next-ai-draw-io/lib/diagram-engine/layout.ts

/**
 * Layout: tree → coordinates.
 *
 * Two passes, the same shape as a flexbox implementation:
 *
 *   measure — bottom-up. A leaf reports its intrinsic size; a container sums its
 *             children along the flow axis, takes the maximum across it, and adds
 *             padding and its title strip. A container therefore always ends up big
 *             enough to hold what is inside it, which is why "child spills out of its
 *             frame" cannot happen by construction.
 *
 *   place   — top-down. Each container distributes its now-known interior among its
 *             children.
 *
 * The model never supplies a coordinate. It declares nesting, direction and gap; every
 * x/y/width/height comes from here.
 *
 * Five container kinds share those two passes, because they differ only in how a parent
 * distributes its interior:
 *
 *   group     — children stacked along one axis. Cloud architecture, nested frames.
 *   grid      — children packed into a fixed number of columns.
 *   pool      — a sparse (lane × column) grid. Swimlane and BPMN diagrams.
 *   sequence  — participants across the top, lifelines below. Sequence diagrams.
 *   radial    — a centre with branches fanning out, or hanging below. Mind maps, org charts.
 *
 * Ported from drawio-ai-kit (MIT) — see NOTICE. The pool geometry follows that project's
 * `pool()` primitive; sequence and radial are original to this repository.
 */

import { resolveShape } from "./shapes"
import { type Role, roleMetrics } from "./theme"
import type {
    Align,
    ContainerNode,
    DiagramNode,
    Justify,
    PoolNode,
    RadialNode,
    Rect,
    SequenceNode,
} from "./types"
import { isContainer } from "./types"

/** Default glyph size for a catalog icon. */
export const ICON_SIZE = 48
/** Interior padding of a container. */
const PAD = 24

/** A group's interior padding: its own `pad` when declared, the default otherwise. */
function padOf(n: ContainerNode): number {
    return n.kind === "group" && n.pad != null ? Math.max(0, n.pad) : PAD
}

/** The flex-grow weight a node declared, 0 when none. */
function growOf(n: DiagramNode): number {
    const g = (n.kind === "box" || n.kind === "group") && n.grow
    return typeof g === "number" && g > 0 ? g : 0
}

/**
 * The cross-axis alignment a node ends up with: its own `align`, else the parent's
 * `alignItems`, else centred. Same cascade as CSS, where align-self overrides the
 * container's align-items.
 */
function alignOf(n: DiagramNode, parent?: ContainerNode): Align {
    const own = (n.kind === "box" || n.kind === "group") && n.align
    if (
        own === "start" ||
        own === "end" ||
        own === "stretch" ||
        own === "center"
    )
        return own
    const inherited = parent?.kind === "group" ? parent.alignItems : undefined
    if (
        inherited === "start" ||
        inherited === "end" ||
        inherited === "stretch" ||
        inherited === "center"
    )
        return inherited
    return "center"
}

/**
 * The main-axis distribution a container declared, or null when it declared none.
 *
 * Null matters: it selects the engine's original per-axis defaults rather than any value
 * in this vocabulary. A row centred its children and padded their gaps, a column packed to
 * the top — neither is expressible as one `Justify`, and both are what every diagram built
 * before this existed relies on. Declaring `justify` opts out of them.
 */
function justifyOf(n: ContainerNode): Justify | null {
    const j = n.kind === "group" ? n.justify : undefined
    return j === "start" ||
        j === "center" ||
        j === "end" ||
        j === "between" ||
        j === "around" ||
        j === "evenly"
        ? j
        : null
}

/** The width cap a node declared, or Infinity. */
function maxWOf(n: DiagramNode): number {
    const m = (n.kind === "box" || n.kind === "group") && n.maxW
    return typeof m === "number" && m > 0 ? m : Number.POSITIVE_INFINITY
}

/**
 * Divide `room` among weighted children, honouring each one's floor and ceiling.
 *
 * The naive version — give each child `room * weight / total` and never go below its
 * content width — overflows: a child whose content is wider than its share keeps the
 * wider figure, and the total then exceeds what there was to divide, so the last child
 * hangs out of the frame.
 *
 * CSS resolves this by FREEZING any item that cannot take its share and re-dividing the
 * rest among those that still can, repeating until nothing changes. That is what this
 * does. It terminates because every round either freezes at least one child or stops.
 *
 * Returns the width for each child, in order; a child with no weight keeps its size.
 */
function shareOut(
    sizes: number[],
    weights: number[],
    caps: number[],
    floors: number[],
    room: number,
): number[] {
    const out = [...sizes]
    const frozen = sizes.map((_, i) => weights[i] <= 0)
    for (;;) {
        const liveTotal = weights.reduce(
            (s, w, i) => s + (frozen[i] ? 0 : w),
            0,
        )
        if (liveTotal <= 0) return out
        // What is left once everything already settled has taken its width.
        const rest = room - out.reduce((s, v, i) => s + (frozen[i] ? v : 0), 0)
        let changed = false
        for (let i = 0; i < out.length; i++) {
            if (frozen[i]) continue
            const share = (rest * weights[i]) / liveTotal
            // A child cannot go below its own content, and cannot pass a declared cap.
            // Either way it settles here and the others divide what is left.
            if (share < floors[i]) {
                out[i] = floors[i]
                frozen[i] = true
                changed = true
            } else if (share > caps[i]) {
                out[i] = caps[i]
                frozen[i] = true
                changed = true
            }
        }
        if (changed) continue
        for (let i = 0; i < out.length; i++)
            if (!frozen[i]) out[i] = (rest * weights[i]) / liveTotal
        return out
    }
}

/**
 * The narrowest a node may be squeezed to when weights divide a row.
 *
 * Its own content width, unless it opted out with `minW0` (CSS's `min-width: 0`), in which
 * case a weight may take it below that. Matching CSS here is deliberate: `min-width`
 * defaults to `auto`, so in a browser too a `flex: 2` column stops shrinking at its text
 * and a declared 2:1 comes out closer to 1.4:1 — surprising, but it is what everyone
 * writing flexbox already works with.
 */
function floorOf(n: DiagramNode, contentW: number): number {
    const opted = (n.kind === "box" || n.kind === "group") && n.minW0
    return opted ? 0 : contentW
}

/**
 * Does this node need the full width of its parent to mean what it says?
 *
 * A row whose children carry `grow` weights does: the weights are shares of the row's
 * width, so if the row is only as wide as its own content there is nothing to share and
 * every declared proportion silently comes out 1:1.
 *
 * This is where CSS and this engine disagree, and the disagreement is why it has to be
 * inferred. CSS and Yoga default `align-items` to `stretch`, so a row inside a column
 * fills that column's width for free. This engine defaults to `center`, which is the
 * better default for diagrams — a lone icon in a wide frame should sit in the middle, not
 * be smeared across it — but it means a row of weighted columns gets no width unless
 * something asks. Declaring weights IS the ask.
 */
function needsFullWidth(n: DiagramNode): boolean {
    return (
        n.kind === "group" &&
        n.dir === "row" &&
        n.children.some((c) => growOf(c) > 0)
    )
}

