Codex instance
d751d1b13e
Represent partial placements as column heights and branch on the narrowest local valley. This removes the board-area cell state and makes first-solution search substantially smaller for feasible orders. Expose direct-search and candidate-order benchmark controls so the skyline core can be measured independently of odd-order construction. Document the completeness argument and the 10/11 test-tier decision. Tests: Release, Debug, ASan, and UBSan CTest (10 passed each) Refs: #4
430 lines
16 KiB
C++
430 lines
16 KiB
C++
/*
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* Copyright 2025, Matthew Gretton-Dann
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* SPDX-License-Identifier: Apache-2.0
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*/
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#define PARTRIDGE_TESTING
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#include "../main.cc"
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#include <algorithm>
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#include <array>
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#include <span>
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#include <sstream>
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#include <string>
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namespace {
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struct Placement {
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std::uint64_t x;
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std::uint64_t y;
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std::uint64_t side;
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auto operator==(Placement const &) const noexcept -> bool = default;
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};
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struct Validation {
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std::vector<std::string> diagnostics;
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[[nodiscard]] auto valid() const noexcept -> bool { return diagnostics.empty(); }
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[[nodiscard]] auto text() const -> std::string {
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std::ostringstream result;
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for (auto const &diagnostic: diagnostics) {
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result << diagnostic << '\n';
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}
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return result.str();
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}
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};
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struct IndependentResult {
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std::uint64_t width;
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std::uint64_t height;
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std::vector<Placement> placements;
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};
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auto describe(std::size_t index, Placement const &placement) -> std::string {
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return "placement " + std::to_string(index) + " at (" +
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std::to_string(placement.x) + ", " + std::to_string(placement.y) +
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") with side " + std::to_string(placement.side);
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}
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auto validate(std::uint64_t order, std::uint64_t width, std::uint64_t height,
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std::vector<Placement> const &placements) -> Validation {
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Validation result;
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auto const expected_side = order * (order + 1) / 2;
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if (width != expected_side || height != expected_side) {
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result.diagnostics.emplace_back(
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"board dimensions must both equal the triangular number for the order");
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}
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std::vector<std::uint64_t> multiplicities(order + 1);
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std::vector<int> occupied(width * height, -1);
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for (std::size_t index = 0; index < placements.size(); ++index) {
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auto const &placement = placements[index];
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if (placement.side == 0 || placement.side > order) {
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result.diagnostics.push_back(describe(index, placement) +
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" has an invalid side length");
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continue;
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}
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++multiplicities[placement.side];
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if (placement.x >= width || placement.y >= height ||
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placement.side > width - placement.x ||
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placement.side > height - placement.y) {
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result.diagnostics.push_back(describe(index, placement) +
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" is outside the board bounds");
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continue;
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}
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int overlapping_placement = -1;
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for (auto y = placement.y; y < placement.y + placement.side; ++y) {
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for (auto x = placement.x; x < placement.x + placement.side; ++x) {
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auto &cell = occupied[x + y * width];
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if (cell != -1) {
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overlapping_placement = cell;
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} else {
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cell = static_cast<int>(index);
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}
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}
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}
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if (overlapping_placement != -1) {
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result.diagnostics.push_back(
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describe(index, placement) + " overlaps placement " +
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std::to_string(overlapping_placement));
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}
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}
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for (std::uint64_t side = 1; side <= order; ++side) {
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if (multiplicities[side] != side) {
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result.diagnostics.push_back(
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"side " + std::to_string(side) + " has multiplicity " +
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std::to_string(multiplicities[side]) + "; expected " +
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std::to_string(side));
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}
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}
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if (std::ranges::find(occupied, -1) != occupied.end()) {
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result.diagnostics.emplace_back("board is not completely covered");
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}
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return result;
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}
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auto to_independent(Results const &result) -> IndependentResult {
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IndependentResult converted{result.length(), result.length(), {}};
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converted.placements.reserve(result.squares().size());
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for (auto const &square: result.squares()) {
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converted.placements.push_back({
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square.pos() % result.length(),
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square.pos() / result.length(),
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square.length(),
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});
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}
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return converted;
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}
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auto validate(std::uint64_t order, Results const &result) -> Validation {
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auto const converted = to_independent(result);
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return validate(order, converted.width, converted.height,
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converted.placements);
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}
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auto known_order_8() -> std::vector<Placement> {
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return {
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{0, 0, 8}, {8, 0, 8}, {16, 0, 8}, {24, 0, 8},
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{32, 0, 4}, {32, 4, 4}, {0, 8, 8}, {8, 8, 8},
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{16, 8, 8}, {24, 8, 6}, {30, 8, 6}, {24, 14, 5},
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{29, 14, 7}, {0, 16, 6}, {6, 16, 3}, {9, 16, 8},
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{17, 16, 7}, {6, 19, 3}, {24, 19, 5}, {29, 21, 7},
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{0, 22, 7}, {7, 22, 2}, {17, 23, 1}, {18, 23, 6},
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{7, 24, 6}, {13, 24, 5}, {24, 24, 5}, {29, 28, 3},
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{32, 28, 4}, {0, 29, 7}, {13, 29, 7}, {20, 29, 7},
