d2/d2layouts/d2grid/layout.go

package d2grid

import (
	"bytes"
	"context"
	"fmt"
	"math"

	"oss.terrastruct.com/d2/d2graph"
	"oss.terrastruct.com/d2/d2target"
	"oss.terrastruct.com/d2/lib/geo"
	"oss.terrastruct.com/d2/lib/label"
	"oss.terrastruct.com/util-go/go2"
)

const (
	CONTAINER_PADDING = 60
	DEFAULT_GAP       = 40
)

// Layout runs the grid layout on containers with rows/columns
// Note: children are not allowed edges or descendants
// 1. Run grid layout on the graph root
// 2. Set the resulting dimensions to the graph root
func Layout(ctx context.Context, g *d2graph.Graph) error {
	obj := g.Root

	gd, err := layoutGrid(g, obj)
	if err != nil {
		return err
	}

	if obj.HasLabel() && obj.LabelPosition == nil {
		obj.LabelPosition = go2.Pointer(label.InsideTopCenter.String())
	}
	if obj.Icon != nil && obj.IconPosition == nil {
		obj.IconPosition = go2.Pointer(label.InsideTopLeft.String())
	}

	if obj.Box != nil {
		// CONTAINER_PADDING is default, but use gap value if set
		horizontalPadding, verticalPadding := CONTAINER_PADDING, CONTAINER_PADDING
		if obj.GridGap != nil || obj.HorizontalGap != nil {
			horizontalPadding = gd.horizontalGap
		}
		if obj.GridGap != nil || obj.VerticalGap != nil {
			verticalPadding = gd.verticalGap
		}

		contentWidth, contentHeight := gd.width, gd.height

		var labelPosition, iconPosition label.Position
		if obj.LabelPosition != nil {
			labelPosition = label.FromString(*obj.LabelPosition)
		}
		if obj.IconPosition != nil {
			iconPosition = label.FromString(*obj.IconPosition)
		}

		// compute how much space the label and icon occupy
		_, padding := obj.Spacing()

		var labelWidth, labelHeight float64
		if obj.LabelDimensions.Width > 0 {
			labelWidth = float64(obj.LabelDimensions.Width) + 2*label.PADDING
		}
		if obj.LabelDimensions.Height > 0 {
			labelHeight = float64(obj.LabelDimensions.Height) + 2*label.PADDING
		}

		if labelWidth > 0 {
			switch labelPosition {
			case label.OutsideTopLeft, label.OutsideTopCenter, label.OutsideTopRight,
				label.InsideTopLeft, label.InsideTopCenter, label.InsideTopRight,
				label.InsideBottomLeft, label.InsideBottomCenter, label.InsideBottomRight,
				label.OutsideBottomLeft, label.OutsideBottomCenter, label.OutsideBottomRight:
				overflow := labelWidth - contentWidth
				if overflow > 0 {
					padding.Left += overflow / 2
					padding.Right += overflow / 2
				}
			}
		}
		if labelHeight > 0 {
			switch labelPosition {
			case label.OutsideLeftTop, label.OutsideLeftMiddle, label.OutsideLeftBottom,
				label.InsideMiddleLeft, label.InsideMiddleCenter, label.InsideMiddleRight,
				label.OutsideRightTop, label.OutsideRightMiddle, label.OutsideRightBottom:
				overflow := labelHeight - contentHeight
				if overflow > 0 {
					padding.Top += overflow / 2
					padding.Bottom += overflow / 2
				}
			}
		}

		// configure spacing for default label+icon
		if iconPosition == label.InsideTopLeft && labelPosition == label.InsideTopCenter {
			// . ├────┤───────├────┤
			// .  icon  label  icon
			// with an icon in top left we need 2x the space to fit the label in the center
			iconSize := float64(d2target.MAX_ICON_SIZE) + 2*label.PADDING
			padding.Left = math.Max(padding.Left, iconSize)
			padding.Right = math.Max(padding.Right, iconSize)
			minWidth := 2*iconSize + float64(obj.LabelDimensions.Width) + 2*label.PADDING
			overflow := minWidth - contentWidth
			if overflow > 0 {
				padding.Left = math.Max(padding.Left, overflow/2)
				padding.Right = math.Max(padding.Right, overflow/2)
			}
		}

		padding.Top = math.Max(padding.Top, float64(verticalPadding))
		padding.Bottom = math.Max(padding.Bottom, float64(verticalPadding))
		padding.Left = math.Max(padding.Left, float64(horizontalPadding))
		padding.Right = math.Max(padding.Right, float64(horizontalPadding))

		totalWidth := padding.Left + contentWidth + padding.Right
		totalHeight := padding.Top + contentHeight + padding.Bottom
		obj.SizeToContent(totalWidth, totalHeight, 0, 0)