/**
 * Where the children start, and how much goes between them — CSS's justify-content.
 *
 * `slack` is what is left after the children and their base gaps. Returning both the
 * leading offset and the per-gap addition covers all six values in one place, so the
 * row and column branches no longer need their own contradictory policies.
 */
function distribute(
    justify: Justify,
    slack: number,
    count: number,
): { lead: number; extraGap: number } {
    if (slack <= 0 || count === 0) return { lead: 0, extraGap: 0 }
    switch (justify) {
        case "center":
            return { lead: slack / 2, extraGap: 0 }
        case "end":
            return { lead: slack, extraGap: 0 }
        case "between":
            return count > 1
                ? { lead: 0, extraGap: slack / (count - 1) }
                : { lead: 0, extraGap: 0 }
        case "around": {
            // Half a share before the first child and after the last, a full share between.
            const share = slack / count
            return { lead: share / 2, extraGap: share }
        }
        case "evenly": {
            const share = slack / (count + 1)
            return { lead: share, extraGap: share }
        }
        default:
            return { lead: 0, extraGap: 0 }
    }
}
/** Height of a container's title strip. Zero when it has no label — an empty strip
 *  reads as a dead band at the top of the frame. */
const HEADER = 36
/** Approximate width of one label character at the engine's font size. */
const CHAR_W = 6.6

// ---- pool geometry, shared with render.ts so the bands land under the nodes ----

/** Interior padding of a pool. Tighter than a group's: lane bands sit flush. */
export const POOL_PAD = 16
/** Width of the lane-name column (height, when the pool is vertical). */
export const LANE_LABEL = 110
/** Height of the milestone band (width, when the pool is vertical). */
const PHASE_LABEL = 26
/** A pool's own title strip. */
const POOL_HEADER = 34
/** Vertical padding inside a lane band, so nodes do not touch the band's edges. */
const LANE_PAD = 14

// ---- sequence geometry ----

/** Height of a participant head. */
const HEAD_H = 44
/** Vertical distance from the participant heads to the first message. */
const LIFELINE_TOP = 28
/** How far the lifeline runs past the last message. */
const LIFELINE_TAIL = 36

/**
 * The geometry a pool needs, derived once and used by both layout and rendering.
 *
 * Rendering has to paint the lane bands and label columns at exactly the positions layout
 * used, or the nodes sit off their bands. Computing it in one place is what keeps the two
 * from drifting.
 */
export interface PoolMetrics {
    horizontal: boolean
    lanes: number
    cols: number
    /** Cell size along the flow axis. */
    cellW: number
    /** Cell size across the lane axis. */
    cellH: number
    header: number
    phaseLabel: number
    /** Where cell (0,0) starts. */
    contentX: number
    contentY: number
    /** Total extent of the cell area. */
    contentW: number
    contentH: number
}

export function poolMetrics(
    n: PoolNode,
    rect: Rect,
    kids: { rect: Rect }[],
): PoolMetrics {
    const horizontal = n.orientation !== "vertical"
    const lanes = Math.max(1, n.lanes.length)
    const cols = Math.max(1, ...n.children.map((c) => poolCellOf(c).col + 1))
    const cellW = Math.max(80, ...kids.map((k) => k.rect.w))
    const cellH = Math.max(40, ...kids.map((k) => k.rect.h)) + LANE_PAD
    const header = n.label ? POOL_HEADER : 0
    const phaseLabel = n.phases.length ? PHASE_LABEL : 0
    const contentW = horizontal
        ? cols * cellW + n.gap * (cols - 1)
        : lanes * cellW
    const contentH = horizontal
        ? lanes * cellH
        : cols * cellH + n.gap * (cols - 1)
    return {
        horizontal,
        lanes,
        cols,
        cellW,
        cellH,
        header,
        phaseLabel,
        contentX: horizontal
            ? rect.x + POOL_PAD + LANE_LABEL
            : rect.x + POOL_PAD,
        contentY: horizontal
            ? rect.y + header + phaseLabel + POOL_PAD
            : rect.y + header + POOL_PAD + LANE_LABEL,
        contentW,
        contentH,
    }
}

/** How far a sequence diagram's lifelines run, and where each message sits. */
export interface SequenceMetrics {
    /** Bottom of the lifeline. */
    bottom: number
    /** Vertical position of message N, for N starting at 1. */
    messageY: (step: number) => number
}

export function sequenceMetrics(
    n: SequenceNode,
    rect: Rect,
    messages: number,
): SequenceMetrics {
    const head = n.label ? HEADER : 0
    // The first message hangs a fixed distance below the participant heads.
    const first = rect.y + head + PAD + HEAD_H + LIFELINE_TOP
    return {
        bottom: first + Math.max(0, messages - 1) * n.step + LIFELINE_TAIL,
        messageY: (step) => first + Math.max(0, step - 1) * n.step,
    }
}

/** A node with its computed box. Layout works on this, leaving the tree untouched. */
export interface Placed {
    node: DiagramNode
    rect: Rect
    children: Placed[]
}

/** One line of a wrapped row: which children sit on it, and how big it is. */
interface WrapLine {
    items: Placed[]
    width: number
    height: number
}

/**
 * Break a row of children into lines that each fit `room`.
 *
 * Greedy, the same rule as a text line-breaker and as CSS flex-wrap: keep adding to the
 * current line while it fits, otherwise start a new one. A single child wider than the
 * whole row still gets its own line rather than being dropped.
 *
 * Shared by measure and place so both agree on where the breaks fall — computing them
 * twice from the same input is cheap, keeping two copies in sync is not.
 */
function wrapLines(kids: Placed[], room: number, gap: number): WrapLine[] {
    const lines: WrapLine[] = []
    let cur: WrapLine | null = null
    for (const k of kids) {
        const next = cur ? cur.width + gap + k.rect.w : k.rect.w
        if (cur && next > room && cur.items.length > 0) {
            lines.push(cur)
            cur = null
        }
        if (!cur) cur = { items: [k], width: k.rect.w, height: k.rect.h }
        else {
            cur.items.push(k)
            cur.width = next
            cur.height = Math.max(cur.height, k.rect.h)
        }
    }
    if (cur) lines.push(cur)
    return lines
}

/**
 * The arrows layout needs, which the node tree alone does not carry.
 *
 * Three of the five container kinds are laid out from the diagram's arrows, not from
 * nesting: a sequence diagram's messages set how tall the lifelines have to be, and a mind
 * map's hierarchy IS its arrows. Links live on the tree, not on the node, so they are
 * passed down rather than read from a parent pointer.
 */
export type LayoutLinks = { source: string; target: string; step?: number }[]

