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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

        }

}