		// compute where the grid should be placed inside shape
		s := obj.ToShape()
		innerTL := s.GetInsidePlacement(totalWidth, totalHeight, 0, 0)
		// depending on the shape innerBox may be larger than totalWidth, totalHeight
		// if this is the case, we want to center the cells within the larger innerBox
		innerBox := s.GetInnerBox()

		var resizeDx, resizeDy float64
		if innerBox.Width > totalWidth {
			resizeDx = (innerBox.Width - totalWidth) / 2
		}
		if innerBox.Height > totalHeight {
			resizeDy = (innerBox.Height - totalHeight) / 2
		}

		// move from horizontalPadding,verticalPadding to innerTL.X+padding.Left, innerTL.Y+padding.Top
		// and if innerBox is larger than content dimensions, adjust to center within innerBox
		dx := -float64(horizontalPadding) + innerTL.X + padding.Left + resizeDx
		dy := -float64(verticalPadding) + innerTL.Y + padding.Top + resizeDy
		if dx != 0 || dy != 0 {
			gd.shift(dx, dy)
		}
	}

	// simple straight line edge routing between grid objects
	for _, e := range g.Edges {
		if !e.Src.Parent.IsDescendantOf(obj) && !e.Dst.Parent.IsDescendantOf(obj) {
			continue
		}
		// if edge is within grid, remove it from outer layout
		gd.edges = append(gd.edges, e)

		if e.Src.Parent != obj || e.Dst.Parent != obj {
			continue
		}
		// if edge is grid child, use simple routing
		e.Route = []*geo.Point{e.Src.Center(), e.Dst.Center()}
		e.TraceToShape(e.Route, 0, 1)
		if e.Label.Value != "" {
			e.LabelPosition = go2.Pointer(label.InsideMiddleCenter.String())
		}
	}

	if g.Root.IsGridDiagram() && len(g.Root.ChildrenArray) != 0 {
		g.Root.TopLeft = geo.NewPoint(0, 0)
	}

	if g.RootLevel > 0 {
		horizontalPadding, verticalPadding := CONTAINER_PADDING, CONTAINER_PADDING
		if obj.GridGap != nil || obj.HorizontalGap != nil {
			horizontalPadding = gd.horizontalGap
		}
		if obj.GridGap != nil || obj.VerticalGap != nil {
			verticalPadding = gd.verticalGap
		}

		// shift the grid from (0, 0)
		gd.shift(
			obj.TopLeft.X+float64(horizontalPadding),
			obj.TopLeft.Y+float64(verticalPadding),
		)
	}
	return nil
}

func layoutGrid(g *d2graph.Graph, obj *d2graph.Object) (*gridDiagram, error) {
	gd := newGridDiagram(obj)

	// position labels and icons
	for _, o := range gd.objects {
		positionedLabel := false
		if o.Icon != nil && o.IconPosition == nil {
			if len(o.ChildrenArray) > 0 {
				o.IconPosition = go2.Pointer(label.OutsideTopLeft.String())
				// don't overwrite position if nested graph layout positioned label/icon
				if o.LabelPosition == nil {
					o.LabelPosition = go2.Pointer(label.OutsideTopRight.String())
					positionedLabel = true
				}
			} else {
				o.IconPosition = go2.Pointer(label.InsideMiddleCenter.String())
			}
		}
		if !positionedLabel && o.HasLabel() && o.LabelPosition == nil {
			if len(o.ChildrenArray) > 0 {
				o.LabelPosition = go2.Pointer(label.OutsideTopCenter.String())
			} else if o.HasOutsideBottomLabel() {
				o.LabelPosition = go2.Pointer(label.OutsideBottomCenter.String())
			} else if o.Icon != nil {
				o.LabelPosition = go2.Pointer(label.InsideTopCenter.String())
			} else {
				o.LabelPosition = go2.Pointer(label.InsideMiddleCenter.String())
			}
		}
	}