/**
 * Reduce a label to the text draw.io will actually lay out.
 *
 * Labels may carry inline HTML (every style has `html=1`): a <br> is a line break, any
 * other tag is invisible markup around visible text. Measuring the raw string counted
 * `<font color="#B85450">` as thirty characters of text, making rich boxes twice as
 * wide as their content.
 */
function visibleText(label: string): string {
    return String(label ?? "")
        .replace(/<br\s*\/?>/gi, "\n")
        .replace(/<\/?(?:b|i|u|s|sub|sup|font|span|div)(?:\s[^<>]*)?>/gi, "")
}

/**
 * Intrinsic size of a text box: widest wrapped line by line count.
 *
 * The role scales the estimate: a banner sets 20px type and a footnote 9px, and layout has
 * to reserve what render will draw or the text overflows its cell.
 *
 * `atWidth` is the width the box will ACTUALLY be drawn at, when that is already known
 * (see the reflow pass in `layoutForest`). Height is then counted for that width while
 * the reported width stays intrinsic — which is what a browser does, and what this was
 * missing: a paragraph measured at its 260px natural width needs eight lines, the same
 * paragraph stretched to 750px needs three, and reserving the eight-line height left
 * every panel with a slab of dead space under its text.
 */
export function autoBoxSize(
    label: string,
    role?: Role,
    shape?: string,
    atWidth?: number,
    maxW?: number,
): { w: number; h: number } {
    const spec = shape ? resolveShape(shape)?.spec : undefined
    // A glyph shape (umlActor…) has a fixed figure with the label below it: the slot is
    // the figure plus a line of text, and the text length does not scale the figure.
    if (spec?.labelOutside && spec.glyph) {
        const text = visibleText(label)
        return {
            w: Math.max(spec.glyph.w + 20, Math.min(160, text.length * 7 + 16)),
            h: spec.glyph.h + 22,
        }
    }
    const r = roleMetrics(role)
    // Two caps: the role's own default, and whatever the model declared. The declared one
    // is allowed to go BELOW the floor of 120 — capping a box at 90px has to mean 90px,
    // or the cap silently does nothing on short labels.
    const roleCap = Math.round(260 * Math.max(1, r.charScale))
    const declared = maxW != null && maxW > 0 ? maxW : Number.POSITIVE_INFINITY
    const explicit = visibleText(label).split("\n")
    const longest = Math.max(1, ...explicit.map((l) => l.length))
    const natural = Math.max(
        120,
        Math.round(longest * CHAR_W * r.charScale + 28),
    )
    const w = Math.min(declared, roleCap, natural)
    const s = spec?.textScale ?? 1
    // Count the lines the text ACTUALLY occupies: draw.io wraps at the box width, so a
    // long line becomes several. Estimating by explicit newlines alone left the box one
    // line tall while the text wrapped to six — and overflowed straight out of it.
    //
    // Wrapping happens at the DRAWN width, which for a stretched box is wider than the
    // intrinsic one. `atWidth` carries it; the shape factor is divided back out because
    // it is applied to the final height below.
    // A declared cap also bounds the reflow hint: a box capped at 200 never gets to count
    // its lines as if it had been drawn at 600, however wide its parent turned out.
    const textW = Math.min(
        declared,
        Math.max(w, atWidth != null ? atWidth / s : 0),
    )
    const charsPerLine = Math.max(
        8,
        Math.floor((textW - 28) / (CHAR_W * r.charScale)),
    )
    const lines = explicit.reduce(
        (sum, l) => sum + Math.max(1, Math.ceil(l.length / charsPerLine)),
        0,
    )
    const lineH = Math.round(r.fontSize * 1.6)
    const h = Math.max(r.minH, lines * lineH + 26)
    // A non-rectangular outline inscribes a smaller text area than its bounding box —
    // a rhombus exactly half — so the box grows by the shape's measured factor.
    // Verified in the real editor: the same sentence overflows a 1.0× rhombus and fits
    // a 1.5× one.
    return { w: Math.round(w * s), h: Math.round(h * s) }
}

/**
 * Intrinsic size of an icon cell: the glyph, plus room for the label underneath, and
 * wide enough that a long label does not overflow the cell it is centred in.
 */
function iconSize(label: string, glyph: number): { w: number; h: number } {
    return {
        w: Math.max(96, glyph + 20, Math.min(200, label.length * 7 + 24)),
        h: glyph + 34,
    }
}

/** A container is never narrower than its own title. */
function titleFloor(label: string, pad: number): number {
    return label ? Math.ceil(label.length * CHAR_W) + pad * 2 : 0
}

function headerFor(n: ContainerNode): number {
    if (n.kind === "pool") return n.label ? POOL_HEADER : 0
    return n.label ? HEADER : 0
}

/**
 * The cell a node occupies inside a pool. Absent means (0,0).
 *
 * No clamping needed: `add_icon`/`add_box` clamp at the boundary where the model's numbers
 * arrive, and the only other way a cell gets set is the parser, whose `dai_cell` pattern
 * matches digits only. So by here it is already non-negative.
 */
export function poolCellOf(n: DiagramNode): { lane: number; col: number } {
    if ((n.kind === "icon" || n.kind === "box") && n.cell) return n.cell
    return { lane: 0, col: 0 }
}

/**
 * How many messages a sequence container has: the highest step number among the links
 * between its participants, or the link count when the model numbered nothing.
 *
 * Steps are what order the messages vertically, so a diagram whose links carry no step
 * still needs one row per message — otherwise every arrow lands on the same y.
 */
export function messageCount(n: SequenceNode, links: LayoutLinks): number {
    const own = new Set(n.children.map((c) => c.id))
    const mine = links.filter((l) => own.has(l.source) && own.has(l.target))
    const steps = mine
        .map((l) => l.step)
        .filter((s): s is number => s != null && s > 0)
    return Math.max(mine.length, ...(steps.length ? steps : [0]))
}

/**
 * One node of a radial tree: a placed box plus the branches hanging off it.
 *
 * Separate from `Placed` because the tree is derived from the LINKS, not from nesting, so it
 * exists only during a radial container's layout.
 */
interface RadialTree {
    p: Placed
    kids: RadialTree[]
    /** How much room this whole subtree needs across the branching axis. */
    extent: number
}

