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import { edgeLine, escape, frame, frameSize, NODE_R, nodeCircle, type Point } from "./svg.js";
export interface ArrayState<T = number> {
values: T[];
/** A stable id per value, so a view can follow a value as swaps move it. */
ids: number[];
/** Indexes the current step looks at, such as a compare. */
active: number[];
/** Indexes whose values the current step moved, such as a swap. */
moved: number[];
/** Index to mark name, such as "sorted" or "found". */
marks: Record<number, string>;
/** Pointer name to index. */
pointers: Record<string, number>;
/** Range name to inclusive [lo, hi]. Cells outside every range are dimmed. */
ranges: Record<string, [number, number]>;
/** A list of values drawn under the array, such as a merge buffer. One at a time. */
list: { name: string; items: T[] } | null;
}
/** Default captions, one per hook. Values arrive as their cell text. Override any of them with the `captions` option. */
export interface ArrayCaptions {
compare(a: string, b: string): string;
swap(a: string, b: string): string;
set(index: number, value: string): string;
mark(value: string, name: string): string;
pointer(name: string, index: number): string;
range(name: string, lo: number, hi: number): string;
list(name: string, items: string[]): string;
clear(name: string): string;
}
export const ARRAY_CAPTIONS: ArrayCaptions = {
compare: (a, b) => `Compare ${a} and ${b}`,
swap: (a, b) => `Swap ${a} and ${b}`,
set: (i, v) => `Set index ${i} to ${v}`,
mark: (v, name) => `${v} is ${name}`,
pointer: (name, i) => `${name} at index ${i}`,
range: (name, lo, hi) => `${name}: indexes ${lo} to ${hi}`,
list: (name, items) => `${name}: ${items.join(", ") || "empty"}`,
clear: (name) => `Clear ${name}`,
};
export interface ArrayOptions<T> {
caption?: string;
/** Replaces default captions, for example to translate them. */
captions?: Partial<ArrayCaptions>;
/** Orders two values like a sort comparator. Required for objects; numbers and strings have a default. */
compare?: (a: T, b: T) => number;
/** Text drawn in a cell. Defaults to the value itself, or its JSON for objects. */
label?: (value: T) => string;
}
/** An array whose hooks record a step each time they run. Every hook takes an optional caption. */
export interface ArrayTrace<T = number> extends Trace<ArrayState<T>> {
readonly length: number;
/** Reads a value without recording a step. */
get(i: number): T;
/** Returns a negative number, zero or a positive number, like a sort comparator. */
compare(i: number, j: number, caption?: string): number;
swap(i: number, j: number, caption?: string): void;
/** Writes a value at an index, such as when a merge copies values back. */
set(i: number, value: T, caption?: string): void;
mark(i: number, name: string, caption?: string): void;
pointer(name: string, i: number, caption?: string): void;
range(name: string, lo: number, hi: number, caption?: string): void;
/** Shows `items` in a row under the array, called `name`. Replaces any earlier list. */
list(name: string, items: readonly T[], caption?: string): void;
/** Removes the pointer, the range and the list called `name`. */
clear(name: string, caption?: string): void;
note(caption: string): void;
}
/** Numbers and strings in their natural order. Objects need their own comparator. */
function naturalOrder(a: unknown, b: unknown): number {
if (typeof a === "number" && typeof b === "number") return a - b;
if (typeof a === "string" && typeof b === "string") return a < b ? -1 : a > b ? 1 : 0;
throw new TypeError("traceArray can only compare numbers or strings by itself; pass options.compare");
}
const defaultLabel = (v: unknown) => (typeof v === "object" && v !== null ? JSON.stringify(v) : String(v));
/**
* Traces an array of numbers, strings or objects. The second argument is a caption, or options
* with a caption, a comparator and a label for each value.