	// to handle objects with outside labels, we adjust their dimensions before layout and
	// after layout, we remove the label adjustment and reposition TopLeft if needed
	revertAdjustments := gd.sizeForOutsideLabels()

	if gd.rows != 0 && gd.columns != 0 {
		gd.layoutEvenly(g, obj)
	} else {
		gd.layoutDynamic(g, obj)
	}

	revertAdjustments()

	return gd, nil
}

func (gd *gridDiagram) layoutEvenly(g *d2graph.Graph, obj *d2graph.Object) {
	// layout objects in a grid with these 2 properties:
	// all objects in the same row should have the same height
	// all objects in the same column should have the same width

	getObject := func(rowIndex, columnIndex int) *d2graph.Object {
		var index int
		if gd.rowDirected {
			index = rowIndex*gd.columns + columnIndex
		} else {
			index = columnIndex*gd.rows + rowIndex
		}
		if index < len(gd.objects) {
			return gd.objects[index]
		}
		return nil
	}

	rowHeights := make([]float64, 0, gd.rows)
	colWidths := make([]float64, 0, gd.columns)
	for i := 0; i < gd.rows; i++ {
		rowHeight := 0.
		for j := 0; j < gd.columns; j++ {
			o := getObject(i, j)
			if o == nil {
				break
			}
			rowHeight = math.Max(rowHeight, o.Height)
		}
		rowHeights = append(rowHeights, rowHeight)
	}
	for j := 0; j < gd.columns; j++ {
		columnWidth := 0.
		for i := 0; i < gd.rows; i++ {
			o := getObject(i, j)
			if o == nil {
				break
			}
			columnWidth = math.Max(columnWidth, o.Width)
		}
		colWidths = append(colWidths, columnWidth)
	}

	horizontalGap := float64(gd.horizontalGap)
	verticalGap := float64(gd.verticalGap)

	cursor := geo.NewPoint(0, 0)
	if gd.rowDirected {
		for i := 0; i < gd.rows; i++ {
			for j := 0; j < gd.columns; j++ {
				o := getObject(i, j)
				if o == nil {
					break
				}
				o.Width = colWidths[j]
				o.Height = rowHeights[i]
				o.MoveWithDescendantsTo(cursor.X, cursor.Y)
				cursor.X += o.Width + horizontalGap
			}
			cursor.X = 0
			cursor.Y += rowHeights[i] + verticalGap
		}
	} else {
		for j := 0; j < gd.columns; j++ {
			for i := 0; i < gd.rows; i++ {
				o := getObject(i, j)
				if o == nil {
					break
				}
				o.Width = colWidths[j]
				o.Height = rowHeights[i]
				o.MoveWithDescendantsTo(cursor.X, cursor.Y)
				cursor.Y += o.Height + verticalGap
			}
			cursor.X += colWidths[j] + horizontalGap
			cursor.Y = 0
		}
	}

	var totalWidth, totalHeight float64
	for _, w := range colWidths {
		totalWidth += w + horizontalGap
	}
	for _, h := range rowHeights {
		totalHeight += h + verticalGap
	}
	totalWidth -= horizontalGap
	totalHeight -= verticalGap
	gd.width = totalWidth
	gd.height = totalHeight
}

func (gd *gridDiagram) layoutDynamic(g *d2graph.Graph, obj *d2graph.Object) {
	// assume we have the following objects to layout:
	// . ┌A──────────────┐  ┌B──┐  ┌C─────────┐  ┌D────────┐  ┌E────────────────┐
	// . └───────────────┘  │   │  │          │  │         │  │                 │
	// .                    │   │  └──────────┘  │         │  │                 │
	// .                    │   │                │         │  └─────────────────┘
	// .                    └───┘                │         │
	// .                                         └─────────┘
	// Note: if the grid is row dominant, all objects should be the same height (same width if column dominant)
	// . ┌A─────────────┐  ┌B──┐  ┌C─────────┐  ┌D────────┐  ┌E────────────────┐
	// . ├ ─ ─ ─ ─ ─ ─ ─┤  │   │  │          │  │         │  │                 │
	// . │              │  │   │  ├ ─ ─ ─ ─ ─┤  │         │  │                 │
	// . │              │  │   │  │          │  │         │  ├ ─ ─ ─ ─ ─ ─ ─ ─ ┤
	// . │              │  ├ ─ ┤  │          │  │         │  │                 │
	// . └──────────────┘  └───┘  └──────────┘  └─────────┘  └─────────────────┘

	horizontalGap := float64(gd.horizontalGap)
	verticalGap := float64(gd.verticalGap)

