Datasets:
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from __future__ import annotations
from dataclasses import dataclass
@dataclass(frozen=True)
class Family:
slug: str
category: str
required: tuple[str, ...]
specification: str
inputs: tuple[dict, ...]
golden: object
FAMILIES: dict[str, Family] = {}
def add(slug, category, required, specification, inputs, golden):
assert slug not in FAMILIES
FAMILIES[slug] = Family(
slug, category, tuple(required.split()), specification, tuple(inputs), golden
)
add(
"word_frequency",
"text",
"text",
"Input: text (string). Tokenize maximal ASCII [a-z0-9]+ runs after lowercasing. Return [{word,count}], sorted by decreasing count then ascending word. Non-ASCII letters are separators.",
[
{"text": "Red blue RED! 42"},
{"text": ""},
{"text": "é É 中文"},
{"text": "a_a a-b"},
{"text": "12 012 12\nX"},
{"text": "z a z b a b"},
],
[
{"word": "red", "count": 2},
{"word": "42", "count": 1},
{"word": "blue", "count": 1},
],
)
add(
"slug_registry",
"text",
"titles",
'Input: titles (list of strings). Lowercase each, replace maximal runs outside ASCII a-z0-9 with a hyphen, strip hyphens, use "item" if empty. Assign in input order. If already used, append -2, -3, ... to the base until globally unique. Return slugs.',
[
{"titles": ["Hello World", "hello world", "hello-world-2", ""]},
{"titles": []},
{"titles": ["!!!", "", "ITEM"]},
{"titles": ["a", "a-2", "a", "a"]},
{"titles": ["Ünicode", " A___B "]},
{"titles": ["1", "1", "1-2"]},
],
["hello-world", "hello-world-2", "hello-world-2-2", "item"],
)
add(
"run_length",
"text",
"text",
"Input: text (string). Return [character,count] pairs for consecutive identical Unicode code points; retain order and include whitespace. Empty text produces [].",
[
{"text": "aaabbcaa"},
{"text": ""},
{"text": "😀😀é"},
{"text": " \n\n "},
{"text": "abcd"},
{"text": "1111000"},
],
[["a", 3], ["b", 2], ["c", 1], ["a", 2]],
)
add(
"bracket_audit",
"text",
"text",
"Input: text. Audit (), [], {} ignoring all other code points. Return {balanced,position}. On first unmatched/mismatched closing bracket, position is its zero-based code-point index. If openings remain at EOF, position is the most recent unmatched opening. Balanced input has position:null.",
[
{"text": "a([)]"},
{"text": ""},
{"text": "abc"},
{"text": "([]{})"},
{"text": "(("},
{"text": "é]"},
{"text": "[(]"},
],
{"balanced": False, "position": 3},
)
add(
"text_wrap",
"text",
"text width",
"Input: text and positive integer width. Split on Unicode whitespace. Greedily pack words into lines with single spaces; a next word fits iff length including separating space <= width. Never split a long word. Return lines without empty lines.",
[
{"text": "one two three four", "width": 7},
{"text": "", "width": 1},
{"text": "abcdef a", "width": 2},
{"text": " a\t b\n c ", "width": 3},
{"text": "éé a", "width": 2},
{"text": "a b c", "width": 20},
],
["one two", "three", "four"],
)
add(
"ngram_index",
"text",
"tokens n",
"Input: tokens (strings), n (positive integer). Return [{tokens,positions}] for each distinct contiguous n-gram, sorted lexicographically by token sequence. Positions are ascending zero-based starting indices. n greater than length produces [].",
[
{"tokens": ["a", "b", "a", "b"], "n": 2},
{"tokens": [], "n": 1},
{"tokens": ["x"], "n": 2},
{"tokens": ["b", "a", "b"], "n": 1},
{"tokens": ["", "a", ""], "n": 2},
{"tokens": ["x", "x", "x"], "n": 3},
],
[
{"tokens": ["a", "b"], "positions": [0, 2]},
{"tokens": ["b", "a"], "positions": [1]},
],
)
add(
"glob_filter",
"text",
"paths pattern",
"Input: paths (strings), pattern. Return sorted unique matches using case-sensitive shell glob semantics: * matches any run including /, ? one character, [abc] a class, [!abc] a negated class. Python fnmatch.fnmatchcase semantics apply. No filesystem access.",
[
{"paths": ["a.py", "B.py", "a.txt", "a.py", "x/a.py"], "pattern": "*.py"},
{"paths": [], "pattern": "*"},
{"paths": ["a", "b", "c"], "pattern": "[!b]"},
{"paths": ["ab", "a", "a/b"], "pattern": "a?"},
{"paths": ["A", "a"], "pattern": "a"},
{"paths": ["", "a"], "pattern": "*"},
],
["B.py", "a.py", "x/a.py"],
)
add(
"edit_distance",
"text",
"a b",
"Input: strings a,b of <=200 code points. Return Levenshtein distance with unit insertion, deletion and substitution costs. Compare Unicode code points, case-sensitive.",
[
{"a": "kitten", "b": "sitting"},
{"a": "", "b": ""},
{"a": "", "b": "abc"},
{"a": "ab", "b": "ba"},
{"a": "é", "b": "e"},
{"a": "banana", "b": "banana"},
],
3,
)
add(
"roman_codec",
"text",
"number",
"Input: integer number in 1..3999. Return canonical uppercase Roman numeral using subtractive pairs IV,IX,XL,XC,CD,CM.",
[
{"number": 1994},
{"number": 1},
{"number": 4},
{"number": 9},
{"number": 3999},
{"number": 944},
{"number": 58},
],
"MCMXCIV",
)
add(
"caesar_cipher",
"text",
"text shift",
"Input: text and integer shift. Rotate only ASCII letters by shift modulo 26, preserving case. All other characters unchanged.",