/**
 * Build the branch hierarchy of a radial container from the diagram's arrows.
 *
 * The root is the node nothing points at. Every other node hangs off whichever node points
 * at it — the FIRST one, if several do, since a mind map is a tree and a second parent has
 * to be drawn as a plain cross-link instead.
 *
 * A node no arrow reaches at all becomes a branch of the root, so it is still drawn. Dropping
 * it would silently lose a box the model asked for.
 */
function radialHierarchy(
    kids: Placed[],
    links: LayoutLinks,
    across: "w" | "h",
    gap: number,
): { root: RadialTree; branches: RadialTree[] } | null {
    if (kids.length === 0) return null
    const own = new Map(kids.map((k) => [k.node.id, k]))
    const parent = new Map<string, string>()
    for (const l of links) {
        if (!own.has(l.source) || !own.has(l.target)) continue
        if (l.source === l.target) continue
        if (!parent.has(l.target)) parent.set(l.target, l.source)
    }
    // Guard against a cycle in the arrows: walking up must terminate.
    const rootOf = (id: string): string => {
        const seen = new Set<string>([id])
        let cur = id
        for (;;) {
            const up = parent.get(cur)
            if (up === undefined || seen.has(up)) return cur
            seen.add(up)
            cur = up
        }
    }
    // The first declared node that is nobody's child is the centre. Falling back to the first
    // child keeps a cycle-only graph drawable.
    const rootId =
        kids.find((k) => !parent.has(k.node.id))?.node.id ??
        rootOf(kids[0].node.id)

    const childrenOf = new Map<string, Placed[]>()
    for (const k of kids) {
        if (k.node.id === rootId) continue
        const up = parent.get(k.node.id)
        // An orphan, or a node whose parent chain loops back on itself, attaches to the root.
        // `up === k.node.id` cannot happen: self-links are skipped when `parent` is built.
        const attach =
            up !== undefined && rootOf(k.node.id) === rootId ? up : rootId
        const list = childrenOf.get(attach)
        if (list) list.push(k)
        else childrenOf.set(attach, [k])
    }

    // No visited-set needed: `parent` records at most one parent per node, so `childrenOf`
    // is a forest by construction, and `rootOf` above already reattached anything whose
    // parent chain looped. The recursion cannot revisit a node.
    const build = (p: Placed): RadialTree => {
        const kidTrees = (childrenOf.get(p.node.id) ?? []).map(build)
        const total =
            kidTrees.reduce((s, t) => s + t.extent, 0) +
            gap * Math.max(0, kidTrees.length - 1)
        return {
            p,
            kids: kidTrees,
            extent: Math.max(p.rect[across], total),
        }
    }
    const root = build(own.get(rootId) as Placed)
    return { root, branches: root.kids }
}

/** Widest node at each generation, for laying a radial tree out in even rings. */
function widestPerLevel(trees: RadialTree[], along: "w" | "h"): number[] {
    const out: number[] = []
    const visit = (t: RadialTree, level: number) => {
        out[level] = Math.max(out[level] ?? 0, t.p.rect[along])
        for (const k of t.kids) visit(k, level + 1)
    }
    for (const t of trees) visit(t, 0)
    return out
}

/**
 * How far one side of a radial map reaches from the centre.
 *
 * Each generation contributes one gap plus the width of the widest node in it. This has to be
 * computed per SIDE, not once for the whole map: a mind map whose left branches go three
 * generations deep and whose right branches go one needs an asymmetric frame, and reserving
 * the same room on both sides would push the deeper side off the page.
 */
function radialReach(
    side: RadialTree[],
    along: "w" | "h",
    gap: number,
): number {
    // widestPerLevel writes one entry per generation that exists, so its length IS the depth
    // of the deepest branch on this side. An empty side yields an empty list, and reducing
    // that from 0 already gives 0.
    return widestPerLevel(side, along).reduce((s, v) => s + v + gap, 0)
}

/**
 * Split a radial map's branches into the two sides they will be drawn on.
 *
 * The same split has to be used by measure and by place, or the frame is sized for one
 * arrangement and the branches are drawn in another.
 */
function radialSides(branches: RadialTree[]): {
    right: RadialTree[]
    left: RadialTree[]
} {
    const half = Math.ceil(branches.length / 2)
    return { right: branches.slice(0, half), left: branches.slice(half) }
}

/**
 * measure: give every node a size, bottom-up.
 *
 * Siblings are equalised across the cross axis — frames in a row share a bottom edge,
 * frames in a column share left and right edges. Only containers stretch; a leaf keeps
 * its natural size, because stretching an icon would distort the glyph.
 */
function measure(
    n: DiagramNode,
    defaultGlyph: number,
    links: LayoutLinks,
    widthHints?: Map<string, number>,
): Placed {
    if (n.kind === "icon") {
        const glyph = n.size ?? defaultGlyph
        const s = iconSize(n.label, glyph)
        return { node: n, rect: { x: 0, y: 0, ...s }, children: [] }
    }
    if (n.kind === "box") {
        // The hint is the width this box was drawn at last pass; its text rewraps to
        // that width, so its height has to be counted there.
        const auto = autoBoxSize(
            n.label,
            n.role,
            n.shape,
            widthHints?.get(n.id),
            n.maxW,
        )
        return {
            node: n,
            rect: { x: 0, y: 0, w: n.w ?? auto.w, h: n.h ?? auto.h },
            children: [],
        }
    }
    if (n.kind === "title") {
        return { node: n, rect: { x: 0, y: 0, w: 0, h: 30 }, children: [] }
    }

    const kids = n.children.map((c) =>
        measure(c, defaultGlyph, links, widthHints),
    )
    const head = headerFor(n)
    const gap = n.gap

    if (n.kind === "pool") {
        const m = poolMetrics(n, { x: 0, y: 0, w: 0, h: 0 }, kids)
        const w = m.horizontal
            ? POOL_PAD * 2 + LANE_LABEL + m.contentW
            : POOL_PAD * 2 + m.contentW + m.phaseLabel
        const h = m.horizontal
            ? m.header + m.phaseLabel + POOL_PAD * 2 + m.contentH
            : m.header + POOL_PAD * 2 + LANE_LABEL + m.contentH
        return {
            node: n,
            rect: {
                x: 0,
                y: 0,
                w: Math.max(w, titleFloor(n.label, POOL_PAD)),
                h,
            },
            children: kids,
        }
    }

    if (n.kind === "sequence") {
        // Participants sit side by side; the lifelines below them set the height.
        const w =
            PAD * 2 +
            kids.reduce((s, k) => s + k.rect.w, 0) +
            gap * Math.max(0, kids.length - 1)
        const m = sequenceMetrics(
            n,
            { x: 0, y: 0, w: 0, h: 0 },
            messageCount(n, links),
        )
        return {
            node: n,
            rect: {
                x: 0,
                y: 0,
                w: Math.max(w, titleFloor(n.label, PAD)),
                h: m.bottom + PAD,
            },
            children: kids,
        }
    }

    if (n.kind === "radial") {
        const down = n.spread === "down"
        const across = down ? "w" : "h"
        const tree = radialHierarchy(kids, links, across, n.gap)
        if (!tree)
            return {
                node: n,
                rect: { x: 0, y: 0, w: PAD * 2, h: head + PAD * 2 },
                children: kids,
            }
        const { root, branches } = tree
        const spanOf = (bs: RadialTree[]) =>
            bs.length === 0
                ? 0
                : bs.reduce((s, b) => s + b.extent, 0) + n.gap * (bs.length - 1)

        if (down) {
            // Everything hangs below the centre: one direction, so one reach.
            const h = root.p.rect.h + radialReach(branches, "h", n.gap)
            const w = Math.max(root.p.rect.w, spanOf(branches))
            return {
                node: n,
                rect: {
                    x: 0,
                    y: 0,
                    w: Math.max(PAD * 2 + w, titleFloor(n.label, PAD)),
                    h: head + PAD * 2 + h,
                },
                children: kids,
            }
        }