	// we want to split up the total width across the N rows or columns as evenly as possible
	var totalWidth, totalHeight float64
	for _, o := range gd.objects {
		totalWidth += o.Width
		totalHeight += o.Height
	}
	totalWidth += horizontalGap * float64(len(gd.objects)-gd.rows)
	totalHeight += verticalGap * float64(len(gd.objects)-gd.columns)

	var layout [][]*d2graph.Object
	if gd.rowDirected {
		targetWidth := totalWidth / float64(gd.rows)
		layout = gd.getBestLayout(targetWidth, false)
	} else {
		targetHeight := totalHeight / float64(gd.columns)
		layout = gd.getBestLayout(targetHeight, true)
	}

	cursor := geo.NewPoint(0, 0)
	var maxY, maxX float64
	if gd.rowDirected {
		// measure row widths
		rowWidths := []float64{}
		for _, row := range layout {
			x := 0.
			for _, o := range row {
				x += o.Width + horizontalGap
			}
			rowWidth := x - horizontalGap
			rowWidths = append(rowWidths, rowWidth)
			maxX = math.Max(maxX, rowWidth)
		}

		// TODO if object is a nested grid, consider growing descendants according to the inner grid layout

		// then expand thinnest objects to make each row the same width
		// . ┌A─────────────┐  ┌B──┐  ┌C─────────┐ ┬ maxHeight(A,B,C)
		// . │              │  │   │  │          │ │
		// . │              │  │   │  │          │ │
		// . │              │  │   │  │          │ │
		// . └──────────────┘  └───┘  └──────────┘ ┴
		// . ┌D────────┬────┐  ┌E────────────────┐ ┬ maxHeight(D,E)
		// . │              │  │                 │ │
		// . │         │    │  │                 │ │
		// . │              │  │                 │ │
		// . │         │    │  │                 │ │
		// . └─────────┴────┘  └─────────────────┘ ┴
		for i, row := range layout {
			rowWidth := rowWidths[i]
			if rowWidth == maxX {
				continue
			}
			delta := maxX - rowWidth
			var widest float64
			for _, o := range row {
				widest = math.Max(widest, o.Width)
			}
			diffs := make([]float64, len(row))
			totalDiff := 0.
			for i, o := range row {
				diffs[i] = widest - o.Width
				totalDiff += diffs[i]
			}
			if totalDiff > 0 {
				// expand smaller nodes up to the size of the larger ones with delta
				// percentage diff
				for i := range diffs {
					diffs[i] /= totalDiff
				}
				growth := math.Min(delta, totalDiff)
				// expand smaller objects to fill remaining space
				for i, o := range row {
					o.Width += diffs[i] * growth
				}
			}
			if delta > totalDiff {
				growth := (delta - totalDiff) / float64(len(row))
				for _, o := range row {
					o.Width += growth
				}
			}
		}

		// if we have 2 rows, then each row's objects should have the same height
		// . ┌A─────────────┐  ┌B──┐  ┌C─────────┐ ┬ maxHeight(A,B,C)
		// . ├ ─ ─ ─ ─ ─ ─ ─┤  │   │  │          │ │
		// . │              │  │   │  ├ ─ ─ ─ ─ ─┤ │
		// . │              │  │   │  │          │ │
		// . └──────────────┘  └───┘  └──────────┘ ┴
		// . ┌D────────┐  ┌E────────────────┐ ┬ maxHeight(D,E)
		// . │         │  │                 │ │
		// . │         │  │                 │ │
		// . │         │  ├ ─ ─ ─ ─ ─ ─ ─ ─ ┤ │
		// . │         │  │                 │ │
		// . └─────────┘  └─────────────────┘ ┴
		for _, row := range layout {
			rowHeight := 0.
			for _, o := range row {
				o.MoveWithDescendantsTo(cursor.X, cursor.Y)
				cursor.X += o.Width + horizontalGap
				rowHeight = math.Max(rowHeight, o.Height)
			}

			// set all objects in row to the same height
			for _, o := range row {
				o.Height = rowHeight
			}

			// new row
			cursor.X = 0
			cursor.Y += rowHeight + verticalGap
		}
		maxY = cursor.Y - verticalGap
	} else {
		// measure column heights
		colHeights := []float64{}
		for _, column := range layout {
			y := 0.
			for _, o := range column {
				y += o.Height + verticalGap
			}
			colHeight := y - verticalGap
			colHeights = append(colHeights, colHeight)
			maxY = math.Max(maxY, colHeight)
		}