[
{"text": "Az-z! 9", "shift": 1},
{"text": "", "shift": 0},
{"text": "Abc", "shift": -1},
{"text": "é中", "shift": 13},
{"text": "XYZ abc", "shift": 52},
{"text": "aZ", "shift": -53},
],
"Ba-a! 9",
)
add(
"csv_records",
"data",
"csv",
"Input: csv (string). Parse comma-separated CSV with double-quoted fields, doubled quote escaping and quoted newlines (Python csv.reader dialect excel). First row is unique nonempty header names. Subsequent rows have the same width. Return objects in source order. Empty document returns []. Blank data rows and malformed CSV are out of scope.",
[
{"csv": "name,n\na,1\nb,2\n"},
{"csv": ""},
{"csv": "x,y\n"},
{"csv": 'a,b\n"hi,there","say ""yes"""\n'},
{"csv": 'x\n"a\nb"\n'},
{"csv": "x,y\r\na,\r\n"},
],
[{"name": "a", "n": "1"}, {"name": "b", "n": "2"}],
)
add(
"record_query",
"data",
"rows where select",
"Input: rows (objects), where (object), select (list of field names). Keep rows containing every where field with an equal JSON value. Return selected fields for each in source order; missing selected fields become null. Values contain no booleans compared with numbers.",
[
{
"rows": [{"a": 1, "b": "x"}, {"a": 2}, {"a": 1}],
"where": {"a": 1},
"select": ["b"],
},
{"rows": [], "where": {}, "select": []},
{"rows": [{"a": None}, {}], "where": {"a": None}, "select": ["a"]},
{"rows": [{"x": 1}], "where": {}, "select": []},
{"rows": [{"x": [1]}, {"x": [2]}], "where": {"x": [1]}, "select": ["x"]},
],
[{"b": "x"}, {"b": None}],
)
add(
"inner_join",
"data",
"left right key",
"Input: left,right (lists of objects), key (string). Return [{left,right}] for all pairs with key present on both sides and equal JSON values. Order by left source index then right source index; duplicates multiply. Null keys can match. No boolean-versus-number comparisons.",
[
{
"left": [{"id": 1}, {"id": 2}],
"right": [{"id": 2}, {"id": 2, "x": 3}],
"key": "id",
},
{"left": [], "right": [], "key": "k"},
{"left": [{}], "right": [{}], "key": "k"},
{"left": [{"k": None}], "right": [{"k": None}], "key": "k"},
{"left": [{"k": 1}, {"k": 1}], "right": [{"k": 1}], "key": "k"},
],
[
{"left": {"id": 2}, "right": {"id": 2}},
{"left": {"id": 2}, "right": {"id": 2, "x": 3}},
],
)
add(
"group_totals",
"data",
"rows group value",
"Input: rows (objects), group,value (field names). Each row has a string group value and integer numeric value. Return [{key,count,sum}] sorted by key. Empty rows returns [].",
[
{
"rows": [{"g": "b", "v": 2}, {"g": "a", "v": 3}, {"g": "b", "v": -1}],
"group": "g",
"value": "v",
},
{"rows": [], "group": "g", "value": "v"},
{"rows": [{"g": "", "v": 0}], "group": "g", "value": "v"},
{"rows": [{"g": "é", "v": 9}, {"g": "A", "v": -9}], "group": "g", "value": "v"},
],
[{"key": "a", "count": 1, "sum": 3}, {"key": "b", "count": 2, "sum": 1}],
)
add(
"json_flatten",
"data",
"value",
'Input: arbitrary JSON value. Return an object mapping JSON Pointer paths to leaves. Root path is "". Escape ~ as ~0 and / as ~1; array indices are decimal. Empty objects/arrays count as leaves. Nonempty containers do not produce their own entries.',
[
{"value": {"a": [1, {"x/y": None}], "b": {}}},
{"value": []},
{"value": None},
{"value": {"~": {"/": 2}, "": 3}},
{"value": [False, {}, []]},
],
{"/a/0": 1, "/a/1/x~1y": None, "/b": {}},
)
add(
"merge_patch",
"data",
"target patch",
"Input: target,patch (JSON values). Apply JSON Merge Patch: a nonobject patch replaces the target. An object patch treats a nonobject target as {}; null-valued members remove keys; other members recursively merge. Arrays replace wholesale. Return resulting value.",
[
{
"target": {"a": 1, "b": {"c": 2, "d": 3}},
"patch": {"a": None, "b": {"c": 9}},
},
{"target": {}, "patch": None},
{"target": [1], "patch": {"x": 2}},
{"target": {"a": [1]}, "patch": {"a": [2, 3]}},
{"target": 4, "patch": {}},
{"target": {"a": 1}, "patch": {"z": None}},
],
{"b": {"c": 9, "d": 3}},
)
add(
"json_pointer",
"data",
"value pointer",
"Input: value (JSON), pointer (empty or starting /, valid ~0/~1 escapes). Resolve object keys or array indices. Array tokens must be 0 or a nonzero decimal digit followed by decimal digits (no leading zero, sign, or -). Return {found:true,value:...}; missing keys, noncontainers or out-of-range indices return {found:false,value:null}. Empty pointer returns root.",
[
{"value": {"a/b": [7]}, "pointer": "/a~1b/0"},
{"value": None, "pointer": ""},
{"value": [1], "pointer": "/01"},
{"value": {"": {"~": 2}}, "pointer": "//~0"},
{"value": [1], "pointer": "/9"},
{"value": {"a": None}, "pointer": "/a/x"},
{"value": [], "pointer": "/-"},
],
{"found": True, "value": 7},
)
add(
"dedupe_records",
"data",
"rows keys",
"Input: rows (objects), keys (field names). Retain first row for each distinct tuple of requested field values; missing fields equal null. Structural JSON equality ignores object key order. Keep source order. Boolean and numeric key values are not mixed.",
[