        // Radial: the two sides reach different distances, so each is measured on its own.
        // Using one figure for both would leave the deeper side hanging outside the frame.
        const { right, left } = radialSides(branches)
        const w =
            radialReach(left, "w", n.gap) +
            root.p.rect.w +
            radialReach(right, "w", n.gap)
        const h = Math.max(root.p.rect.h, spanOf(right), spanOf(left))
        return {
            node: n,
            rect: {
                x: 0,
                y: 0,
                w: Math.max(PAD * 2 + w, titleFloor(n.label, PAD)),
                h: head + PAD * 2 + h,
            },
            children: kids,
        }
    }

    if (n.kind === "grid") {
        const cols = Math.max(1, n.cols)
        const rows = Math.ceil(kids.length / cols) || 1
        const cellW = Math.max(0, ...kids.map((k) => k.rect.w))
        const cellH = Math.max(0, ...kids.map((k) => k.rect.h))
        const w = PAD * 2 + cols * cellW + gap * (cols - 1)
        const h = head + PAD * 2 + rows * cellH + gap * (rows - 1)
        return {
            node: n,
            rect: {
                x: 0,
                y: 0,
                w: Math.max(w, titleFloor(n.label, PAD)),
                h,
            },
            children: kids,
        }
    }

    // group: row or col
    const pad = padOf(n)
    // A declared cap wins over the measured content, so a row of six cards capped at 900
    // reports 900 and the place pass below has real negative slack to shrink into.
    const cap = maxWOf(n)
    if (n.dir === "row") {
        const tallest = Math.max(0, ...kids.map((k) => k.rect.h))
        // Only a group stretches to match its siblings. A leaf keeps its natural size,
        // because stretching an icon distorts the glyph; and a grid, pool, sequence or
        // radial computes its interior from its own rule, so forcing one bigger leaves dead
        // space inside rather than filling anything — and for a pool it would detach the
        // lane bands from the nodes sitting on them.
        for (const k of kids)
            if (k.node.kind === "group") k.rect.h = Math.max(k.rect.h, tallest)
        // A capped row wraps into as many lines as it takes, so the cap is a real limit
        // rather than something the content silently overflows. Sized here and positioned
        // by the same line-breaking in `place`, so measure and place cannot disagree.
        if (cap < Number.POSITIVE_INFINITY) {
            const lines = wrapLines(kids, cap - pad * 2, gap)
            const h =
                head +
                pad * 2 +
                lines.reduce((s, l) => s + l.height, 0) +
                gap * Math.max(0, lines.length - 1)
            const widestLine = Math.max(0, ...lines.map((l) => l.width))
            return {
                node: n,
                rect: {
                    x: 0,
                    y: 0,
                    w: Math.max(
                        Math.min(cap, pad * 2 + widestLine),
                        titleFloor(n.label, pad),
                    ),
                    h,
                },
                children: kids,
            }
        }
        const w =
            pad * 2 +
            kids.reduce((s, k) => s + k.rect.w, 0) +
            gap * Math.max(0, kids.length - 1)
        const h = head + pad * 2 + Math.max(0, ...kids.map((k) => k.rect.h))
        return {
            node: n,
            rect: {
                x: 0,
                y: 0,
                w: Math.max(w, titleFloor(n.label, pad)),
                h,
            },
            children: kids,
        }
    }

    const widest = Math.max(0, ...kids.map((k) => k.rect.w))
    // Only a group stretches — same reasoning as the row branch above.
    for (const k of kids)
        if (k.node.kind === "group") k.rect.w = Math.max(k.rect.w, widest)
    // A row of weighted columns divides a width it does not have yet (see needsFullWidth).
    // Its share of the extra has to be handed out during MEASURE: `place` runs top-down, so
    // a child widened there leaves this container already sized for the narrow version, and
    // the child then sticks out of the frame that is supposed to contain it.
    //
    // Distributed by weight rather than to the full interior, because that is the answer
    // `place` will independently arrive at — the two passes have to agree or the frame is
    // sized for one arrangement and drawn as another.
    for (const k of kids) {
        if (!needsFullWidth(k.node) || k.node.kind !== "group") continue
        const kp = padOf(k.node)
        const room =
            widest - kp * 2 - k.node.gap * Math.max(0, k.children.length - 1)
        const weights = k.children.map((c) => growOf(c.node))
        // Unweighted children keep their size and take their width off the top; the rest is
        // what the weights divide.
        const fixed = k.children.reduce(
            (s, c, i) => s + (weights[i] ? 0 : c.rect.w),
            0,
        )
        const widths = shareOut(
            k.children.map((c) => c.rect.w),
            weights,
            k.children.map((c) => maxWOf(c.node)),
            k.children.map((c) => floorOf(c.node, c.rect.w)),
            room - fixed,
        )
        k.children.forEach((c, i) => {
            if (weights[i]) c.rect.w = widths[i]
        })
        k.rect.w = Math.max(
            k.rect.w,
            kp * 2 +
                k.children.reduce((s, c) => s + c.rect.w, 0) +
                k.node.gap * Math.max(0, k.children.length - 1),
        )
    }
    const w = pad * 2 + Math.max(0, ...kids.map((k) => k.rect.w))
    const h =
        head +
        pad * 2 +
        kids.reduce((s, k) => s + k.rect.h, 0) +
        gap * Math.max(0, kids.length - 1)
    return {
        node: n,
        rect: {
            x: 0,
            y: 0,
            w: Math.min(cap, Math.max(w, titleFloor(n.label, pad))),
            h,
        },
        children: kids,
    }
}