		// then expand shortest objects to make each column the same height
		// . ├maxWidth(A,B)─┤  ├maxW(C,D)─┤  ├maxWidth(E)──────┤
		// . ┌A─────────────┐  ┌C─────────┐  ┌E────────────────┐
		// . ├ ─ ─ ─ ─ ─ ─  ┤  │          │  │                 │
		// . │              │  └──────────┘  │                 │
		// . └──────────────┘  ┌D─────────┐  ├ ─ ─ ─ ─ ─ ─ ─ ─ ┤
		// . ┌B─────────────┐  │          │  │                 │
		// . │              │  │          │  │                 │
		// . │              │  │          │  │                 │
		// . │              │  │          │  │                 │
		// . └──────────────┘  └──────────┘  └─────────────────┘
		for i, column := range layout {
			colHeight := colHeights[i]
			if colHeight == maxY {
				continue
			}
			delta := maxY - colHeight
			var tallest float64
			for _, o := range column {
				tallest = math.Max(tallest, o.Height)
			}
			diffs := make([]float64, len(column))
			totalDiff := 0.
			for i, o := range column {
				diffs[i] = tallest - o.Height
				totalDiff += diffs[i]
			}
			if totalDiff > 0 {
				// expand smaller nodes up to the size of the larger ones with delta
				// percentage diff
				for i := range diffs {
					diffs[i] /= totalDiff
				}
				growth := math.Min(delta, totalDiff)
				// expand smaller objects to fill remaining space
				for i, o := range column {
					o.Height += diffs[i] * growth
				}
			}
			if delta > totalDiff {
				growth := (delta - totalDiff) / float64(len(column))
				for _, o := range column {
					o.Height += growth
				}
			}
		}
		// if we have 3 columns, then each column's objects should have the same width
		// . ├maxWidth(A,B)─┤  ├maxW(C,D)─┤  ├maxWidth(E)──────┤
		// . ┌A─────────────┐  ┌C─────────┐  ┌E────────────────┐
		// . └──────────────┘  │          │  │                 │
		// . ┌B──┬──────────┐  └──────────┘  │                 │
		// . │              │  ┌D────────┬┐  └─────────────────┘
		// . │   │          │  │          │
		// . │              │  │         ││
		// . └───┴──────────┘  │          │
		// .                   │         ││
		// .                   └─────────┴┘
		for _, column := range layout {
			colWidth := 0.
			for _, o := range column {
				o.MoveWithDescendantsTo(cursor.X, cursor.Y)
				cursor.Y += o.Height + verticalGap
				colWidth = math.Max(colWidth, o.Width)
			}
			// set all objects in column to the same width
			for _, o := range column {
				o.Width = colWidth
			}

			// new column
			cursor.Y = 0
			cursor.X += colWidth + horizontalGap
		}
		maxX = cursor.X - horizontalGap
	}
	gd.width = maxX
	gd.height = maxY
}

// generate the best layout of objects aiming for each row to be the targetSize width
// if columns is true, each column aims to have the targetSize height
func (gd *gridDiagram) getBestLayout(targetSize float64, columns bool) [][]*d2graph.Object {
	debug := false
	var nCuts int
	if columns {
		nCuts = gd.columns - 1
	} else {
		nCuts = gd.rows - 1
	}
	if nCuts == 0 {
		return GenLayout(gd.objects, nil)
	}

	var bestLayout [][]*d2graph.Object
	bestDist := math.MaxFloat64
	fastIsBest := false
	// try fast layout algorithm as a baseline
	if fastLayout := gd.fastLayout(targetSize, nCuts, columns); fastLayout != nil {
		dist := getDistToTarget(fastLayout, targetSize, float64(gd.horizontalGap), float64(gd.verticalGap), columns)
		if debug {
			fmt.Printf("fast dist %v dist per row %v\n", dist, dist/(float64(nCuts)+1))
		}
		if dist == 0 {
			return fastLayout
		}
		bestDist = dist
		bestLayout = fastLayout
		fastIsBest = true
	}

	var gap float64
	if columns {
		gap = float64(gd.verticalGap)
	} else {
		gap = float64(gd.horizontalGap)
	}
	getSize := func(o *d2graph.Object) float64 {
		if columns {
			return o.Height
		} else {
			return o.Width
		}
	}

	sizes := []float64{}
	for _, obj := range gd.objects {
		size := getSize(obj)
		sizes = append(sizes, size)
	}
	sd := stddev(sizes)
	if debug {
		fmt.Printf("sizes (%d): %v\n", len(sizes), sizes)
		fmt.Printf("std dev: %v; targetSize %v\n", sd, targetSize)
	}

