heap.go

package paths

// This file is based on container/heap from the standard library with the
// following license mention:
//
// 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.

// pqInit establishes the heap invariants required by the other routines in this file.
// Init is idempotent with respect to the heap invariants
// and may be called whenever the heap invariants may have been invalidated.
// The complexity is O(n) where n = h.Len().
func pqInit(h *priorityQueue) {
	// heapify
	n := h.Len()
	for i := n/2 - 1; i >= 0; i-- {
		down(h, i, n)
	}
}

// pqPush pushes the element x onto the heap.
// The complexity is O(log n) where n = h.Len().
func pqPush(h *priorityQueue, x *node) {
	h.Push(x)
	up(h, h.Len()-1)
}

// pqPop removes and returns the minimum element (according to Less) from the heap.
// The complexity is O(log n) where n = h.Len().
// Pop is equivalent to Remove(h, 0).
func pqPop(h *priorityQueue) *node {
	n := h.Len() - 1
	h.Swap(0, n)
	down(h, 0, n)
	return h.Pop()
}

// pqRemove removes and returns the element at index i from the heap.
// The complexity is O(log n) where n = h.Len().
func pqRemove(h *priorityQueue, i int) *node {
	n := h.Len() - 1
	if n != i {
		h.Swap(i, n)
		if !down(h, i, n) {
			up(h, i)
		}
	}
	return h.Pop()
}

// pqFix re-establishes the heap ordering after the element at index i has changed its value.
// Changing the value of the element at index i and then calling Fix is equivalent to,
// but less expensive than, calling Remove(h, i) followed by a Push of the new value.
// The complexity is O(log n) where n = h.Len().
//func pqFix(h *priorityQueue, i int) {
//if !down(h, i, h.Len()) {
//up(h, i)
//}
//}

func up(h *priorityQueue, j int) {
	for {
		i := (j - 1) / 2 // parent
		if i == j || !h.Less(j, i) {
			break
		}
		h.Swap(i, j)
		j = i
	}
}

func down(h *priorityQueue, i0, n int) bool {
	i := i0
	for {
		j1 := 2*i + 1
		if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
			break
		}
		j := j1 // left child
		if j2 := j1 + 1; j2 < n && h.Less(j2, j1) {
			j = j2 // = 2*i + 2  // right child
		}
		if !h.Less(j, i) {
			break
		}
		h.Swap(i, j)
		i = j
	}
	return i > i0
}