{"rows": [{"id": 1, "x": "a"}, {"id": 1, "x": "b"}, {"id": 2}], "keys": ["id"]},
{"rows": [], "keys": []},
{"rows": [{"x": 1}, {"x": 2}], "keys": []},
{"rows": [{}, {"x": None}], "keys": ["x"]},
{"rows": [{"x": {"a": 1, "b": 2}}, {"x": {"b": 2, "a": 1}}], "keys": ["x"]},
],
[{"id": 1, "x": "a"}, {"id": 2}],
)
add(
"pivot_table",
"data",
"rows row column value",
"Input: rows, row,column,value field names. Row/column values are strings; numeric values are integers. Return {rows:sorted row labels,columns:sorted column labels,values:2D sums}, filling missing cells with 0. Empty input yields three empty arrays.",
[
{
"rows": [
{"r": "a", "c": "x", "v": 2},
{"r": "b", "c": "y", "v": 3},
{"r": "a", "c": "x", "v": -1},
],
"row": "r",
"column": "c",
"value": "v",
},
{"rows": [], "row": "r", "column": "c", "value": "v"},
{"rows": [{"r": "", "c": "", "v": 0}], "row": "r", "column": "c", "value": "v"},
{
"rows": [{"r": "z", "c": "b", "v": -5}, {"r": "a", "c": "a", "v": 1}],
"row": "r",
"column": "c",
"value": "v",
},
],
{"rows": ["a", "b"], "columns": ["x", "y"], "values": [[1, 0], [0, 3]]},
)
add(
"schema_check",
"data",
"schema value",
'Input: schema object maps field names to {type,required}; value is an object. Types: string,integer,number,boolean,array,object,null. Booleans are neither integers nor numbers. For each schema field in lexical order, report {field,error:"required"} if missing and required, or {field,error:"type"} if present with wrong type. Optional missing fields and extra fields are ignored. No recursive validation.',
[
{
"schema": {
"a": {"type": "integer", "required": True},
"b": {"type": "string", "required": True},
},
"value": {"a": True},
},
{"schema": {}, "value": {"a": 1}},
{"schema": {"x": {"type": "null", "required": False}}, "value": {}},
{"schema": {"x": {"type": "number", "required": True}}, "value": {"x": 1.5}},
{"schema": {"x": {"type": "array", "required": True}}, "value": {"x": []}},
],
[{"field": "a", "error": "type"}, {"field": "b", "error": "required"}],
)
add(
"interval_union",
"intervals",
"intervals",
"Input: intervals, list of [start,end] integer pairs with start<=end. Return sorted merged intervals, combining overlaps and touching endpoints. Retain isolated zero-length intervals.",
[
{"intervals": [[5, 7], [1, 3], [3, 6], [9, 9]]},
{"intervals": []},
{"intervals": [[0, 0], [0, 0]]},
{"intervals": [[-4, -1], [-2, 3]]},
{"intervals": [[1, 10], [2, 3], [12, 14]]},
],
[[1, 7], [9, 9]],
)
add(
"interval_gaps",
"intervals",
"intervals bounds",
"Input: intervals ([a,b] with a<=b), bounds [low,high] with low<=high. Return positive-length gaps in [low,high] after unioning and clipping occupied intervals. Touching endpoints do not make gaps. Sorted ascending; no zero-length results.",
[
{"intervals": [[2, 4], [6, 9]], "bounds": [0, 10]},
{"intervals": [], "bounds": [0, 5]},
{"intervals": [[-3, 8]], "bounds": [0, 5]},
{"intervals": [[8, 9], [-3, -1]], "bounds": [0, 5]},
{"intervals": [[2, 2]], "bounds": [0, 5]},
{"intervals": [], "bounds": [2, 2]},
],
[[0, 2], [4, 6], [9, 10]],
)
add(
"booking_peak",
"intervals",
"bookings",
"Input: bookings ([start,end] integer pairs, start<=end). Intervals are half-open; zero-length bookings ignored. Return {peak,at} for maximum simultaneous active bookings and earliest timestamp attaining that maximum. Empty effective input: {peak:0,at:null}. Endings at t happen before starts at t.",
[
{"bookings": [[1, 4], [2, 3], [3, 5]]},
{"bookings": []},
{"bookings": [[1, 1]]},
{"bookings": [[0, 1], [1, 2]]},
{"bookings": [[-2, 2], [-2, 2]]},
],
{"peak": 2, "at": 2},
)
add(
"business_days",
"calendar",
"start end holidays",
"Input: start,end ISO dates (start<=end) and holidays (ISO dates). Return all Monday-Friday dates in [start,end) excluding holidays, ascending. Duplicate holidays have no additional effect. Dates are valid in years 1900..2100, range <=400 days.",
[
{"start": "2024-02-28", "end": "2024-03-04", "holidays": ["2024-02-29"]},
{"start": "2024-01-01", "end": "2024-01-01", "holidays": []},
{"start": "2024-01-06", "end": "2024-01-08", "holidays": []},
{
"start": "2024-12-30",
"end": "2025-01-03",
"holidays": ["2025-01-01", "2025-01-01"],
},
{"start": "2000-02-28", "end": "2000-03-02", "holidays": []},
],
["2024-02-28", "2024-03-01"],
)
add(
"calendar_month",
"calendar",
"year month",
"Input: year (1900..2100), month (1..12). Return weeks as arrays of seven day numbers, Monday first. Use 0 for days outside the month; include only weeks intersecting this month.",
[
{"year": 2021, "month": 2},
{"year": 2024, "month": 2},
{"year": 1900, "month": 2},
{"year": 2023, "month": 1},
{"year": 2000, "month": 12},
],
[
[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],
],
)
add(
"moving_average",
"numeric",
"values window",
"Input: values (finite numbers), window (positive integer). Return arithmetic means for all contiguous full windows. Empty input or window>length gives [].",
[
{"values": [1, 2, 3, 4], "window": 2},
