop to give us the highest, not lowest, priority so we use greater than here.
	return pq[i].priority > pq[j].priority
}
func (pq PriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}
func (pq *PriorityQueue) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Item)
	item.index = n
	*pq = append(*pq, item)
}
func (pq *PriorityQueue) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}

// update modifies the priority and value of an Item in the queue.
func (pq *PriorityQueue) update(item *Item, value string, priority int) {
	item.value = value
	item.priority = priority
	heap.Fix(pq, item.index)
}

// This example creates a PriorityQueue with some items, adds and manipulates an item,
// and then removes the items in priority order.
func main() {
	// Some items and their priorities.
	items := map[string]int{
		"banana": 3, "apple": 2, "pear": 4,
	}
	// Create a priority queue, put the items in it, and
	// establish the priority queue (heap) invariants.
	pq := make(PriorityQueue, len(items))
	i := 0
	for value, priority := range items {
		pq[i] = &Item{
			value:    value,
			priority: priority,
			index:    i,
		}
		i++
	}
	heap.Init(&pq)
	// Insert a new item and then modify its priority.
	item := &Item{
		value:    "orange",
		priority: 1,
	}
	heap.Push(&pq, item)
	pq.update(item, item.value, 5)
	// Take the items out; they arrive in decreasing priority order.
	for pq.Len() > 0 {
		item := heap.Pop(&pq).(*Item)
		fmt.Printf("%.2d:%s ", item.priority, item.value)
	}
	fmt.Println()
	// Output:
	// 05:orange 04:pear 03:banana 02:apple
}

執行結果:
05:orange 04:pear 03:banana 02:apple