	skipCount := 0
	count := 0
	// quickly eliminate bad row groupings
	startingCache := make(map[int]bool)
	// Note: we want a low threshold to explore good options within attemptLimit,
	// but the best option may require a few rows that are far from the target size.
	okThreshold := STARTING_THRESHOLD
	rowOk := func(row []*d2graph.Object, starting bool) (ok bool) {
		if starting {
			// we can cache results from starting positions since they repeat and don't change
			// with starting=true it will always be the 1st N objects based on len(row)
			if ok, has := startingCache[len(row)]; has {
				return ok
			}
			defer func() {
				// cache result before returning
				startingCache[len(row)] = ok
			}()
		}

		rowSize := 0.
		for _, obj := range row {
			rowSize += getSize(obj)
		}
		if len(row) > 1 {
			rowSize += gap * float64(len(row)-1)
			// if multiple nodes are too big, it isn't ok. but a single node can't shrink so only check here
			if rowSize > okThreshold*targetSize {
				skipCount++
				// there may even be too many to skip
				return skipCount >= SKIP_LIMIT
			}
		}
		// row is too small to be good overall
		if rowSize < targetSize/okThreshold {
			skipCount++
			return skipCount >= SKIP_LIMIT
		}
		return true
	}

	// get all options for where to place these cuts, preferring later cuts over earlier cuts
	// with 5 objects and 2 cuts we have these options:
	// .       A   B   C │ D │ E     <- these cuts would produce: ┌A─┐ ┌B─┐ ┌C─┐
	// .       A   B │ C   D │ E                                  └──┘ └──┘ └──┘
	// .       A │ B   C   D │ E                                  ┌D───────────┐
	// .       A   B │ C │ D   E                                  └────────────┘
	// .       A │ B   C │ D   E                                  ┌E───────────┐
	// .       A │ B │ C   D   E                                  └────────────┘
	// of these divisions, find the layout with rows closest to the targetSize
	tryDivision := func(division []int) bool {
		layout := GenLayout(gd.objects, division)
		dist := getDistToTarget(layout, targetSize, float64(gd.horizontalGap), float64(gd.verticalGap), columns)
		if dist < bestDist {
			bestLayout = layout
			bestDist = dist
			fastIsBest = false
		} else if fastIsBest && dist == bestDist {
			// prefer ordered search solution to fast layout solution
			bestLayout = layout
			fastIsBest = false
		}
		count++
		// with few objects we can try all options to get best result but this won't scale, so only try up to 100k options
		return count >= ATTEMPT_LIMIT || skipCount >= SKIP_LIMIT
	}

	// try number of different okThresholds depending on std deviation of sizes
	thresholdAttempts := int(math.Ceil(sd))
	if thresholdAttempts < MIN_THRESHOLD_ATTEMPTS {
		thresholdAttempts = MIN_THRESHOLD_ATTEMPTS
	} else if thresholdAttempts > MAX_THRESHOLD_ATTEMPTS {
		thresholdAttempts = MAX_THRESHOLD_ATTEMPTS
	}
	for i := 0; i < thresholdAttempts || bestLayout == nil; i++ {
		count = 0.
		skipCount = 0.
		iterDivisions(gd.objects, nCuts, tryDivision, rowOk)
		okThreshold += THRESHOLD_STEP_SIZE
		if debug {
			fmt.Printf("count %d, skip count %d, bestDist %v increasing ok threshold to %v\n", count, skipCount, bestDist, okThreshold)
		}
		startingCache = make(map[int]bool)
		if skipCount == 0 {
			// threshold isn't skipping anything so increasing it won't help
			break
		}
		// okThreshold isn't high enough yet, we skipped every option so don't count it
		if count == 0 && thresholdAttempts < MAX_THRESHOLD_ATTEMPTS {
			thresholdAttempts++
		}
	}

	if debug {
		fmt.Printf("best layout: %v\n", layoutString(bestLayout, sizes))
	}
	return bestLayout
}

func sum(values []float64) float64 {
	s := 0.
	for _, v := range values {
		s += v
	}
	return s
}

func avg(values []float64) float64 {
	return sum(values) / float64(len(values))
}

func variance(values []float64) float64 {
	mean := avg(values)
	total := 0.
	for _, value := range values {
		dev := mean - value
		total += dev * dev
	}
	return total / float64(len(values))
}