{"values": [], "window": 1},
{"values": [1], "window": 3},
{"values": [-2, 0, 2], "window": 1},
{"values": [1, 2], "window": 2},
{"values": [0.1, 0.2, 0.3], "window": 2},
],
[1.5, 2.5, 3.5],
)
add(
"statistics",
"numeric",
"values",
"Input: values (finite numbers). Return {count,min,max,mean,median,variance}. Variance is population variance (divide by n); even-length median is mean of middle two. Empty values: count=0 and all other fields null.",
[
{"values": [1, 2, 3, 4]},
{"values": []},
{"values": [7]},
{"values": [-2, -2, 2, 2]},
{"values": [0.1, 0.2, 0.3]},
{"values": [9, 1, 3]},
],
{"count": 4, "min": 1, "max": 4, "mean": 2.5, "median": 2.5, "variance": 1.25},
)
add(
"histogram",
"numeric",
"values edges",
"Input: finite numeric values and strictly increasing edges (>=2). Bins are [edge[i],edge[i+1]); values below first edge underflow, values >=last edge overflow. Return {counts,underflow,overflow}.",
[
{"values": [-1, 0, 1, 2, 3], "edges": [0, 1, 3]},
{"values": [], "edges": [0, 1]},
{"values": [0, 1, 2], "edges": [0, 1, 2]},
{"values": [-5, -3, -1], "edges": [-4, -2, 0]},
{"values": [0.1, 0.2], "edges": [0, 0.2, 1]},
],
{"counts": [1, 2], "underflow": 1, "overflow": 1},
)
add(
"matrix_product",
"numeric",
"a b",
"Input: a (m by n), b (n by p), nonempty rectangular integer matrices of compatible dimensions, each dimension <=20. Return matrix product.",
[
{"a": [[1, 2], [3, 4]], "b": [[5], [6]]},
{"a": [[0]], "b": [[9]]},
{"a": [[-2, 3, 1]], "b": [[1, 0], [0, 1], [2, 2]]},
{"a": [[1, 0], [0, 1]], "b": [[3, 4], [5, 6]]},
{"a": [[2], [3]], "b": [[4, 5]]},
],
[[17], [39]],
)
add(
"polynomial",
"numeric",
"coefficients points",
"Input: integer coefficients in ascending power order (c0,c1,...) and integer evaluation points. Return values at each point. Empty coefficients denote zero polynomial.",
[
{"coefficients": [1, 2, 3], "points": [0, 1, -1, 2]},
{"coefficients": [], "points": [1, 0]},
{"coefficients": [7], "points": []},
{"coefficients": [0, 0, 1], "points": [-3, 3]},
{"coefficients": [-1, 1], "points": [100, -100]},
],
[1, 6, 2, 17],
)
add(
"prime_factors",
"numeric",
"number",
"Input: integer number in 1..10000000. Return [prime,exponent] pairs in ascending prime order; 1 returns [].",
[
{"number": 360},
{"number": 1},
{"number": 2},
{"number": 9973},
{"number": 65536},
{"number": 99991},
],
[[2, 3], [3, 2], [5, 1]],
)
add(
"base_convert",
"numeric",
"digits from_base to_base",
'Input: digits (valid integer representation, optional leading -, case-insensitive ASCII), from_base,to_base (2..36). Convert to lowercase digits 0-9a-z with no leading zero or plus; zero is "0". Magnitude <=2^100.',
[
{"digits": "ff", "from_base": 16, "to_base": 2},
{"digits": "-0", "from_base": 10, "to_base": 36},
{"digits": "-101", "from_base": 2, "to_base": 10},
{"digits": "ZZ", "from_base": 36, "to_base": 16},
{"digits": "00042", "from_base": 10, "to_base": 10},
{"digits": "10000000000000000", "from_base": 16, "to_base": 10},
],
"11111111",
)
add(
"money_split",
"numeric",
"amount weights",
"Input: nonnegative integer amount in cents, nonempty nonnegative integer weights with positive sum. Allocate by largest remainder: floor exact proportional shares, then give leftover cents to greatest fractional remainders, ties to lowest index. Return integer shares totaling amount.",
[
{"amount": 10, "weights": [1, 1, 1]},
{"amount": 0, "weights": [1]},
{"amount": 2, "weights": [0, 1, 1]},
{"amount": 7, "weights": [1, 2]},
{"amount": 1, "weights": [3, 3, 3]},
{"amount": 1000001, "weights": [9, 1]},
],
[4, 3, 3],
)
add(
"invoice_total",
"numeric",
"items tax_rate",
"Input: items [{price:nonnegative decimal string,quantity:nonnegative integer}], tax_rate (nonnegative decimal string). Sum exact price*quantity then round subtotal to cents using ROUND_HALF_UP. Tax = rounded subtotal * tax_rate, rounded half-up to cents. Total=subtotal+tax. Return {subtotal,tax,total} as strings with exactly two decimal places; do not use binary floating point for monetary arithmetic.",
[
{"items": [{"price": "0.335", "quantity": 3}], "tax_rate": "0.20"},
{"items": [], "tax_rate": "0"},
{"items": [{"price": "0.05", "quantity": 1}], "tax_rate": "0.1"},
{"items": [{"price": "1.005", "quantity": 1}], "tax_rate": "0"},
{
"items": [
{"price": "19.99", "quantity": 2},
{"price": "3.50", "quantity": 3},
],
"tax_rate": "0.075",
},
],
{"subtotal": "1.01", "tax": "0.20", "total": "1.21"},
)
add(
"coin_change",
"numeric",
"coins amount",
"Input: coins (positive integer denominations, duplicates allowed), amount (0..10000). Unlimited supply of each coin. Return minimum number of coins or null if impossible. Empty coins can make only zero.",
[
{"coins": [1, 3, 4], "amount": 6},
{"coins": [], "amount": 0},
{"coins": [2], "amount": 3},
{"coins": [2, 2, 5], "amount": 10},
{"coins": [], "amount": 4},
{"coins": [7, 3], "amount": 11},
],
2,
)
add(
"graph_reach",
"graphs",
"nodes edges start",
