Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 | 4x 11x 13x 20x 27x 13x 28x 2x 76x 37x 37x 124x 123x 36x 92x 91x 90x 89x 89x 33x 30x 29x 30x 30x 30x 30x 69x 30x 30x 380x 30x 51x 99x 51x 49x 211x 30x 14x 14x 14x 14x 14x 66x 14x 23x 31x 31x 31x 31x 35x 35x 35x 32x 32x 35x 30x 41x 72x 16x 103x 103x 42x 42x 41x 30x 30x 30x 35x 35x 35x 25x 25x 25x 24x 25x 8x 23x 6x 6x 8x 4x 4x 4x 4x 2x 6x 5x 6x 2x 2x 6x 5x 5x 5x 2x 6x 6x 6x 6x 21x 30x 15x 15x 6x 8x 8x 8x 28x 23x 8x 8x 28x 8x 5x 5x 5x 5x 30x 5x 8x 8x 8x 8x 20x 20x 20x 20x 20x 2x 8x 28x 8x 1x 1x 8x 8x 8x | import { createTrace, type Trace } from "../core/trace.js";
import { edgeLine, escape, frame, NODE_R, nodeCircle, type Point } from "./svg.js";
/** An edge between two node ids, with an optional weight. */
export type Edge = [from: string, to: string] | [from: string, to: string, weight: number];
export interface GraphInput {
nodes: string[];
edges: Edge[];
/** Edges go from their first node to their second. Undirected by default. */
directed?: boolean;
}
type ListKind = "queue" | "stack";
export interface GraphState {
nodes: string[];
edges: Edge[];
directed: boolean;
/** Node ids in the order they were visited. */
visited: string[];
/** The node being worked on, set by `focus`, `shift` and `pop`. */
current: string | null;
/** `edgeKey(u, v, directed)` to mark name, such as "tree". */
edgeMarks: Record<string, string>;
/** The queue or stack drawn under the graph. One at a time. */
list: { kind: ListKind; items: string[] } | null;
/** Short text drawn under a node, such as a distance in Dijkstra's algorithm. */
tags: Record<string, string>;
}
/** Default captions, one per hook. Override any of them with the `captions` option. */
export interface GraphCaptions {
start(kind: ListKind, items: string[]): string;
add(kind: ListKind, id: string): string;
take(kind: ListKind, id: string): string;
visit(id: string): string;
focus(id: string): string;
edge(u: string, v: string, mark: string): string;
tag(id: string, text: string | null): string;
}
export const GRAPH_CAPTIONS: GraphCaptions = {
start: (kind, items) => `Start a ${kind}: ${items.join(", ") || "empty"}`,
add: (kind, id) => `${kind === "queue" ? "Enqueue" : "Push"} ${id}`,
take: (kind, id) => `${kind === "queue" ? "Dequeue" : "Pop"} ${id}`,
visit: (id) => `Visit ${id}`,
focus: (id) => `Work on ${id}`,
edge: (u, v, mark) => `Edge ${u}-${v} is a ${mark} edge`,
tag: (id, text) => (text === null ? `Clear the label of ${id}` : `${id}: ${text}`),
};
export interface GraphOptions {
caption?: string;
/** Replaces default captions, for example to translate them. */
captions?: Partial<GraphCaptions>;
}
interface GraphList {
readonly length: number;
push(id: string, caption?: string): void;
}
export interface GraphQueue extends GraphList {
/** Takes the front item and makes it the current node. */
shift(caption?: string): string;
}
export interface GraphStack extends GraphList {
/** Takes the top item and makes it the current node. */
pop(caption?: string): string;
}
/** A graph whose hooks record a step each time they run. Every hook takes an optional caption. */
export interface GraphTrace extends Trace<GraphState> {
/** Neighbors in the order their edges were given; for a directed graph, the nodes edges go to. Does not record a step. */
neighbors(id: string): readonly string[];
/** The weight of the edge from `u` to `v`, or 1 when it has none. Does not record a step. */
weight(u: string, v: string): number;
/** Does not record a step. */
visited(id: string): boolean;
visit(id: string, caption?: string): void;
focus(id: string, caption?: string): void;
edge(u: string, v: string, mark: string, caption?: string): void;
/** Draws short text under a node, such as its distance. `null` removes it. */
tag(id: string, text: string | number | null, caption?: string): void;
queue(items?: string[], caption?: string): GraphQueue;
stack(items?: string[], caption?: string): GraphStack;
note(caption: string): void;
}
/** Key for an edge's mark. Order-free unless the graph is directed. */