/**
 * place: assign absolute positions, top-down.
 *
 * When a container ended up larger than its content — because a sibling forced it
 * wider, or its own title did — the slack is shared between the children rather than
 * left as dead margin on one side. The extra spacing is capped at one base gap so a
 * stretched frame reads as deliberately spaced instead of sparse, and the resulting
 * cluster is centred.
 */
function place(
    p: Placed,
    x: number,
    y: number,
    links: LayoutLinks,
    /**
     * True when this container's width was decided from outside its own content — the page
     * aspect gave the top level a width, or an ancestor stretched it. Only then do `grow`
     * weights read as absolute proportions ("3:1"), because only then is there a total to
     * take a share OF. It passes down through stretched children: a full-width column that
     * inherited its width hands that same certainty to the row inside it.
     */
    definiteWidth = false,
): void {
    p.rect.x = Math.round(x)
    p.rect.y = Math.round(y)
    const n = p.node
    if (!isContainer(n)) return

    const head = headerFor(n)
    const pad = n.kind === "group" ? padOf(n) : PAD
    const innerX = p.rect.x + pad
    const innerTop = p.rect.y + head + pad
    const innerW = p.rect.w - pad * 2
    const innerH = p.rect.h - head - pad * 2
    const kids = p.children

    if (n.kind === "grid") {
        const cols = Math.max(1, n.cols)
        const cellW = Math.max(0, ...kids.map((k) => k.rect.w))
        const cellH = Math.max(0, ...kids.map((k) => k.rect.h))
        kids.forEach((k, i) => {
            const r = Math.floor(i / cols)
            const c = i % cols
            const cx = innerX + c * (cellW + n.gap)
            const cy = innerTop + r * (cellH + n.gap)
            // centre each child in its cell so a short label does not sit off-axis
            place(
                k,
                cx + (cellW - k.rect.w) / 2,
                cy + (cellH - k.rect.h) / 2,
                links,
            )
        })
        return
    }

    if (n.kind === "pool") {
        // Each child goes to the (lane, column) cell it declared. Empty cells stay empty:
        // in a swimlane diagram, "this role does nothing at this step" is information.
        const m = poolMetrics(n, p.rect, kids)
        for (const k of kids) {
            const { lane, col } = poolCellOf(k.node)
            const cx = m.horizontal
                ? m.contentX + col * (m.cellW + n.gap)
                : m.contentX + Math.min(lane, m.lanes - 1) * m.cellW
            const cy = m.horizontal
                ? m.contentY + Math.min(lane, m.lanes - 1) * m.cellH
                : m.contentY + col * (m.cellH + n.gap)
            place(
                k,
                cx + (m.cellW - k.rect.w) / 2,
                cy + (m.cellH - k.rect.h) / 2,
                links,
            )
        }
        return
    }

    if (n.kind === "sequence") {
        // Participants in a row across the top. Their lifelines hang below, emitted by the
        // renderer, so nothing else has to be placed here.
        let cur = innerX
        for (const k of kids) {
            place(k, cur, innerTop, links)
            cur += k.rect.w + n.gap
        }
        return
    }

    if (n.kind === "radial") {
        placeRadial(p, n, innerX, innerTop, innerW, innerH, links)
        return
    }

    const alongRow = n.dir === "row"

    // A capped row that had to WRAP lays each line out like its own row, so the two passes
    // cannot disagree about where the breaks fall. A capped row that still fits on one line
    // falls through to the ordinary path below — it is an ordinary row, and skipping that
    // path would skip `grow`, leaving declared proportions unapplied.
    const wrapped =
        alongRow && maxWOf(n) < Number.POSITIVE_INFINITY && kids.length > 0
            ? wrapLines(kids, innerW, n.gap)
            : null
    if (wrapped && wrapped.length > 1) {
        const lines = wrapped
        let lineTop = innerTop
        for (const line of lines) {
            const used = line.items.reduce((s, k) => s + k.rect.w, 0)
            const room = Math.max(
                0,
                innerW - used - n.gap * (line.items.length - 1),
            )
            // A wrapped line follows the same row default as an unwrapped one: centred,
            // with its gaps padded by up to one extra gap.
            const declared = justifyOf(n)
            const { lead, extraGap } = declared
                ? distribute(declared, room, line.items.length)
                : line.items.length > 1
                  ? (() => {
                        const e = Math.min(
                            n.gap,
                            room / (line.items.length - 1),
                        )
                        return {
                            lead: Math.max(
                                0,
                                (room - e * (line.items.length - 1)) / 2,
                            ),
                            extraGap: e,
                        }
                    })()
                  : { lead: room / 2, extraGap: 0 }
            let x = innerX + lead
            for (const kid of line.items) {
                const a = alignOf(kid.node, n)
                const off =
                    a === "start"
                        ? 0
                        : a === "end"
                          ? line.height - kid.rect.h
                          : a === "stretch"
                            ? 0
                            : (line.height - kid.rect.h) / 2
                if (a === "stretch") kid.rect.h = line.height
                place(kid, x, lineTop + Math.max(0, off), links)
                x += kid.rect.w + n.gap + extraGap
            }
            lineTop += line.height + n.gap
        }
        return
    }

    const sizes = kids.map((k) => (alongRow ? k.rect.w : k.rect.h))
    const content = sizes.reduce((s, v) => s + v, 0)
    const extent = alongRow ? innerW : innerH
    const k = kids.length
    let slack = Math.max(0, extent - content - n.gap * (k - 1))

    // flex-grow: children with a weight split the leftover space between them, TeX's
    // glue. This runs before the justify distribution below — declared weights are a
    // statement about where the slack should go, and spreading it into the gaps instead
    // would silently override that statement.
    //
    // A LEAF box never grows along a column: growing its height just inflates a text
    // box around its own text — the giant hollow panels of an early poster. Along a row
    // it stays legal (two bars splitting a card's width is real layout), and containers
    // grow on either axis, since they distribute the space onwards.
    const weights = kids.map((kid) =>
        !alongRow && kid.node.kind === "box" ? 0 : growOf(kid.node),
    )
    const totalWeight = weights.reduce((s, v) => s + v, 0)
    if (totalWeight > 0 && slack > 0) {
        // Along a ROW, when the container's width was set from OUTSIDE (a declared page
        // aspect, or its own cap), the weights divide the whole track: `grow: 3` beside
        // `grow: 1` then really is three times as wide, which is what writing those numbers
        // means and what CSS's `flex: 3` shorthand does by zeroing flex-basis.
        //
        // Otherwise only the slack is divided, which is the older contract: the width came
        // from the content itself, so treating the weights as absolute proportions would
        // shrink a column below the text already in it.
        const proportional =
            alongRow &&
            (definiteWidth ||
                needsFullWidth(n) ||
                maxWOf(n) < Number.POSITIVE_INFINITY)
        if (proportional) {
            // The weights divide the whole track. shareOut settles anyone who cannot take
            // their share — too wide already, or capped — and re-divides among the rest, so
            // the total never exceeds the room available and no child spills out.
            const fixed = kids.reduce(
                (s, kid, i) => s + (weights[i] ? 0 : kid.rect.w),
                0,
            )
            const widths = shareOut(
                kids.map((kid) => kid.rect.w),
                weights,
                kids.map((kid) => maxWOf(kid.node)),
                kids.map((kid) => floorOf(kid.node, kid.rect.w)),
                extent - n.gap * (k - 1) - fixed,
            )
            kids.forEach((kid, i) => {
                if (weights[i]) kid.rect.w = widths[i]
            })
        } else {
            kids.forEach((kid, i) => {
                if (!weights[i]) return
                const share = (slack * weights[i]) / totalWeight
                // Never past a declared cap: min/max outranks grow, Yoga's rule too.
                if (alongRow)
                    kid.rect.w = Math.min(maxWOf(kid.node), kid.rect.w + share)
                else kid.rect.h += share
            })
        }
        // Recompute: a child clamped by its cap or its content refused part of its share,
        // and that remainder is still free space the distribution below has to place.
        const used = kids.reduce(
            (s, kid) => s + (alongRow ? kid.rect.w : kid.rect.h),
            0,
        )
        slack = Math.max(0, extent - used - n.gap * (k - 1))
    }