"Input: nodes (unique strings), edges ([from,to] directed pairs, endpoints in nodes), start (in nodes). Return sorted nodes reachable from start including itself. Allow cycles, self-edges and duplicate edges; <=100 nodes.",
[
{
"nodes": ["a", "b", "c", "d"],
"edges": [["a", "b"], ["b", "c"]],
"start": "a",
},
{"nodes": ["a"], "edges": [], "start": "a"},
{"nodes": ["a", "b"], "edges": [["b", "a"]], "start": "a"},
{
"nodes": ["a", "b"],
"edges": [["a", "b"], ["b", "a"], ["a", "b"]],
"start": "b",
},
{"nodes": ["x", "y"], "edges": [["x", "x"]], "start": "x"},
],
["a", "b", "c"],
)
add(
"shortest_path",
"graphs",
"nodes edges start",
"Input: nodes (unique strings), edges ([from,to,nonnegative integer weight], directed), start. Endpoints and start are in nodes. Return object mapping each node to shortest distance or null if unreachable. Cycles, parallel edges, zero weights allowed; <=100 nodes.",
[
{
"nodes": ["a", "b", "c", "d"],
"edges": [["a", "b", 5], ["a", "c", 1], ["c", "b", 1]],
"start": "a",
},
{"nodes": ["a"], "edges": [], "start": "a"},
{"nodes": ["a", "b"], "edges": [["b", "a", 1]], "start": "a"},
{
"nodes": ["a", "b", "c"],
"edges": [["a", "b", 0], ["b", "a", 0], ["b", "c", 2], ["a", "c", 9]],
"start": "a",
},
{"nodes": ["a", "b"], "edges": [["a", "b", 8], ["a", "b", 2]], "start": "a"},
],
{"a": 0, "b": 2, "c": 1, "d": None},
)
add(
"topological_order",
"graphs",
"nodes edges",
"Input: unique string nodes, directed edges [from,to]. Return topological order choosing lexicographically smallest currently available node each step, or null on any cycle. Duplicate edges allowed and do not change dependencies. Endpoints in nodes; <=100 nodes.",
[
{"nodes": ["c", "a", "b"], "edges": [["a", "c"]]},
{"nodes": [], "edges": []},
{"nodes": ["a", "b"], "edges": [["a", "b"], ["b", "a"]]},
{"nodes": ["a"], "edges": [["a", "a"]]},
{"nodes": ["a", "b"], "edges": [["a", "b"], ["a", "b"]]},
{"nodes": ["z", "a", "b"], "edges": []},
],
["a", "b", "c"],
)
add(
"connected_components",
"graphs",
"nodes edges",
"Input: unique string nodes, undirected edges [a,b], endpoints in nodes. Return components as sorted lists of nodes, ordered by each component first node. Include isolated vertices; allow duplicate edges and self-loops.",
[
{"nodes": ["d", "c", "b", "a"], "edges": [["a", "b"], ["c", "d"]]},
{"nodes": [], "edges": []},
{"nodes": ["a"], "edges": [["a", "a"]]},
{"nodes": ["z", "a"], "edges": []},
{"nodes": ["a", "b", "c"], "edges": [["a", "b"], ["b", "a"], ["b", "c"]]},
],
[["a", "b"], ["c", "d"]],
)
add(
"grid_route",
"graphs",
"grid start end",
"Input: grid (nonempty equal-length strings containing . or #), start,end ([row,column], valid coordinates). Move one cell up/down/left/right through . cells. Return shortest step count, or null if blocked/unreachable, including blocked start or end. Grid <=50x50.",
[
{"grid": ["...", ".#.", "..."], "start": [0, 0], "end": [2, 2]},
{"grid": ["."], "start": [0, 0], "end": [0, 0]},
{"grid": ["#"], "start": [0, 0], "end": [0, 0]},
{"grid": [".#."], "start": [0, 0], "end": [0, 2]},
{"grid": ["..", ".."], "start": [1, 1], "end": [0, 0]},
],
4,
)
add(
"tree_outline",
"graphs",
"nodes",
"Input: nodes [{id:unique string,parent:string or null}], forming a forest (all nonnull parents exist, no cycles), <=100 nodes. Return preorder [{id,depth}], roots and each sibling list sorted by id, roots depth 0.",
[
{
"nodes": [
{"id": "b", "parent": "a"},
{"id": "a", "parent": None},
{"id": "c", "parent": None},
]
},
{"nodes": []},
{"nodes": [{"id": "x", "parent": None}]},
{
"nodes": [
{"id": "c", "parent": "b"},
{"id": "b", "parent": "a"},
{"id": "a", "parent": None},
]
},
{"nodes": [{"id": "z", "parent": None}, {"id": "a", "parent": None}]},
],
[{"id": "a", "depth": 0}, {"id": "b", "depth": 1}, {"id": "c", "depth": 0}],
)
add(
"dependency_build",
"graphs",
"dependencies targets",
"Input: dependencies (object of string node -> dependency string list), targets (strings). Every referenced name exists. DFS each distinct target in sorted order, visit dependencies in sorted order, append each node after dependencies once. Return build order; return null on a cycle reachable from a target. Unreachable cycles ignored; <=100 nodes.",
[
{
"dependencies": {
"app": ["lib", "cfg"],
"lib": ["cfg"],
"cfg": [],
"unused": [],
},
"targets": ["app"],
},
{"dependencies": {}, "targets": []},
{"dependencies": {"a": ["b"], "b": ["a"]}, "targets": ["a"]},
{"dependencies": {"a": [], "x": ["x"]}, "targets": ["a"]},
{"dependencies": {"a": [], "b": ["a"]}, "targets": ["b", "a", "b"]},
],
["cfg", "lib", "app"],
)
add(
"path_normalize",
"systems",
"paths",
"Input: paths (POSIX path strings). Treat all paths as rooted at /. Remove repeated / and . segments; .. pops a segment if available and is ignored at root. Preserve other segment code points and backslashes literally. Return absolute paths without trailing / except root. No filesystem access.",
[
{"paths": ["a/../b//c/", "/../../x", ""]},
