jx/internal/search/binary.go

// Copyright 2024 Matthew Rich <matthewrich.conf@gmail.com>. All rights reserved.

package search

import (
	"log/slog"
	"cmp"
	"math"
)

var (
)

const (
	BSTDATAOFFSET = 1
	BSTROOTNODEID = 0
	LEFTOFFSET = 1
	RIGHTOFFSET = 2
)

/*
 * Binary Search Tree using a slice
 */

type Binary[Key cmp.Ordered] []Key

type BinaryTree[Key cmp.Ordered] struct {
	*Binary[Key]
	zeroIndex int
	least, greatest, lastNode int
}

func NewBinaryTree[Key cmp.Ordered](capacity int) (bst *BinaryTree[Key]) {
	tree := make(Binary[Key], 1, capacity)
	bst = &BinaryTree[Key]{ Binary: &tree, least: 0, greatest: 0, lastNode: 0 }
	return
}

func (b *Binary[Key]) Empty() Key {
	return (*b)[0]
}

func (b *Binary[Key]) IsInternal(index int) bool {
	childIdx := 2 * index
	return ! b.IsEmpty(childIdx + LEFTOFFSET) && ! b.IsEmpty(childIdx + RIGHTOFFSET)
	//return (*b)[leftIdx] != (*b)[0] && (*b)[leftIdx + 1] != (*b)[0]
}

func (b *Binary[Key]) IsRight(index int) bool {
	return index % 2 == 0
}

func (b *Binary[Key]) Left(index int) int {
	return (2 * index) + LEFTOFFSET
}

func (b *Binary[Key]) Right(index int) int {
	return (2 * index) + RIGHTOFFSET
}

func (b *Binary[Key]) Get(index int) (Key) {
	return (*b)[index + BSTDATAOFFSET]
}

func (b *Binary[Key]) Set(index int, v Key) {
	(*b)[index + BSTDATAOFFSET] = v
}

func (b *BinaryTree[Key]) Set(index int, v Key) {
	b.Binary.Set(index, v)
	if v == b.Empty() {
		b.setZeroIndex(index)
	}
	b.setLastNode(index)
}

func (b *Binary[Key]) SetEmpty(index int) {
	(*b)[index + BSTDATAOFFSET] = b.Empty()
}

func (b *BinaryTree[Key]) SetEmpty(index int) {
	b.Binary.SetEmpty(index)
	if index == b.zeroIndex {
		b.setZeroIndex(-1)
	}
	b.setLastNode(index)
}

func (b *Binary[Key]) SetEmptyRange(start int, end int) {
	empty := b.Empty()
	for i := start; i <= end; i++ {
		(*b)[i + BSTDATAOFFSET] = empty
	}
}

func (b *BinaryTree[Key]) SetEmptyRange(start int, end int) {
	b.Binary.SetEmptyRange(start, end)
	if b.zeroIndex >= start && b.zeroIndex <= end {
		b.setZeroIndex(-1)
	}
	b.setLastNode(start)
}

func (b *BinaryTree[Key]) setZeroIndex(index int) {
	b.zeroIndex = index
}

func (b *BinaryTree[Key]) setLastNode(index int) {
	b.lastNode = max(b.lastNode, index)
}

func (b *BinaryTree[key]) LastNode() int {
	return b.lastNode
}

func (b *BinaryTree[key]) MaxDepth() int {
	return b.Depth(b.lastNode)
}

/*
func (b *Binary[Key]) Median(index int) {
	
  length := len(*b)
}
*/

func (b *Binary[Key]) Copy(from int, to int) {
	(*b)[to + BSTDATAOFFSET] = (*b)[from + BSTDATAOFFSET]
}

func (b *BinaryTree[Key]) Copy(from, to int) {
	b.Binary.Copy(from, to)
	if b.zeroIndex == from {
		b.setZeroIndex(to)
	}
	slog.Info("Copy()", "from", from, "to", to, "value", b.Get(from), "zero", b.zeroIndex)
}

func (b *Binary[Key]) LevelRange(index int, treeIndex int) (start int, end int) {
	treeDepth := b.Depth(treeIndex)
	depth := b.Depth(index)
	diff := depth - treeDepth
	switch diff {
	case 0:
		if index == treeIndex {
			return index, index
		}
	case 1:
		leftIdx := (2 * treeIndex) + 1
		if index >= leftIdx && index <= leftIdx + 1 {
			return leftIdx, leftIdx + 1
		}
	default:
		exp := int(math.Exp2(float64(diff)))
		level := exp * treeIndex
		childOffset := exp - 1
	