export const edgeKey = (u: string, v: string, directed = false) => JSON.stringify(directed ? [u, v] : [u, v].sort());
/** Each node's outgoing edges, as [neighbor, weight]. Undirected edges go both ways. */
function adjacency({ nodes, edges, directed = false }: GraphInput): Map<string, [string, number][]> {
const adj = new Map<string, [string, number][]>();
for (const id of nodes) {
if (adj.has(id)) throw new RangeError(`duplicate node ${id}`);
adj.set(id, []);
}
for (const [u, v, w = 1] of edges) {
if (!adj.has(u) || !adj.has(v)) throw new RangeError(`edge ${u}-${v} uses an unknown node`);
if (u === v) throw new RangeError(`edge ${u}-${v} is a loop; graphs are simple`);
if (!Number.isFinite(w)) throw new RangeError(`edge ${u}-${v} has weight ${w}; weights must be finite numbers`);
adj.get(u)!.push([v, w]);
if (!directed) adj.get(v)!.push([u, w]);
}
return adj;
}
/** The second argument is a caption, or options with a caption and translated captions. */
export function traceGraph(input: GraphInput, options: string | GraphOptions = {}): GraphTrace {
if (input.nodes.length === 0) throw new RangeError("traceGraph needs at least one node");
const { caption = "", captions } = typeof options === "string" ? { caption: options } : options;
const say: GraphCaptions = { ...GRAPH_CAPTIONS, ...captions };
const adj = adjacency(input);
const directed = input.directed ?? false;
const s: GraphState = {
nodes: [...input.nodes],
edges: input.edges.map((e) => [...e] as Edge),
directed,
visited: [],
current: null,
edgeMarks: {},
list: null,
tags: {},
};
const t = createTrace(s, caption);
const check = (...ids: string[]) => {
for (const id of ids) if (!adj.has(id)) throw new RangeError(`unknown node ${id}`);
};
const outgoing = (u: string, v: string) => {
check(u, v);
const found = adj.get(u)!.find(([to]) => to === v);
if (!found) throw new RangeError(`no edge ${u}-${v}`);
return found;
};
const step = (op: string, caption: string) => t.record(op, s, caption);
const list = (kind: ListKind, items: string[], caption: string | undefined) => {
check(...items);
const own = { kind, items: [...items] };
s.list = own;
step(kind, caption ?? say.start(kind, items));
const live = () => {
if (s.list !== own) throw new RangeError(`this ${kind} was replaced by a newer queue or stack`);
};
return {
get length() {
return own.items.length;
},
push(id: string, caption?: string) {
live();
check(id);
own.items.push(id);
step("push", caption ?? say.add(kind, id));
},
take(caption?: string) {
live();
const id = kind === "queue" ? own.items.shift() : own.items.pop();
if (id === undefined) throw new RangeError(`the ${kind} is empty`);
s.current = id;
step("take", caption ?? say.take(kind, id));
return id;
},
};
};
return {
...t,
view: graphView,
neighbors(id) {
check(id);
return adj.get(id)!.map(([v]) => v);
},
weight(u, v) {
return outgoing(u, v)[1];
},
visited(id) {
check(id);
return s.visited.includes(id);
},
visit(id, caption) {
check(id);
if (!s.visited.includes(id)) s.visited.push(id);
step("visit", caption ?? say.visit(id));
},
focus(id, caption) {
check(id);
s.current = id;
step("focus", caption ?? say.focus(id));
},
edge(u, v, mark, caption) {
outgoing(u, v);
s.edgeMarks[edgeKey(u, v, directed)] = mark;
step("edge", caption ?? say.edge(u, v, mark));
},
tag(id, text, caption) {
check(id);
const value = text === null ? null : String(text);
if (value === null) delete s.tags[id];
else s.tags[id] = value;
step("tag", caption ?? say.tag(id, value));
},
queue(items = [], caption) {
const l = list("queue", items, caption);
return { get length() { return l.length; }, push: l.push, shift: l.take };
},
stack(items = [], caption) {
const l = list("stack", items, caption);
return { get length() { return l.length; }, push: l.push, pop: l.take };
},
note(caption) {
step("note", caption);
},
};
}
const GAP_X = 72;
const GAP_Y = 72;
const TAG_D = NODE_R * 0.8; // a tag sits off the node's upper right, clear of edges straight up, down and sideways
const ARROW = 9;
// shortcut: rows by layer (directed, no cycle) or BFS depth from the first node; edges inside a row can cross nodes. Add a real layout if a target needs it.