func stddev(values []float64) float64 {
	return math.Sqrt(variance(values))
}

func (gd *gridDiagram) fastLayout(targetSize float64, nCuts int, columns bool) (layout [][]*d2graph.Object) {
	var gap float64
	if columns {
		gap = float64(gd.verticalGap)
	} else {
		gap = float64(gd.horizontalGap)
	}

	debt := 0.
	fastDivision := make([]int, 0, nCuts)
	rowSize := 0.
	for i := 0; i < len(gd.objects); i++ {
		o := gd.objects[i]
		var size float64
		if columns {
			size = o.Height
		} else {
			size = o.Width
		}
		if rowSize == 0 {
			// if a single object meets the target size, end the row here
			if size > targetSize-debt {
				// cut row with just this object
				fastDivision = append(fastDivision, i)
				// we build up a debt of distance past the target size across rows
				newDebt := size - targetSize
				debt += newDebt
			} else {
				rowSize += size
			}
			continue
		}
		// debt is paid by decreasing threshold to start new row and ending below targetSize
		if rowSize+gap+(size)/2. > targetSize-debt {
			// start a new row before this object since it is mostly past the target size
			// .              size
			// ├...row─┼gap┼───┼───┤
			// ├──targetSize──┤ (debt=0)
			fastDivision = append(fastDivision, i-1)
			newDebt := rowSize - targetSize
			debt += newDebt
			rowSize = size
		} else {
			rowSize += gap + size
		}
	}
	if len(fastDivision) == nCuts {
		layout = GenLayout(gd.objects, fastDivision)
	}

	return layout
}

func layoutString(layout [][]*d2graph.Object, sizes []float64) string {
	buf := &bytes.Buffer{}
	i := 0
	fmt.Fprintf(buf, "[\n")
	for _, r := range layout {
		vals := sizes[i : i+len(r)]
		fmt.Fprintf(buf, "%v:\t%v\n", sum(vals), vals)
		i += len(r)
	}
	fmt.Fprintf(buf, "]\n")
	return buf.String()
}

// process current division, return true to stop iterating
type iterDivision func(division []int) (done bool)
type checkCut func(objects []*d2graph.Object, starting bool) (ok bool)

// get all possible divisions of objects by the number of cuts
func iterDivisions(objects []*d2graph.Object, nCuts int, f iterDivision, check checkCut) {
	if len(objects) < 2 || nCuts == 0 {
		return
	}
	done := false
	// we go in this order to prefer extra objects in starting rows rather than later ones
	lastObj := len(objects) - 1
	// with objects=[A, B, C, D, E]; nCuts=2
	// d:depth; i:index; n:nCuts;
	// ┌────┬───┬───┬─────────────────────┬────────────┐
	// │ d  │ i │ n │ objects             │ cuts       │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ 0  │ 4 │ 2 │ [A   B   C   D | E] │            │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 3 │ 1 │ [A   B   C | D]     │ + | E]     │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 2 │ 1 │ [A   B | C   D]     │ + | E]     │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 1 │ 1 │ [A | B   C   D]     │ + | E]     │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ 0  │ 3 │ 2 │ [A   B   C | D   E] │            │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 2 │ 1 │ [A   B | C]         │ + | D E]   │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 1 │ 1 │ [A | B   C]         │ + | D E]   │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ 0  │ 2 │ 2 │ [A   B | C   D   E] │            │
	// ├────┼───┼───┼─────────────────────┼────────────┤
	// │ └1 │ 1 │ 1 │ [A | B]             │ + | C D E] │
	// └────┴───┴───┴─────────────────────┴────────────┘
	for index := lastObj; index >= nCuts; index-- {
		if !check(objects[index:], false) {
			// optimization: if current cut gives a bad grouping, don't recurse
			continue
		}
		if nCuts > 1 {
			iterDivisions(objects[:index], nCuts-1, func(inner []int) bool {
				done = f(append(inner, index-1))
				return done
			}, check)
		} else {
			if !check(objects[:index], true) {
				// e.g. [A   B   C | D] if [A,B,C] is bad, skip it
				continue
			}
			done = f([]int{index - 1})
		}
		if done {
			return
		}
	}
}