*/
export function traceArray<T = number>(values: readonly T[], options: string | ArrayOptions<T> = {}): ArrayTrace<T> {
if (values.length === 0) throw new RangeError("traceArray needs at least one value");
const { caption = "", compare: order = naturalOrder, label = defaultLabel, captions } = typeof options === "string" ? { caption: options } : options;
const say: ArrayCaptions = { ...ARRAY_CAPTIONS, ...captions };
const s: ArrayState<T> = {
values: [...values],
ids: values.map((_, i) => i),
active: [],
moved: [],
marks: {},
pointers: {},
ranges: {},
list: null,
};
const t = createTrace(s, caption);
const last = s.values.length - 1;
const text = (i: number) => label(s.values[i]);
const check = (...indexes: number[]) => {
for (const i of indexes) {
if (!Number.isInteger(i) || i < 0 || i > last) throw new RangeError(`index ${i} is outside 0..${last}`);
}
};
const step = (op: string, active: number[], caption: string, moved: number[] = []) => {
s.active = active;
s.moved = moved;
t.record(op, s, caption);
};
const swapIn = <V>(list: V[], i: number, j: number) => {
[list[i], list[j]] = [list[j], list[i]];
};
return {
...t,
view: label === defaultLabel ? arrayView : (state) => arrayView(state, label),
size: (state) => arraySize(state, label),
length: s.values.length,
get(i) {
check(i);
return s.values[i];
},
compare(i, j, caption) {
check(i, j);
const result = order(s.values[i], s.values[j]);
step("compare", [i, j], caption ?? say.compare(text(i), text(j)));
return result;
},
swap(i, j, caption) {
check(i, j);
swapIn(s.values, i, j);
swapIn(s.ids, i, j);
step("swap", [], caption ?? say.swap(text(j), text(i)), [i, j]);
},
set(i, value, caption) {
check(i);
s.values[i] = value;
step("set", [], caption ?? say.set(i, text(i)), [i]);
},
mark(i, name, caption) {
check(i);
s.marks[i] = name;
step("mark", [i], caption ?? say.mark(text(i), name));
},
pointer(name, i, caption) {
check(i);
s.pointers[name] = i;
step("pointer", [i], caption ?? say.pointer(name, i));
},
range(name, lo, hi, caption) {
check(lo, hi);
if (lo > hi) throw new RangeError(`range ${name}: lo ${lo} is above hi ${hi}`);
s.ranges[name] = [lo, hi];
step("range", [], caption ?? say.range(name, lo, hi));
},
list(name, items, caption) {
s.list = { name, items: [...items] };
step("list", s.active, caption ?? say.list(name, items.map(label)), s.moved);
},
clear(name, caption) {
delete s.pointers[name];
delete s.ranges[name];
if (s.list?.name === name) s.list = null;
step("clear", [], caption ?? say.clear(name));
},
note(caption) {
step("note", s.active, caption, s.moved);
},
};
}
const CELL = 40;
const GAP = 4;
const CHAR_W = 10; // rough width of one character at the default font size
const TOP = 24; // room for range brackets above the cells
const BOTTOM = TOP + CELL;
/** At least CELL, wider when a label would not fit. */
const cellWidth = (labels: readonly string[]) => Math.max(CELL, ...labels.map((l) => l.length * CHAR_W + 12));
interface Geometry { w: number; pitch: number; center: (i: number) => number }
const geometry = (labels: readonly string[]): Geometry => {
const w = cellWidth(labels);
const pitch = w + GAP;
return { w, pitch, center: (i) => i * pitch + w / 2 };
};
const stateOf = (s: ArrayState<unknown>, i: number) =>
s.moved.includes(i) ? "moved" : s.active.includes(i) ? "active" : i in s.marks ? "marked" : "idle";
const outside = (ranges: [number, number][], i: number) => ranges.length > 0 && !ranges.some(([lo, hi]) => i >= lo && i <= hi);
// Each cell is a group keyed by its value's id and placed with a translate, so render can slide it when a swap moves it.
function cell(s: ArrayState<unknown>, g: Geometry, ranges: [number, number][], text: string, i: number): string {
return `<g data-key="${s.ids[i]}" transform="translate(${i * g.pitch} ${TOP})"${outside(ranges, i) ? ' data-dim=""' : ""}>`
+ `<rect data-state="${stateOf(s, i)}" width="${g.w}" height="${CELL}" rx="4"/>`
+ `<text x="${g.w / 2}" y="${CELL / 2}" text-anchor="middle" dominant-baseline="central">${escape(text)}</text></g>`;
}
// shortcut: overlapping ranges draw on top of each other; stack them if a target needs two at once.