{"paths": []},
{"paths": ["/", ".", "..", "a/./b"]},
{"paths": ["a\\b/c", "/a/.../b"]},
{"paths": ["é/../中", "a/../../"]},
],
["/b/c", "/x", "/"],
)
add(
"url_query",
"systems",
"query",
"Input: query string (without leading ?). Parse &-separated key/value pairs using first =, retain blank values and bare keys, decode + as space and percent-encoded UTF-8. Return object of decoded keys -> lists of values in source order. Empty segments ignored. Python urllib.parse.parse_qsl with keep_blank_values=True semantics.",
[
{"query": "a=1&a=2&x=hello+world&empty="},
{"query": ""},
{"query": "flag&&=x"},
{"query": "q=%C3%A9&a%2Fb=x%3Dy"},
{"query": "x=%2B&x=+&x=a=b"},
],
{"a": ["1", "2"], "x": ["hello world"], "empty": [""]},
)
add(
"version_sort",
"systems",
"versions",
"Input: versions valid MAJOR.MINOR.PATCH optionally -prerelease.identifiers; no build metadata, numeric components/identifiers have no leading zeros. Sort by semantic version precedence: numeric core, prerelease before release, numeric prerelease identifiers numerically and before nonnumeric; nonnumeric ASCII lexical; shorter equal prefix first. Stable equal versions retained.",
[
{"versions": ["1.0.0", "1.0.0-beta", "1.0.0-alpha.10", "1.0.0-alpha.2"]},
{"versions": []},
{"versions": ["2.0.0", "10.0.0", "1.9.9"]},
{"versions": ["1.0.0-a", "1.0.0-1", "1.0.0-a.1", "1.0.0"]},
{"versions": ["1.0.0", "1.0.0"]},
],
["1.0.0-alpha.2", "1.0.0-alpha.10", "1.0.0-beta", "1.0.0"],
)
add(
"lru_trace",
"systems",
"capacity accesses",
"Input: nonnegative capacity and accesses (string keys). Simulate initially empty LRU cache. Hit moves key to most recent. Miss inserts and evicts oldest if full. Capacity 0 stores nothing. Return {hits,misses,keys}, keys oldest to newest.",
[
{"capacity": 2, "accesses": ["a", "b", "a", "c", "b"]},
{"capacity": 0, "accesses": ["a", "a"]},
{"capacity": 3, "accesses": []},
{"capacity": 1, "accesses": ["a", "a", "b"]},
{"capacity": 9, "accesses": ["x", "y", "x"]},
],
{"hits": 1, "misses": 4, "keys": ["c", "b"]},
)
add(
"rate_limit",
"systems",
"events window limit",
"Input: events [{key:string,time:integer}] in nondecreasing time order, positive integer window, nonnegative limit. Per key, accept if fewer than limit previously accepted events have timestamps in (time-window,time]. Rejected events do not count. Process same-time events in input order. Return boolean decisions.",
[
{
"events": [{"key": "a", "time": t} for t in [0, 0, 1, 5]],
"window": 5,
"limit": 2,
},
{"events": [], "window": 1, "limit": 1},
{"events": [{"key": "x", "time": 0}], "window": 1, "limit": 0},
{
"events": [
{"key": "a", "time": 0},
{"key": "b", "time": 0},
{"key": "a", "time": 1},
],
"window": 1,
"limit": 1,
},
{
"events": [{"key": "a", "time": t} for t in [-3, -2, -1, 0]],
"window": 2,
"limit": 1,
},
],
[True, True, False, True],
)
add(
"priority_queue",
"systems",
"events",
'Input: events of {op:"push",priority:integer,value:JSON} or {op:"pop"}. Smaller priority first, FIFO ties. Pop empty produces null. Return {popped:list of pop results,remaining:list of queued values in pop order}.',
[
{
"events": [
{"op": "push", "priority": 2, "value": "a"},
{"op": "push", "priority": 1, "value": "b"},
{"op": "pop"},
]
},
{"events": []},
{"events": [{"op": "pop"}, {"op": "pop"}]},
{
"events": [
{"op": "push", "priority": 0, "value": {"x": 1}},
{"op": "push", "priority": 0, "value": None},
{"op": "pop"},
]
},
{"events": [{"op": "push", "priority": -1, "value": 3}]},
],
{"popped": ["b"], "remaining": ["a"]},
)
add(
"round_robin",
"systems",
"jobs quantum",
"Input: jobs [{id:unique string,duration:positive integer}], positive integer quantum. All jobs arrive at 0 in input order. Repeatedly run first job min(remaining,quantum) time, append unfinished job to end. Return {slices:[{id,start,end}],completion:{id:completion time}}. Empty jobs gives empty structures.",
[
{
"jobs": [{"id": "a", "duration": 3}, {"id": "b", "duration": 2}],
"quantum": 2,
},
{"jobs": [], "quantum": 1},
{"jobs": [{"id": "a", "duration": 1}], "quantum": 10},
{
"jobs": [{"id": "a", "duration": 2}, {"id": "b", "duration": 1}],
"quantum": 1,
},
{"jobs": [{"id": "x", "duration": 4}], "quantum": 2},
],
{
"slices": [
{"id": "a", "start": 0, "end": 2},
{"id": "b", "start": 2, "end": 4},
{"id": "a", "start": 4, "end": 5},
],
"completion": {"b": 4, "a": 5},
},
)
add(
"inventory_ledger",
"business",
"events",
"Input: events [{sku:string,delta:integer}]. Stock initially absent/zero. Apply in order, rejecting an event if stock would become negative; rejected events leave no state. Accepted events create the SKU even if delta=0. Return {stock:object,rejected:zero-based event indices}.",
[
{
"events": [
{"sku": "a", "delta": 3},
{"sku": "a", "delta": -4},
{"sku": "a", "delta": -2},
]
},
{"events": []},
{"events": [{"sku": "x", "delta": -1}]},
{
"events": [
{"sku": "x", "delta": 0},
{"sku": "y", "delta": 2},
{"sku": "y", "delta": -2},
]
},
