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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
// highest-valued node in its subtree.
//
// A heap is a common way to impement 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.
//
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 j = 2*i+1 or 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().
// 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
        }
}