# package heap

`import "container/heap"`

heap包提供了对任意类型（实现了heap.Interface接口）的堆操作。（最小）堆是具有“每个节点都是以其为根的子树中最小值”属性的树。

树的最小元素为其根元素，索引0的位置。

heap是常用的实现优先队列的方法。要创建一个优先队列，实现一个具有使用（负的）优先级作为比较的依据的Less方法的Heap接口，如此一来可用Push添加项目而用Pop取出队列最高优先级的项目。

Example (IntHeap)

    // This example demonstrates an integer heap built using the heap interface.
    package heap_test
    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{}) {
        // Push and Pop use pointer receivers because they modify the slice's length,
        // not just its contents.
        *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
    }
    // This example inserts several ints into an IntHeap, checks the minimum,
    // and removes them in order of priority.
    func Example_intHeap() {
        h := &IntHeap{2, 1, 5}
        heap.Init(h)
        heap.Push(h, 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
    }

Example (PriorityQueue)

    // This example demonstrates a priority queue built using the heap interface.
    package heap_test
    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 Example_priorityQueue() {
        // 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)
        }
        // Output:
        // 05:orange 04:pear 03:banana 02:apple
    }

## type Interface

    type Interface interface {
        sort.Interface
        Push(x interface{}) // 向末尾添加元素
        Pop() interface{}   // 从末尾删除元素
    }

任何实现了本接口的类型都可以用于构建最小堆。最小堆可以通过heap.Init建立，数据是递增顺序或者空的话也是最小堆。最小堆的约束条件是：

    !h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()

注意接口的Push和Pop方法是供heap包调用的，请使用heap.Push和heap.Pop来向一个堆添加或者删除元素。

## func Init

    func Init(h Interface)

一个堆在使用任何堆操作之前应先初始化。Init函数对于堆的约束性是幂等的（多次执行无意义），并可能在任何时候堆的约束性被破坏时被调用。本函数复杂度为O(n)，其中n等于h.Len()。

## func Push

    func Push(h Interface, x interface{})

向堆h中插入元素x，并保持堆的约束性。复杂度O(log(n))，其中n等于h.Len()。

## func Pop

    func Pop(h Interface) interface{}

删除并返回堆h中的最小元素（不影响约束性）。复杂度O(log(n))，其中n等于h.Len()。等价于Remove(h, 0)。

## func Remove

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

删除堆中的第i个元素，并保持堆的约束性。复杂度O(log(n))，其中n等于h.Len()。

## func Fix

    func Fix(h Interface, i int)

在修改第i个元素后，调用本函数修复堆，比删除第i个元素后插入新元素更有效率。

复杂度O(log(n))，其中n等于h.Len()。