{"events": [{"sku": "", "delta": 1}]},
],
{"stock": {"a": 1}, "rejected": [1]},
)
add(
"bank_ledger",
"business",
"balances transfers",
"Input: balances (account -> nonnegative integer cents), transfers [{from,to,amount:positive integer}]. Reject missing accounts or insufficient source balance; otherwise subtract then add, including self-transfers. Return {balances,rejected:event indices}. Rejected transfers change nothing; never create accounts.",
[
{
"balances": {"a": 10, "b": 0},
"transfers": [
{"from": "a", "to": "b", "amount": 7},
{"from": "a", "to": "b", "amount": 4},
],
},
{"balances": {}, "transfers": []},
{"balances": {"a": 2}, "transfers": [{"from": "a", "to": "a", "amount": 2}]},
{"balances": {"a": 3}, "transfers": [{"from": "a", "to": "x", "amount": 1}]},
{"balances": {"a": 0}, "transfers": [{"from": "x", "to": "a", "amount": 1}]},
],
{"balances": {"a": 3, "b": 7}, "rejected": [1]},
)
add(
"ballot_count",
"business",
"candidates votes",
"Input: candidates (unique strings), votes (strings). Count candidate votes, unrecognized votes invalid. Return {ranking:[{candidate,votes}],invalid}. Include zero-vote candidates. Rank by decreasing votes then ascending name.",
[
{"candidates": ["b", "a", "c"], "votes": ["a", "b", "a", "x"]},
{"candidates": [], "votes": []},
{"candidates": ["a"], "votes": ["x", ""]},
{"candidates": ["b", "a"], "votes": ["b", "a"]},
{"candidates": [], "votes": ["x"]},
],
{
"ranking": [
{"candidate": "a", "votes": 2},
{"candidate": "b", "votes": 1},
{"candidate": "c", "votes": 0},
],
"invalid": 1,
},
)
add(
"search_rank",
"business",
"documents query",
"Input: documents [{id:unique string,text:string}], query string. Tokenize lowercase ASCII [a-z0-9]+. Score each document by total occurrence counts of distinct query tokens. Omit score=0 docs. Return [{id,score}] sorted by decreasing score then id.",
[
{
"documents": [
{"id": "b", "text": "red blue"},
{"id": "a", "text": "red red"},
{"id": "c", "text": "green"},
],
"query": "RED red blue",
},
{"documents": [], "query": "x"},
{"documents": [{"id": "a", "text": "x"}], "query": ""},
{
"documents": [{"id": "z", "text": "x"}, {"id": "a", "text": "x"}],
"query": "x",
},
{"documents": [{"id": "a", "text": "é RED_42"}], "query": "red 42"},
],
[{"id": "a", "score": 2}, {"id": "b", "score": 2}],
)
add(
"log_summary",
"business",
"events",
"Input: events [{level:string,message:string}]. Return {counts:level->count,errors:messages of exactly ERROR-level events in source order}. Levels are case-sensitive; include only encountered levels.",
[
{
"events": [
{"level": "INFO", "message": "start"},
{"level": "ERROR", "message": "bad"},
{"level": "ERROR", "message": "worse"},
]
},
{"events": []},
{"events": [{"level": "error", "message": "x"}]},
{
"events": [
{"level": "WARN", "message": ""},
{"level": "INFO", "message": "ok"},
]
},
{"events": [{"level": "ERROR", "message": "é"}]},
],
{"counts": {"INFO": 1, "ERROR": 2}, "errors": ["bad", "worse"]},
)
add(
"uptime_report",
"business",
"start end downtime",
"Input: integer start<=end, downtime intervals [a,b] with a<=b. Clip to [start,end), merge overlaps, count duration without double-counting. Return {down,up}, up=end-start-down.",
[
{"start": 0, "end": 10, "downtime": [[-2, 3], [2, 5], [8, 12]]},
{"start": 0, "end": 0, "downtime": []},
{"start": 0, "end": 5, "downtime": []},
{"start": 0, "end": 5, "downtime": [[-10, 10]]},
{"start": 0, "end": 5, "downtime": [[1, 1], [5, 8]]},
],
{"down": 7, "up": 3},
)
add(
"segment_intersection",
"geometry",
"a b c d",
"Input: a,b,c,d each [integer x,integer y]. Return boolean whether closed segments ab and cd intersect, including collinear overlap, endpoint touches and degenerate point-segments. Coordinates magnitude <=100000.",
[
{"a": [0, 0], "b": [2, 2], "c": [0, 2], "d": [2, 0]},
{"a": [0, 0], "b": [1, 0], "c": [2, 0], "d": [3, 0]},
{"a": [0, 0], "b": [2, 0], "c": [1, 0], "d": [3, 0]},
{"a": [0, 0], "b": [0, 0], "c": [-1, 0], "d": [1, 0]},
{"a": [0, 0], "b": [0, 1], "c": [0, 1], "d": [1, 1]},
{"a": [0, 0], "b": [0, 0], "c": [1, 1], "d": [1, 1]},
],
True,
)
add(
"polygon_area",
"geometry",
"points",
"Input: points, ordered integer [x,y] vertices of a simple polygon (clockwise or counterclockwise), possibly empty or fewer than three points. Return nonnegative area by shoelace, implicitly close last to first. Degenerate polygon has zero area.",
[
{"points": [[0, 0], [4, 0], [4, 3], [0, 3]]},
{"points": []},
{"points": [[1, 2]]},
{"points": [[0, 0], [1, 0], [0, 1]]},
{"points": [[0, 0], [0, 3], [4, 3], [4, 0]]},
{"points": [[-1, -1], [1, 1]]},
],
12,
)
add(
"skyline",
"geometry",
"buildings",
"Input: buildings [left,right,height], integer left<right and positive height. Return skyline keypoints [x,height] in ascending x where max active height changes. Buildings cover [left,right); omit redundant same-height points; finish with height 0 at last active end. Empty input returns [].",
[
{"buildings": [[1, 4, 3], [2, 6, 5], [7, 8, 2]]},