		left := level + childOffset
		right := level + (childOffset * 2)
		return left, right
	}
	return -1, -1
}

func (b *Binary[Key]) InSubTree(index, treeIndex int) bool {
	if treeIndex > index {
		return false
	}
	left, right := b.LevelRange(index, treeIndex)
	if index >= left && index <= right {
		return true
	}
	return false
}

func (b *BinaryTree[Key]) MoveSubTree(from, to int) {
	if ! b.IsLeaf(to) {
		panic("this move would overwrite the target subtree")
	}
	srccursor := b.Left(from)
	dstcursor := b.Left(to)
	for srccursor < b.lastNode && srccursor < len(*b.Binary) {
		srcstart, srcend := b.LevelRange(srccursor, from)
		dststart, dstend := b.LevelRange(dstcursor, to)
		slog.Info("MoveSubTree()", "srcstart", srcstart, "srcend", srcend, "dststart", dststart, "dstend", dstend, "source", (*b.Binary)[srcstart + BSTDATAOFFSET:srcend + BSTDATAOFFSET + 1], "dest", (*b.Binary)[dststart + BSTDATAOFFSET:dstend + BSTDATAOFFSET + 1])
		copy((*b.Binary)[dststart + BSTDATAOFFSET:dstend + BSTDATAOFFSET + 1], (*b.Binary)[srcstart + BSTDATAOFFSET:srcend + BSTDATAOFFSET + 1])
		b.SetEmptyRange(srcstart, srcend)

		srccursor = b.Left(srccursor)
		dstcursor = b.Left(dstcursor)
		slog.Info("MoveSubTree() post-copy", "srcstart", srcstart, "srcend", srcend, "dststart", dststart, "dstend", dstend, "data", b.Binary)
	}
	b.Copy(from, to)
}

func (b *Binary[Key]) IsLeaf(index int) bool {
	childIdx := 2 * (index)
	return (*b)[childIdx + LEFTOFFSET + BSTDATAOFFSET] == (*b)[childIdx + RIGHTOFFSET + BSTDATAOFFSET]
}

func (b *BinaryTree[Key]) IsLeaf(index int) bool {
	childIdx := 2 * (index)
	leftIdx := childIdx + LEFTOFFSET 
	rightIdx := childIdx + RIGHTOFFSET
	return b.Get(leftIdx) == b.Get(rightIdx) && leftIdx != b.zeroIndex && rightIdx != b.zeroIndex
}

func (b *Binary[Key]) ParentIndex(index int) (parent int) {
	parent = index
	if b.IsRight(index) {
		parent -= RIGHTOFFSET
	} else {
		parent -= LEFTOFFSET
	}
	parent = parent / 2
	return
}

func (b *Binary[Key]) Depth(index int) int {
	return int(math.Ceil(math.Log2(float64(index + 2))))
}

func (b *Binary[Key]) Width(index int) int {
	return int(math.Exp2(float64(b.Depth(index) - 1)))
}

func (b *Binary[Key]) IsFullLevel(index int) bool {
	width := b.Width(index)
	start := width - 1
	for _, v := range (*b)[start + BSTDATAOFFSET: start + width + BSTDATAOFFSET] {
		if v == b.Empty() {
			return false
		}
	}
	return true
}

func (b *Binary[Key]) IsEmpty(index int) bool {
	return (*b)[index + BSTDATAOFFSET] == b.Empty()
}

func (b *Binary[Key]) Ascend(idx int, item Key) int {
	if item < b.Get(idx) {
		return b.Left(idx)
	}
	return b.Right(idx)
}

func (b *Binary[Key]) Grow(index int) {
	size := len(*b) - BSTDATAOFFSET
	slog.Info("Grow()", "size", size, "index", index, "cap", cap(*b))
	if index >= size / 2 {
		targetSize := (size + (2 * index + 1) * 3) + BSTDATAOFFSET 
		if cap(*b) < targetSize {
			expandArray := make(Binary[Key], ((targetSize - cap(*b)) * 2) + BSTDATAOFFSET)
			*b = append(*b, expandArray...)
			slog.Info("Grow()", "size", size, "index", index, "targetsize", targetSize, "cap", cap(*b), "new", cap(expandArray))
		}
		*b = (*b)[:targetSize]
	}
	slog.Info("Grow()", "size", len(*b))
}