    // How the remaining slack is spread. A declared `justify` decides it; otherwise the
    // engine's original per-axis defaults stand, because they are what every diagram built
    // before `justify` existed was laid out with:
    //
    //   ROW — spread the gaps by up to one extra gap, then centre the result. A flowchart
    //   layer reads as a pyramid, and dead space at the right edge of a row looks like a
    //   mistake.
    //   COLUMN — pack to the top and leave the slack at the bottom. A column is usually
    //   tall because a SIBLING made it tall, and stretching its gaps turns every panel into
    //   a big frame with three lines floating in the middle.
    const declared = justifyOf(n)
    let lead: number
    let extraGap: number
    if (declared) {
        ;({ lead, extraGap } = distribute(declared, slack, k))
    } else if (alongRow && k > 1) {
        extraGap = Math.min(n.gap, slack / (k - 1))
        lead = Math.max(0, (slack - extraGap * (k - 1)) / 2)
    } else {
        lead = 0
        extraGap = 0
    }
    const gap = n.gap + extraGap
    let cur = (alongRow ? innerX : innerTop) + lead

    for (const kid of kids) {
        // A stretching role fills the cross axis: a masthead spans its page, a section
        // heading spans its column. Measured at its text width, then widened here — the
        // container's size still comes from the widest ordinary child.
        const kn = kid.node
        const a = alignOf(kn, n)
        const stretches =
            a === "stretch" ||
            (kn.kind === "box" && kn.role && roleMetrics(kn.role).stretch) ||
            // A row of weighted columns fills this column, whatever the alignment default
            // says — see needsFullWidth. Only along a column: across a row the cross axis
            // is height, and a row does not hand its height out proportionally.
            (!alongRow && needsFullWidth(kn))
        // Cross-axis position: centred unless the child asked for an edge.
        const cross = (room: number, size: number): number => {
            if (a === "start") return 0
            if (a === "end") return Math.max(0, room - size)
            return (room - size) / 2
        }
        if (alongRow) {
            if (stretches) kid.rect.h = innerH
            // A row's child got its width from the weights above, so if this row's own
            // width was definite the child's is too.
            place(
                kid,
                cur,
                innerTop + cross(innerH, kid.rect.h),
                links,
                definiteWidth && growOf(kn) > 0,
            )
            cur += kid.rect.w + gap
        } else {
            // Stretching along a column still respects a declared cap.
            if (stretches) kid.rect.w = Math.min(maxWOf(kn), innerW)
            // A stretched child fills a width this column already knew, so it inherits
            // that certainty; an unstretched one is still sized by its own content.
            place(
                kid,
                innerX + cross(innerW, kid.rect.w),
                cur,
                links,
                definiteWidth && stretches,
            )
            cur += kid.rect.h + gap
        }
    }
}

/**
 * Place a radial container: a centre with its branches fanning out.
 *
 * Two shapes, because a mind map and an org chart want opposite things. A mind map reads
 * best with branches on both sides of the centre, which keeps it compact and balanced. An
 * org chart must hang everything downwards — a reporting line drawn upwards or sideways
 * reads as the wrong relationship, no matter how much space it saves.
 *
 * Each generation sits in its own ring, the ring's depth set by the widest node in it, so
 * siblings line up instead of stepping raggedly outwards.
 */
function placeRadial(
    p: Placed,
    n: RadialNode,
    innerX: number,
    innerTop: number,
    innerW: number,
    innerH: number,
    links: LayoutLinks,
): void {
    const down = n.spread === "down"
    const along = down ? "h" : "w"
    const across = down ? "w" : "h"
    const tree = radialHierarchy(p.children, links, across, n.gap)
    if (!tree) return
    const { root, branches } = tree
    const centre = root.p

    /**
     * Lay one generation out along the cross axis, then recurse.
     *
     * `start` is the middle of the band this generation has to fill; each branch gets a slice
     * of it as wide as its own subtree needs, and is centred in that slice. Sizing slices by
     * subtree extent — not by branch count — is what keeps a bushy branch from being drawn
     * over a bare sibling.
     */
    const spread = (
        items: RadialTree[],
        start: number,
        alongPos: number,
        sign: 1 | -1,
    ) => {
        const total =
            items.reduce((s, b) => s + b.extent, 0) +
            n.gap * Math.max(0, items.length - 1)
        let cur = start - total / 2
        for (const b of items) {
            const mid = cur + b.extent / 2
            // On the left side the ring position is the branch's FAR edge, so its own size has
            // to come off to get its origin.
            const a = sign > 0 ? alongPos : alongPos - b.p.rect[along]
            if (down) place(b.p, mid - b.p.rect.w / 2, a, links)
            else place(b.p, a, mid - b.p.rect.h / 2, links)

            if (b.kids.length) {
                // `alongPos` means the NEAR edge going outwards and the FAR edge coming back,
                // which is why the two directions are not symmetric here: on the left the
                // recursion subtracts the child's own width, so subtracting the ring width as
                // well would place it a full ring too far out — off the frame.
                const next = sign > 0 ? a + b.p.rect[along] + n.gap : a - n.gap
                spread(b.kids, mid, next, sign)
            }
            cur += b.extent + n.gap
        }
    }

    if (down) {
        place(centre, innerX + (innerW - centre.rect.w) / 2, innerTop, links)
        spread(
            branches,
            centre.rect.x + centre.rect.w / 2,
            centre.rect.y + centre.rect.h + n.gap,
            1,
        )
        return
    }