/** Rows for a directed graph with no cycle: each node one row below the deepest node pointing to it. Null if there is a cycle. */
function layers(s: GraphState): Map<string, number> | null {
const out = adjacency({ nodes: s.nodes, edges: s.edges, directed: true });
const incoming = new Map(s.nodes.map((id) => [id, 0]));
for (const [, v] of s.edges) incoming.set(v, incoming.get(v)! + 1);
const depth = new Map(s.nodes.filter((id) => incoming.get(id) === 0).map((id) => [id, 0]));
const order = [...depth.keys()];
for (const u of order) {
for (const [v] of out.get(u)!) {
depth.set(v, Math.max(depth.get(v) ?? 0, depth.get(u)! + 1));
incoming.set(v, incoming.get(v)! - 1);
if (incoming.get(v) === 0) order.push(v);
}
}
return order.length === s.nodes.length ? depth : null;
}
/** Rows by BFS distance from the first node, ignoring direction. Nodes it cannot reach share a last row. */
function rings(s: GraphState): Map<string, number> {
const adj = adjacency({ nodes: s.nodes, edges: s.edges });
const depth = new Map([[s.nodes[0], 0]]);
const order = [s.nodes[0]];
for (const u of order) {
for (const [v] of adj.get(u)!) {
if (!depth.has(v)) {
depth.set(v, depth.get(u)! + 1);
order.push(v);
}
}
}
return depth;
}
function layout(s: GraphState): { pos: Map<string, Point>; width: number; height: number } {
const depth = (s.directed && layers(s)) || rings(s);
const unreached = Math.max(...depth.values()) + 1;
const rows: string[][] = [];
for (const id of s.nodes) (rows[depth.get(id) ?? unreached] ??= []).push(id);
const width = Math.max(...rows.map((r) => r.length)) * GAP_X;
const pos = new Map<string, Point>();
rows.forEach((row, d) =>
row.forEach((id, c) => pos.set(id, [((c + 0.5) * width) / row.length, d * GAP_Y + NODE_R + 2])),
);
return { pos, width, height: (rows.length - 1) * GAP_Y + 2 * NODE_R + 4 };
}
/** An arrowhead touching the edge of the circle at `to`, pointing away from `from`. */
function arrowhead([x1, y1]: Point, [x2, y2]: Point, state: string): string {
const len = Math.hypot(x2 - x1, y2 - y1) || 1;
const [ux, uy] = [(x2 - x1) / len, (y2 - y1) / len];
const [tx, ty] = [x2 - ux * NODE_R, y2 - uy * NODE_R];
const [bx, by] = [tx - ux * ARROW, ty - uy * ARROW];
const r = (n: number) => Math.round(n * 10) / 10;
return `<path class="stepthru-arrow" data-state="${state}" d="M${r(tx)} ${r(ty)}L${r(bx - uy * ARROW / 2)} ${r(by + ux * ARROW / 2)}L${r(bx + uy * ARROW / 2)} ${r(by - ux * ARROW / 2)}Z"/>`;
}
/** Draws nodes in rows by distance from the first node, with the queue or stack underneath. */
export function graphView(s: GraphState): string {
const { pos, width, height } = layout(s);
const lines: string[] = [];
const marks: string[] = [];
for (const [u, v, w] of s.edges) {
const [a, b] = [pos.get(u)!, pos.get(v)!];
const state = edgeKey(u, v, s.directed) in s.edgeMarks ? "marked" : "idle";
lines.push(edgeLine(a, b, state));
if (s.directed) marks.push(arrowhead(a, b, state));
if (w !== undefined) {
marks.push(`<text class="stepthru-weight" x="${(a[0] + b[0]) / 2}" y="${(a[1] + b[1]) / 2}" text-anchor="middle" dominant-baseline="central" font-size="11">${escape(w)}</text>`);
}
}
const nodes = s.nodes.map((id) =>
nodeCircle(pos.get(id)!, id, id === s.current ? "active" : s.visited.includes(id) ? "marked" : "idle"),
);
const tags = Object.entries(s.tags).map(([id, text]) => {
const [x, y] = pos.get(id)!;
return `<text class="stepthru-tag" x="${x + TAG_D}" y="${y - TAG_D}" font-size="12">${escape(text)}</text>`;
});
const tagged = Object.entries(s.tags).map(([id, text]) => `${id} ${text}`).join(", ");
const label = [
`visited ${s.visited.join(", ") || "none"}`,
s.current && `current ${s.current}`,
tagged && `labels ${tagged}`,
s.list && `${s.list.kind} ${s.list.items.join(", ") || "empty"}`,
].filter(Boolean).join("; ");
return frame(
`${s.directed ? "Directed graph" : "Graph"}: ${label}`,
// Lines first, so circles cover their ends; arrowheads and weights on top of the lines.
{ svg: lines.join("") + nodes.join("") + marks.join("") + tags.join(""), width, height },
s.list && { label: s.list.kind, items: s.list.items },
);
}
|