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* Order-statistic index over one container's children (SPEC.md §4.2).
*
* ## The question it answers
*
* An expanded container renders as
*
* ```text
* 0 { <- the container's own opening row
* 1..n …children… <- this index addresses THIS region
* n+1 } <- the closing row
* ```
*
* Child `c` occupies `rows(c)` rows — exactly 1 when it is a leaf or a
* collapsed container, more when it is itself expanded. Given a row offset
* inside the children region, {@link OrderIndex.locate} must say *which child*
* that is, and it must do so on every rendered row of every frame.
*
* ## Why there are two representations
*
* The textbook answer is a Fenwick tree over all `k` children. That is
* `O(log k)` for both query and update — and `O(k)` **memory**, which is the
* problem: expanding a single element inside a 1 M-item array would allocate a
* 4 MB `Int32Array` to record that 999 999 of its entries are `1`.
*
* So the default is {@link SparseOrder}, which stores only the children that
* are actually expanded: `O(e)` memory and `O(log e)` queries, where `e` is
* what the user has clicked. Its weakness is mutation — an `O(e)` splice — so
* once `e` grows past `denseThreshold` the container is promoted to
* {@link DenseOrder}. Both satisfy the same interface and are tested against
* the same brute-force reference, including across the promotion boundary.
*/
/** Row bookkeeping for the children of one expanded container. */
export interface OrderIndex {
/** Number of children, `k`. Fixed for the lifetime of the index. */
readonly size: number;
/** Children that occupy more than one row. */
readonly expandedCount: number;
/** Total rows the children region occupies. */
totalRows(): number;
/** Rows occupied by child `c` (always ≥ 1). */
rowsOf(child: number): number;
/** Row offset, within the children region, at which child `c` starts. */
rowStartOf(child: number): number;
/** Which child contains `localRow`, and how far into it that row is. */
locate(localRow: number): Located;
/** Record that child `c` now occupies `rows` rows. */
set(child: number, rows: number): void;
}
/** The child a row belongs to. `offset` is 0 for the child's own first row. */
export interface Located {
child: number;
offset: number;
}
/**
* Sparse representation: only children with `rows > 1` are stored.
*
* Three parallel arrays kept sorted by child index — `idx` the child, `ext`
* its *extra* rows (`rows - 1`), and `pre` the running sum of `ext` before
* each position, which is what makes `rowStartOf` a binary search instead of
* a scan.
*/
export class SparseOrder implements OrderIndex {
private idx: number[] = [];
private ext: number[] = [];
private pre: number[] = [];
private total = 0;
constructor(readonly size: number) {}
get expandedCount(): number {
return this.idx.length;
}
/** The `(child, rows)` pairs currently stored — used to promote to dense. */
entries(): readonly (readonly [number, number])[] {
return this.idx.map((child, i) => [child, this.ext[i]! + 1] as const);
}
/**
* Build the whole index in one pass.
*
* Bulk expansion must never go through repeated {@link set}: inserting `e`
* children one at a time is `O(e²)`, which is minutes for a large
* `expandAll`.
*
* @param pairs `(child, rows)` pairs. Sorted here, so callers need not be.
*/
bulk(pairs: readonly (readonly [number, number])[]): void {
const sorted = pairs
.filter(([, rows]) => rows > 1)
.slice()
.sort((a, b) => a[0] - b[0]);
this.idx = sorted.map(([child]) => child);
this.ext = sorted.map(([, rows]) => rows - 1);
this.pre = new Array(this.ext.length);
let running = 0;
for (let i = 0; i < this.ext.length; i++) {
this.pre[i] = running;
running += this.ext[i]!;
}
this.total = running;
}
totalRows(): number {
return this.size + this.total;
}
rowsOf(child: number): number {
const p = this.find(child);
return p >= 0 ? this.ext[p]! + 1 : 1;
}
rowStartOf(child: number): number {
return child + this.extraBefore(child);
}
/** Sum of extra rows contributed by children before `child`. */
private extraBefore(child: number): number {
const p = this.lowerBound(child);
return p < this.pre.length ? this.pre[p]! : this.total;
}
locate(localRow: number): Located {
// Find the last expanded child that starts at or before `localRow`.
let lo = 0;
let hi = this.idx.length - 1;
let p = -1;
while (lo <= hi) {
const mid = (lo + hi) >> 1;
if (this.idx[mid]! + this.pre[mid]! <= localRow) {
p = mid;
lo = mid + 1;
} else {
hi = mid - 1;
}
}
// Before every expanded child: the region is one row per child.
if (p < 0) return { child: localRow, offset: 0 };
const start = this.idx[p]! + this.pre[p]!;
const last = start + this.ext[p]!;
if (localRow <= last) return { child: this.idx[p]!, offset: localRow - start };
// Past that child, back to one row each until the next expanded sibling.