    // Radial: split the branches between the two sides, keeping declaration order within each
    // side so the model can predict where a branch lands.
    //
    // The centre goes at the LEFT side's reach, not at the frame's middle. Those are the same
    // only when both sides are equally deep; centring a lopsided map would push the deeper
    // side out past the frame's edge and off the page.
    const { right, left } = radialSides(branches)
    place(
        centre,
        innerX + radialReach(left, "w", n.gap),
        innerTop + (innerH - centre.rect.h) / 2,
        links,
    )
    const midY = centre.rect.y + centre.rect.h / 2
    spread(right, midY, centre.rect.x + centre.rect.w + n.gap, 1)
    spread(left, midY, centre.rect.x - n.gap, -1)
}

export interface LayoutResult {
    /** Placed roots, in the order given. */
    roots: Placed[]
    /** Page size that fits everything, with a margin. */
    page: { w: number; h: number }
}

/** Where the tree starts on the page. Leaves room for a title above it. */
const ORIGIN = { x: 40, y: 90 }
const MARGIN = { right: 40, bottom: 50 }
/**
 * Area of draw.io's default page (A4 at 850x1100), the yardstick a declared aspect ratio
 * is measured against. Using the editor's own page size means aspect 1 lands on a square
 * about one page in area, rather than on some number invented here.
 */
const PAGE_AREA = 850 * 1100

/**
 * Lay out a forest of roots side by side and report the page size that fits them.
 *
 * A pinned node keeps the position it already had: the user moved it deliberately, and
 * the whole point of the pin is that a re-layout does not undo that.
 */
export function layoutForest(
    roots: DiagramNode[],
    opts: {
        iconSize?: number
        gap?: number
        /** The diagram's links. Needed by sequence containers, which size themselves from
         *  the number of messages between their participants. */
        links?: LayoutLinks
        /**
         * Target width : height for the page. When set, the top level is given a width
         * that lands near it, which is the only way a proportional rule has anything to
         * divide: without a definite width there is no leftover space, so every `grow`
         * weight resolves to zero. Yoga's own docs say the same — a container distributes
         * "any remaining space" among its children, so some space has to remain.
         */
        aspect?: number
    } = {},
): LayoutResult {
    const glyph = opts.iconSize ?? ICON_SIZE
    const gap = opts.gap ?? 70
    const links: LayoutLinks = opts.links ?? []

    const run = (hints?: Map<string, number>, target?: number): Placed[] => {
        // A target page width narrower than the content is a request to WRAP, and wrapping
        // has to happen during measure — the line breaks change every height. So the cap is
        // pushed onto the root group before measuring, unless it declared its own.
        const rootCap = new Map<string, number>()
        if (target) {
            for (const r of roots)
                if (
                    r.kind === "group" &&
                    r.dir === "row" &&
                    !r.pinned &&
                    r.maxW == null
                ) {
                    rootCap.set(r.id, target)
                    r.maxW = target
                }
        }
        const placed = roots.map((r) => measure(r, glyph, links, hints))
        // Widen the roots to the target width when they came out narrower. Only a group can
        // absorb it — a grid, pool, sequence or radial computes its interior from its own
        // rule, so forcing one wider just adds dead space inside it.
        if (target) {
            const own = placed.filter(
                (p) => p.node.kind !== "title" && !p.node.pinned,
            )
            const spread = gap * Math.max(0, own.length - 1)
            const share = (target - spread) / Math.max(1, own.length)
            for (const p of own)
                if (p.node.kind === "group")
                    p.rect.w = Math.min(
                        maxWOf(p.node),
                        Math.max(p.rect.w, share),
                    )
        }
        let cur = ORIGIN.x
        for (const p of placed) {
            const n = p.node
            const held =
                n.kind === "title" ? null : n.pinned ? (n.rect ?? null) : null
            if (held) {
                place(p, held.x, held.y, links)
            } else {
                // A target width makes the top level's width definite, which is what lets
                // grow weights inside it read as proportions of a whole.
                place(p, cur, ORIGIN.y, links, Boolean(target))
                cur += p.rect.w + gap
            }
        }
        // Undo only now: `place` needs the cap to break lines in the same places `measure`
        // did, but `roots` is the caller's tree and must come back exactly as it went in.
        for (const r of roots)
            if (rootCap.has(r.id) && r.kind === "group") r.maxW = undefined
        return placed
    }

    const extent = (placed: Placed[]) => {
        let maxX = 0
        let maxY = 0
        const visit = (p: Placed) => {
            maxX = Math.max(maxX, p.rect.x + p.rect.w)
            maxY = Math.max(maxY, p.rect.y + p.rect.h)
            p.children.forEach(visit)
        }
        placed.forEach(visit)
        return { maxX, maxY }
    }

    let placed = run()

    if (opts.aspect && opts.aspect > 0) {
        // The target width has to come from OUTSIDE the content, or it cannot create the
        // spare space that proportional rules divide: deriving it from the area the content
        // already occupies just returns that content's own width back, leaving nothing over.
        // draw.io's page is the natural external reference — one A4 at 850x1100 — so
        // width = sqrt(pageArea x aspect) is the first guess.
        let want = Math.round(Math.sqrt(PAGE_AREA * opts.aspect))

        // Then iterate, because width and height are not independent: widening the page
        // makes every paragraph rewrap to fewer lines, which SHORTENS it, which changes the
        // ratio that was being aimed at. One pass therefore lands wide of the mark — asking
        // for 0.8 gave 1.13. Each round measures what the last width actually produced and
        // corrects toward the target; three is enough to get inside a few percent, and the
        // loop stops early once the correction is negligible.
        //
        // The hint map is what makes the correction real: it carries the width each box was
        // drawn at, so its text is re-counted at that width instead of at its intrinsic one.
        for (let pass = 0; pass < 4; pass++) {
            placed = run(undefined, want)
            const hints = new Map<string, number>()
            const collect = (p: Placed) => {
                if (p.node.kind === "box") hints.set(p.node.id, p.rect.w)
                p.children.forEach(collect)
            }
            placed.forEach(collect)
            placed = run(hints, want)

            const { maxX, maxY } = extent(placed)
            const w = maxX + MARGIN.right
            const h = maxY + MARGIN.bottom
            const err = w / h / opts.aspect
            if (Math.abs(err - 1) < 0.04) break
            // Geometric correction: to move the ratio by a factor, move the width by its
            // square root, since shrinking the width lengthens the page and vice versa.
            const next = Math.round(want / Math.sqrt(err))
            if (next === want) break
            want = next
        }
    }

    const { maxX, maxY } = extent(placed)

    return {
        roots: placed,
        page: {
            w: Math.round(maxX + MARGIN.right),
            h: Math.round(maxY + MARGIN.bottom),
        },
    }
}

/** Flatten a placed forest into (node, rect, parentId) triples in document order. */
export function flatten(
    roots: Placed[],
): { node: DiagramNode; rect: Rect; parent: string }[] {
    const out: { node: DiagramNode; rect: Rect; parent: string }[] = []
    const walk = (p: Placed, parent: string) => {
        out.push({ node: p.node, rect: p.rect, parent })
        for (const c of p.children) walk(c, p.node.id)
    }
    for (const r of roots) walk(r, "1")
    return out
}