feat: add go package for tool

go/heap/example_intheap_test.go

@@ -0,0 +1,50 @@
+// Copyright 2012 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 example demonstrates an integer heap built using the heap interface.
+package heap_test
+
+import (
+	"fmt"
+
+	"github.com/things-go/proc/go/heap"
+)
+
+var _ heap.Interface[int] = (*IntHeap)(nil)
+
+// 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 int) {
+	// Push and Pop use pointer receivers because they modify the slice's length,
+	// not just its contents.
+	*h = append(*h, x)
+}
+
+func (h *IntHeap) Pop() int {
+	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
+}

go/heap/example_pq_test.go

@@ -0,0 +1,101 @@
+// Copyright 2012 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 example demonstrates a priority queue built using the heap interface.
+package heap_test
+
+import (
+	"fmt"
+
+	"github.com/things-go/proc/go/heap"
+)
+
+var _ heap.Interface[*Item] = (*PriorityQueue)(nil)
+
+// 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 *Item) {
+	n := len(*pq)
+	item := x
+	item.index = n
+	*pq = append(*pq, item)
+}
+
+func (pq *PriorityQueue) Pop() *Item {
+	old := *pq
+	n := len(old)
+	item := old[n-1]
+	old[n-1] = nil  // avoid memory leak
+	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[*Item](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[*Item](&pq)
+
+	// Insert a new item and then modify its priority.
+	item := &Item{
+		value:    "orange",
+		priority: 1,
+	}
+	heap.Push[*Item](&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[*Item](&pq)
+		fmt.Printf("%.2d:%s ", item.priority, item.value)
+	}
+	// Output:
+	// 05:orange 04:pear 03:banana 02:apple
+}

go/heap/heap.go

@@ -0,0 +1,118 @@
+// 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
+// minimum-valued node in its subtree.
+//
+// The minimum element in the tree is the root, at index 0.
+//
+// A heap is a common way to implement 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. The Examples include such an
+// implementation; the file example_pq_test.go has the complete source.
+package heap
+
+import "sort"
+
+// The Interface type describes the requirements
+// for a type using the routines in this package.
+// Any type that implements it 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 2*i+1 <= j <= 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[T any] interface {
+	sort.Interface
+	Push(x T) // add x as element Len()
+	Pop() T   // remove and return element Len() - 1.
+}
+
+// Init establishes the heap invariants required by the other routines in this package.
+// 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 Init[T any](h Interface[T]) {
+	// 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[T any](h Interface[T], x T) {
+	h.Push(x)
+	up(h, h.Len()-1)
+}
+
+// Pop 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 Pop[T any](h Interface[T]) T {
+	n := h.Len() - 1
+	h.Swap(0, n)
+	down(h, 0, n)
+	return h.Pop()
+}
+
+// Remove removes and returns the element at index i from the heap.
+// The complexity is O(log n) where n = h.Len().
+func Remove[T any](h Interface[T], i int) T {
+	n := h.Len() - 1
+	if n != i {
+		h.Swap(i, n)
+		if !down(h, i, n) {
+			up(h, i)
+		}
+	}
+	return h.Pop()
+}
+
+// Fix 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 Fix[T any](h Interface[T], i int) {
+	if !down(h, i, h.Len()) {
+		up(h, i)
+	}
+}
+
+func up[T any](h Interface[T], j int) {
+	for {
+		i := (j - 1) / 2 // parent
+		if i == j || !h.Less(j, i) {
+			break
+		}
+		h.Swap(i, j)
+		j = i
+	}
+}
+
+func down[T any](h Interface[T], 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
+}