return { child: this.idx[p]! + 1 + (localRow - last - 1), offset: 0 };
}
set(child: number, rows: number): void {
const extra = rows - 1;
const p = this.lowerBound(child);
const present = p < this.idx.length && this.idx[p] === child;
if (extra <= 0) {
if (!present) return;
this.idx.splice(p, 1);
this.ext.splice(p, 1);
this.pre.splice(p, 1);
this.reprefix(p);
return;
}
if (present) {
if (this.ext[p] === extra) return;
this.ext[p] = extra;
this.reprefix(p);
return;
}
this.idx.splice(p, 0, child);
this.ext.splice(p, 0, extra);
this.pre.splice(p, 0, 0);
this.reprefix(p);
}
/** Recompute prefix sums from `from` onward — everything before is unchanged. */
private reprefix(from: number): void {
let running = from > 0 ? this.pre[from - 1]! + this.ext[from - 1]! : 0;
for (let i = from; i < this.ext.length; i++) {
this.pre[i] = running;
running += this.ext[i]!;
}
this.total = running;
}
/** First position whose child index is ≥ `child`. */
private lowerBound(child: number): number {
let lo = 0;
let hi = this.idx.length;
while (lo < hi) {
const mid = (lo + hi) >> 1;
if (this.idx[mid]! < child) lo = mid + 1;
else hi = mid;
}
return lo;
}
/** Exact position of `child`, or -1. */
private find(child: number): number {
const p = this.lowerBound(child);
return p < this.idx.length && this.idx[p] === child ? p : -1;
}
}
/**
* Dense representation: a Fenwick tree over all `k` children holding `rows(c)`.
*
* `O(log k)` for query *and* update, `O(k)` memory. Worth it only once enough
* children are expanded that {@link SparseOrder}'s `O(e)` splice costs more
* than the allocation.
*/
export class DenseOrder implements OrderIndex {
/** 1-indexed Fenwick storage; `tree[0]` is unused. */
private readonly tree: Int32Array;
private readonly rows: Int32Array;
private total: number;
private expanded = 0;
/** Highest power of two ≤ size, for the binary-lifting search. */
private readonly pivot: number;
constructor(readonly size: number, initial?: readonly (readonly [number, number])[]) {
this.rows = new Int32Array(size).fill(1);
if (initial) {
for (const [child, rows] of initial) {
Eif (child >= 0 && child < size && rows > 1) {
this.rows[child] = rows;
this.expanded++;
}
}
}
// Build in O(k) rather than k × O(log k) insertions.
this.tree = new Int32Array(size + 1);
for (let i = 0; i < size; i++) this.tree[i + 1] = this.rows[i]!;
for (let i = 1; i <= size; i++) {
const parent = i + (i & -i);
if (parent <= size) this.tree[parent]! += this.tree[i]!;
}
let total = 0;
for (let i = 0; i < size; i++) total += this.rows[i]!;
this.total = total;
let pivot = 1;
while (pivot * 2 <= size) pivot *= 2;
this.pivot = pivot;
}
get expandedCount(): number {
return this.expanded;
}
totalRows(): number {
return this.total;
}
rowsOf(child: number): number {
return this.rows[child] ?? 1;
}
rowStartOf(child: number): number {
let sum = 0;
for (let i = child; i > 0; i -= i & -i) sum += this.tree[i]!;
return sum;
}
locate(localRow: number): Located {
let pos = 0;
let remaining = localRow;
for (let step = this.pivot; step > 0; step >>= 1) {
const next = pos + step;
if (next <= this.size && this.tree[next]! <= remaining) {
pos = next;
remaining -= this.tree[next]!;
}
}
// `rows ≥ 1` makes the prefix strictly increasing, so `pos` lands inside
// the array for any in-range row; clamp anyway rather than trusting it.
Iif (pos >= this.size) {
const child = this.size - 1;
return { child, offset: localRow - this.rowStartOf(child) };
}
return { child: pos, offset: remaining };
}
set(child: number, rows: number): void {
const next = Math.max(1, rows);
const current = this.rows[child]!;
if (current === next) return;
if (current === 1 && next > 1) this.expanded++;
else if (current > 1 && next === 1) this.expanded--;
this.rows[child] = next;
this.total += next - current;
const delta = next - current;
for (let i = child + 1; i <= this.size; i += i & -i) this.tree[i]! += delta;
}
}
/**
* Promote a sparse index to a dense one, preserving every row count.
*
* @example
* ```ts
* let order: OrderIndex = new SparseOrder(1_000_000);
* order.set(42, 5);
* if (order.expandedCount > threshold) order = toDense(order as SparseOrder);
* ```
*/
export function toDense(sparse: SparseOrder): DenseOrder {
return new DenseOrder(sparse.size, sparse.entries());
}
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