func (b *BinaryTree[Key]) RotateRight(index, right, left int) int {
	slog.Info("PreRotateRight", "index", index, "leftindex", left, "rightindex", right, "left", b.Get(left), "node", b.Get(index), "right", b.Get(right))
	b.Copy(index, right)
	b.Copy(left, index)
	b.SetEmpty(left)
	slog.Info("RotateRight", "index", index, "leftindex", left, "rightindex", right, "left", b.Get(left), "node", b.Get(index), "right", b.Get(right))
	return left
}

func (b *BinaryTree[Key]) RotateLeft(index, left, right int) int {
	slog.Info("PreRotateLeft", "index", index, "leftindex", left, "rightindex", right, "left", b.Get(left), "node", b.Get(index), "right", b.Get(right))
	b.Copy(index, left)
	b.Copy(right, index)
	b.SetEmpty(right)
	slog.Info("RotateLeft", "index", index, "leftindex", left, "rightindex", right, "left", b.Get(left), "node", b.Get(index), "right", b.Get(right))
	return right
}
/*
func (b *Binary[Key]) Insert(item Key) (idx int) {
	idx = BSTROOTNODEID
	
	slog.Info("Insert()", "item", item)
	for {
		b.Grow(idx)

		if b.IsEmpty(idx) {
			b.Set(idx, item)
			return
		} else {
			rightIdx := b.Right(idx)
			leftIdx := b.Left(idx)
			if b.IsInternal(idx) {
				
				idx = b.Ascend(idx, item)
			} else if b.IsLeaf(idx) {
				
				idx = b.Ascend(idx, item)
			} else {
				slog.Info("Insert()", "item", item, "index", idx)
				if item < b.Get(idx) {
					if ! b.IsEmpty(rightIdx) {
						idx = leftIdx
					} else {
						if ! b.IsLeaf(leftIdx) {
							panic("the left node is not a leaf")
						}
						idx = b.RotateRight(idx, rightIdx, leftIdx)
					}
				} else {
					if ! b.IsEmpty(leftIdx) {
						idx = rightIdx
					} else {
						if ! b.IsLeaf(rightIdx) {
							panic("the right node is not a leaf")
						}
						idx = b.RotateLeft(idx, leftIdx, rightIdx)
					}
				}
			}
		}
	}
}
*/

func (b *BinaryTree[Key]) Insert(item Key) (idx int) {
	idx = BSTROOTNODEID
	slog.Info("Insert()", "item", item)
	
	for {
		b.Grow(idx)

		if b.IsEmpty(idx) {
			b.Set(idx, item)
			return
		} else {
			rightIdx := b.Right(idx)
			leftIdx := b.Left(idx)
			if b.IsInternal(idx) {
				idx = b.Ascend(idx, item)
			} else if b.IsLeaf(idx) {// && b.IsFullLevel(idx) {
				/*
				if ! b.IsFullLevel(idx) {
					parent := b.ParentIndex(idx)
					if b.IsRight(parent) {
						idx = b.RotateLeft(parent, b.Left(parent), b.Right(parent))
					} else {
						idx = b.RotateRight(parent, b.Right(parent), b.Left(parent))
					}
				}
				*/
				idx = b.Ascend(idx, item)
			} else {

				slog.Info("Insert()", "item", item, "index", idx)
				if item < b.Get(idx) { // left
					slog.Info("Insert()", "item", item, "index", idx)
					if ! b.IsEmpty(rightIdx) {
						idx = leftIdx
					} else {
						if ! b.IsLeaf(leftIdx) {
							panic("the left node is not a leaf")
						}
						idx = b.RotateRight(idx, rightIdx, leftIdx)
					}
				} else { // right
					if ! b.IsEmpty(leftIdx) {
						idx = rightIdx
					} else {
						if ! b.IsLeaf(rightIdx) {
							idx = rightIdx
							//panic("the right node is not a leaf")
						} else {
							idx = b.RotateLeft(idx, leftIdx, rightIdx)
						}
					}
				}
			}
		}
	}
}

type BinaryBFSItem[Key cmp.Ordered] func(index int, depth int, v Key)

func (b *Binary[Key]) BFS(c BinaryBFSItem[Key]) (depth int) {
	queue := []int{ BSTROOTNODEID }
	for len(queue) > 0 {
		x := queue[0]
		queue = queue[1:]
		depth = b.Depth(x)
		c(x, depth, b.Get(x))
		leftIdx := b.Left(x)
		rightIdx := b.Right(x)
		if ! b.IsEmpty(leftIdx) {
			queue = append(queue, leftIdx)
		}
		if ! b.IsEmpty(rightIdx) {
			queue = append(queue, b.Right(x))
		}
	}
	return
}