// generate a grid of objects from the given cut indices
// each cut index applies after the object at that index
// e.g. [0 1 2 3 4 5 6 7] with cutIndices [0, 2, 6] => [[0], [1, 2], [3,4,5,6], [7]]
func GenLayout(objects []*d2graph.Object, cutIndices []int) [][]*d2graph.Object {
	layout := make([][]*d2graph.Object, len(cutIndices)+1)
	objIndex := 0
	for i := 0; i <= len(cutIndices); i++ {
		var stop int
		if i < len(cutIndices) {
			stop = cutIndices[i]
		} else {
			stop = len(objects) - 1
		}
		if stop >= objIndex {
			layout[i] = make([]*d2graph.Object, 0, stop-objIndex+1)
		}
		for ; objIndex <= stop; objIndex++ {
			layout[i] = append(layout[i], objects[objIndex])
		}
	}
	return layout
}

func getDistToTarget(layout [][]*d2graph.Object, targetSize float64, horizontalGap, verticalGap float64, columns bool) float64 {
	totalDelta := 0.
	for _, row := range layout {
		rowSize := 0.
		for _, o := range row {
			if columns {
				rowSize += o.Height + verticalGap
			} else {
				rowSize += o.Width + horizontalGap
			}
		}
		if len(row) > 0 {
			if columns {
				rowSize -= verticalGap
			} else {
				rowSize -= horizontalGap
			}
		}
		totalDelta += math.Abs(rowSize - targetSize)
	}
	return totalDelta
}

func (gd *gridDiagram) sizeForOutsideLabels() (revert func()) {
	margins := make(map[*d2graph.Object]geo.Spacing)

	for _, o := range gd.objects {
		margin := o.GetMargin()
		margins[o] = margin

		o.Height += margin.Top + margin.Bottom
		o.Width += margin.Left + margin.Right
	}

	// Example: a single column with 3 shapes and
	// `x.label: long label {near: outside-bottom-left}`
	// `y.label: outsider {near: outside-right-center}`
	// . ┌───────────────────┐
	// . │ widest shape here │
	// . └───────────────────┘
	// . ┌───┐
	// . │ x │
	// . └───┘
	// . long label
	// . ├─────────┤ x's new width
	// .     ├─mr──┤ margin.right added to width during layout
	// . ┌───┐
	// . │ y │ outsider
	// . └───┘
	// . ├─────────────┤ y's new width
	// .     ├───mr────┤ margin.right added to width during layout

	// BEFORE LAYOUT
	// . ┌───────────────────┐
	// . │ widest shape here │
	// . └───────────────────┘
	// . ┌─────────┐
	// . │ x       │
	// . └─────────┘
	// . ┌─────────────┐
	// . │ y           │
	// . └─────────────┘

	// AFTER LAYOUT
	// . ┌───────────────────┐
	// . │ widest shape here │
	// . └───────────────────┘
	// . ┌───────────────────┐
	// . │ x                 │
	// . └───────────────────┘
	// . ┌───────────────────┐
	// . │ y                 │
	// . └───────────────────┘

	// CLEANUP 1/2
	// . ┌───────────────────┐
	// . │ widest shape here │
	// . └───────────────────┘
	// . ┌─────────────┐
	// . │ x           │
	// . └─────────────┘
	// . long label    ├─mr──┤ remove margin we added
	// . ┌─────────┐
	// . │ y       │ outsider
	// . └─────────┘
	// .           ├───mr────┤ remove margin we added
	// CLEANUP 2/2
	// . ┌───────────────────┐
	// . │ widest shape here │
	// . └───────────────────┘
	// . ┌───────────────────┐
	// . │ x                 │
	// . └───────────────────┘
	// . long label    ├─mr──┤ we removed too much so add back margin we subtracted, then subtract new margin
	// . ┌─────────┐
	// . │ y       │ outsider
	// . └─────────┘
	// .           ├───mr────┤ margin.right is still needed

	return func() {
		for _, o := range gd.objects {
			m, has := margins[o]
			if !has {
				continue
			}
			dy := m.Top + m.Bottom
			dx := m.Left + m.Right
			o.Height -= dy
			o.Width -= dx

			// less margin may be needed if layout grew the object
			// compute the new margin after removing the old margin we added
			margin := o.GetMargin()
			marginX := margin.Left + margin.Right
			marginY := margin.Top + margin.Bottom
			if marginX < dx {
				// layout grew width and now we need less of a margin (but we subtracted too much)
				// add back dx and subtract the new amount
				o.Width += dx - marginX
			}
			if marginY < dy {
				o.Height += dy - marginY
			}

			if margin.Left > 0 || margin.Top > 0 {
				o.MoveWithDescendants(margin.Left, margin.Top)
			}
		}
	}
}