function range(g: Geometry, name: string, [lo, hi]: [number, number]): string {
const x1 = lo * g.pitch;
const x2 = hi * g.pitch + g.w;
return `<path class="stepthru-range" d="M${x1} ${TOP - 4}V${TOP - 10}H${x2}V${TOP - 4}"/>`
+ `<text x="${(x1 + x2) / 2}" y="${TOP - 14}" text-anchor="middle" font-size="11">${escape(name)}</text>`;
}
function pointers(s: ArrayState<unknown>, { center }: Geometry): string[] {
const names = new Map<number, string[]>();
for (const [name, i] of Object.entries(s.pointers)) names.set(i, [...(names.get(i) ?? []), name]);
return [...names].map(
([i, list]) => `<path class="stepthru-pointer" d="M${center(i)} ${BOTTOM + 6}l5 8h-10z"/>`
+ `<text x="${center(i)}" y="${BOTTOM + 30}" text-anchor="middle" font-size="11">${escape(list.join(", "))}</text>`,
);
}
const ARRAY_H = BOTTOM + 36;
/** The array drawing shared by arrayView and heapView: brackets, cells, pointers, and the text that describes them. */
function arrayBody<T>(s: ArrayState<T>, label: (value: T) => string) {
const labels = s.values.map(label);
const g = geometry(labels);
const ranges = Object.values(s.ranges);
const svg = [
...Object.entries(s.ranges).map(([name, r]) => range(g, name, r)),
...labels.map((l, i) => cell(s, g, ranges, l, i)),
...pointers(s, g),
].join("");
const list = s.list && { label: s.list.name, items: s.list.items.map(label) };
const described = labels.map((l, i) => (i in s.marks ? `${l} (${s.marks[i]})` : l)).join(", ")
+ (list ? `; ${list.label}: ${list.items.join(", ") || "empty"}` : "");
return { svg, width: s.values.length * g.pitch - GAP, height: ARRAY_H, labels, ranges, list, described };
}
/** The size arrayView draws a state at, without building its markup. */
function arraySize<T>(s: ArrayState<T>, label: (value: T) => string) {
const width = s.values.length * (cellWidth(s.values.map(label)) + GAP) - GAP;
return frameSize({ width, height: ARRAY_H }, s.list && { label: s.list.name, items: s.list.items.map(label) });
}
/** Draws cells with their values, range brackets above, pointers below and the list under those. */
export function arrayView<T>(s: ArrayState<T>, label: (value: T) => string = defaultLabel): string {
const body = arrayBody(s, label);
return frame(`Array: ${body.described}`, body, body.list);
}
const LEVEL_Y = 56;
const SLOT = 2 * NODE_R + 8;
/** Where index `i` sits when the array is read as a binary heap: children of `i` are `2i + 1` and `2i + 2`. */
const heapDepth = (n: number) => Math.floor(Math.log2(n));
const heapTreeSize = (n: number, arrayWidth: number) =>
[Math.max(2 ** heapDepth(n) * SLOT, arrayWidth), heapDepth(n) * LEVEL_Y + 2 * NODE_R + 12] as const;
/**
* Draws the array as a binary heap: a tree on top, the array underneath. Pass it as `render`'s `view`
* for heapsort or a priority queue. Values slide along the tree and the array when swapped.
*/
export function heapView<T>(s: ArrayState<T>, label: (value: T) => string = defaultLabel): string {
const body = arrayBody(s, label);
const [treeW, treeH] = heapTreeSize(s.values.length, body.width);
const at = (i: number): Point => {
const d = Math.floor(Math.log2(i + 1));
return [((i + 1 - 2 ** d + 0.5) * treeW) / 2 ** d, d * LEVEL_Y + NODE_R + 2];
};
const parts: string[] = [];
for (let i = 1; i < s.values.length; i++) {
const line = edgeLine(at((i - 1) >> 1), at(i), "idle");
parts.push(outside(body.ranges, i) ? `<g data-dim="">${line}</g>` : line);
}
body.labels.forEach((l, i) =>
parts.push(nodeCircle(at(i), l, stateOf(s, i), { key: `n${s.ids[i]}`, dim: outside(body.ranges, i) })));
parts.push(`<g transform="translate(${(treeW - body.width) / 2} ${treeH})">${body.svg}</g>`);
return frame(`Heap: ${body.described}`, { svg: parts.join(""), width: treeW, height: treeH + body.height }, body.list);
}
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