{"buildings": []},
{"buildings": [[0, 1, 2], [1, 2, 2]]},
{"buildings": [[0, 5, 4], [1, 2, 1]]},
{"buildings": [[-2, 0, 3], [-2, 0, 3]]},
],
[[1, 3], [2, 5], [6, 0], [7, 2], [8, 0]],
)
add(
"knapsack",
"optimization",
"items capacity",
"Input: items [{weight:positive integer,value:nonnegative integer}], capacity (0..1000). Each item usable at most once; return maximum total value within capacity. Identical items remain independently usable; no need to return selected indices.",
[
{
"items": [
{"weight": 2, "value": 3},
{"weight": 3, "value": 4},
{"weight": 4, "value": 8},
],
"capacity": 5,
},
{"items": [], "capacity": 5},
{"items": [{"weight": 1, "value": 2}], "capacity": 0},
{
"items": [{"weight": 2, "value": 3}, {"weight": 2, "value": 3}],
"capacity": 4,
},
{"items": [{"weight": 9, "value": 20}], "capacity": 3},
],
8,
)
add(
"task_selection",
"optimization",
"tasks",
"Input: tasks [{id:unique string,start:integer,end:integer}], start<end. Greedy maximum-count nonoverlapping schedule: sort by (end,start,id), choose each task iff start>=previous chosen end. Return chosen IDs. Intervals are half-open, negative times allowed.",
[
{
"tasks": [
{"id": "a", "start": 0, "end": 3},
{"id": "b", "start": 1, "end": 2},
{"id": "c", "start": 2, "end": 4},
]
},
{"tasks": []},
{
"tasks": [
{"id": "b", "start": 0, "end": 1},
{"id": "a", "start": 0, "end": 1},
]
},
{
"tasks": [
{"id": "a", "start": -3, "end": -1},
{"id": "b", "start": -1, "end": 0},
]
},
{"tasks": [{"id": "x", "start": 0, "end": 9}]},
],
["b", "c"],
)
add(
"sequence_diff",
"optimization",
"a b",
'Input: a,b (lists of strings, length<=100). Produce minimal insert/delete edit script via longest common subsequence. If current tokens equal, emit ["keep",token] and advance both. Otherwise choose deletion when remaining LCS lengths tie; else choose operation retaining longer LCS. Emit ["delete",token] or ["insert",token]; process until both exhausted.',
[
{"a": ["a", "b"], "b": ["b", "c"]},
{"a": [], "b": []},
{"a": ["a"], "b": []},
{"a": [], "b": ["x", "y"]},
{"a": ["a", "b"], "b": ["b", "a"]},
{"a": ["x", "x"], "b": ["x"]},
],
[["delete", "a"], ["keep", "b"], ["insert", "c"]],
)
add(
"finite_automaton",
"languages",
"start accepting transitions words",
"Input: start (state string), accepting (state strings), transitions [{from,symbol,to}] with unique (from,symbol) and one-code-point symbols, words (strings). Simulate DFA separately per word. Missing transition rejects immediately. Return acceptance booleans. Empty word accepted iff start accepting.",
[
{
"start": "a",
"accepting": ["a"],
"transitions": [
{"from": "a", "symbol": "x", "to": "b"},
{"from": "b", "symbol": "x", "to": "a"},
],
"words": ["", "x", "xx", "y"],
},
{"start": "s", "accepting": [], "transitions": [], "words": ["", "a"]},
{"start": "s", "accepting": ["s"], "transitions": [], "words": [""]},
{
"start": "s",
"accepting": ["t"],
"transitions": [{"from": "s", "symbol": "é", "to": "t"}],
"words": ["é", "éé"],
},
{"start": "s", "accepting": ["s"], "transitions": [], "words": []},
],
[True, False, True, False],
)
add(
"content_manifest",
"systems",
"files",
"Input: files (object of logical file path -> text). Do not read filesystem. Return [{path,bytes,sha256}] sorted by path; bytes is length of UTF-8 encoding and sha256 is lowercase hexadecimal SHA-256 of that encoding. No newline insertion or Unicode normalization.",
[
{"files": {"empty": ""}},
{"files": {}},
{"files": {"b": "hello", "a": "é"}},
{"files": {"x": "a\n", "y": "a"}},
{"files": {"中": "😀", "nul": "\u0000"}},
],
[
{
"path": "empty",
"bytes": 0,
"sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855",
}
],
)
add(
"cellular_automaton",
"simulation",
"live steps",
"Input: live (integer [row,column] pairs, duplicates ignored), steps (0..20). Simulate Conway Life on infinite 2D grid, eight neighbors: live survives with 2 or 3, dead born with 3. Return sorted unique live pairs lexicographically. Initial <=50 cells.",
[
{"live": [[0, 0], [0, 1], [0, 2]], "steps": 1},
{"live": [], "steps": 10},
{"live": [[0, 0]], "steps": 1},
{"live": [[0, 0], [0, 1], [1, 0], [1, 1]], "steps": 5},
{"live": [[1, 2], [1, 2], [-1, 0]], "steps": 0},
{"live": [[0, 0], [0, 1], [0, 2]], "steps": 2},
],
[[-1, 1], [0, 1], [1, 1]],
)
add(
"expression_eval",
"languages",
"tokens",
"Input: tokens, a valid postfix integer expression as strings with binary operators +,-,*,/. Return integer result. Division truncates toward zero, including negative operands; all divisors nonzero. Other tokens are signed base-10 integers. All intermediate magnitudes <=2^100; expression leaves exactly one value.",
[
{"tokens": ["5", "2", "-", "4", "*"]},
{"tokens": ["-7", "3", "/"]},
{"tokens": ["7", "-3", "/"]},
{"tokens": ["42"]},
{"tokens": ["2", "3", "4", "*", "+"]},
{"tokens": ["100000000000000000001", "3", "/"]},
],
12,
)
assert len(FAMILIES) == 65
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