Source file src/pkg/container/heap/heap.go

// 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.

// This package provides heap operations for any type that implements
// heap.Interface.
//
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):
//
//	!h.Less(j, i) for 0 <= i < h.Len() and j = 2*i+1 or 2*i+2 and j < h.Len()
//
type Interface interface {
    sort.Interface
    Push(x interface{})
    Pop() interface{}
}


// A heaper 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
    }
}