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{27, 29, 2}, {7, 30, 6}, {27, 31, 5}, {32, 32, 4},
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};
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}
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auto renderable_result(std::uint64_t side,
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std::vector<Placement> const &placements) -> Results {
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std::vector<Square> squares;
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squares.reserve(placements.size());
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for (auto const &placement: placements) {
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squares.emplace_back(placement.x + placement.y * side, placement.side);
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}
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return Results(side, std::move(squares));
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}
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auto expect(bool condition, std::string const &message) -> int {
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if (condition) {
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return 0;
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}
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std::cerr << "FAIL: " << message << '\n';
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return 1;
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}
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auto has(Validation const &validation, std::string_view diagnostic) -> bool {
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return std::ranges::any_of(validation.diagnostics,
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[diagnostic](std::string const &candidate) {
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return candidate.find(diagnostic) != std::string::npos;
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});
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}
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auto test_validator() -> int {
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int failures = 0;
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auto const valid = known_order_8();
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auto validation = validate(8, 36, 36, valid);
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failures += expect(validation.valid(),
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"known order-8 solution was rejected:\n" + validation.text());
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validation = validate(8, 35, 36, valid);
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failures += expect(has(validation, "dimensions"),
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"invalid board dimensions were not diagnosed");
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auto invalid = valid;
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invalid.pop_back();
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validation = validate(8, 36, 36, invalid);
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failures += expect(has(validation, "side 4 has multiplicity 3; expected 4"),
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"invalid square multiplicity lacked side and counts");
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failures += expect(has(validation, "completely covered"),
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"incomplete coverage was not diagnosed");
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invalid = valid;
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invalid.front().x = 36;
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validation = validate(8, 36, 36, invalid);
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failures += expect(
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has(validation,
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"placement 0 at (36, 0) with side 8 is outside the board bounds"),
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"out-of-bounds diagnostic lacked placement details");
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invalid = valid;
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invalid[1].x = invalid[0].x;
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invalid[1].y = invalid[0].y;
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validation = validate(8, 36, 36, invalid);
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failures += expect(
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has(validation,
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"placement 1 at (0, 0) with side 8 overlaps placement 0"),
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"overlap diagnostic lacked placement details");
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invalid = valid;
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invalid.front().side = 9;
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validation = validate(8, 36, 36, invalid);
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failures += expect(
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has(validation,
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"placement 0 at (0, 0) with side 9 has an invalid side length"),
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"invalid-side diagnostic lacked placement details");
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return failures;
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}
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auto test_construction() -> int {
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auto predecessor = renderable_result(36, known_order_8());
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auto const predecessor_count = predecessor.squares().size();
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auto const constructed = construct_odd_solution(9, std::move(predecessor));
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auto const converted = to_independent(constructed);
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auto const validation = validate(9, constructed);
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int failures = 0;
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failures += expect(
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validation.valid(),
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"even-to-odd construction was rejected:\n" + validation.text());
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failures += expect(constructed.length() == 45,
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"constructed board has the wrong side length");
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failures += expect(converted.placements.size() == predecessor_count + 9,
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"construction did not add exactly nine squares");
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auto const expected_border = std::array<Placement, 9>{{
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{36, 0, 9}, {36, 9, 9}, {36, 18, 9}, {36, 27, 9},
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{0, 36, 9}, {9, 36, 9}, {18, 36, 9}, {27, 36, 9},
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{36, 36, 9},
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}};
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failures += expect(
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std::ranges::equal(
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std::span(converted.placements).subspan(predecessor_count),
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expected_border),
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"constructed border coordinates are incorrect");
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failures += expect(
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std::ranges::equal(
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std::span(converted.placements).first(predecessor_count),
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known_order_8()),
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"construction translated predecessor coordinates unexpectedly");
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return failures;
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}
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auto test_odd_solver_route() -> int {
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SearchCounters even_counters;
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SearchCounters odd_counters;
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auto const even = find_solution_instrumented(8, even_counters);
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auto const odd = find_solution_instrumented(9, odd_counters);
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int failures = 0;
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failures += expect(
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!uses_odd_construction(1) && !uses_odd_construction(7) &&
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!uses_odd_construction(8) && uses_odd_construction(9) &&
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!uses_odd_construction(10) && uses_odd_construction(11),
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"odd construction route does not preserve direct handling boundaries");
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auto const validation = validate(9, odd);
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failures += expect(validation.valid(),
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"order-9 routed result is invalid:\n" + validation.text());
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failures += expect(odd.squares().size() == even.squares().size() + 9,
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"order-9 route did not construct from order 8");
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failures += expect(
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odd_counters.search_nodes == even_counters.search_nodes &&
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odd_counters.loop_iterations == even_counters.loop_iterations &&
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odd_counters.attempted_placements ==
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even_counters.attempted_placements &&
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odd_counters.backtracks == even_counters.backtracks,
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"order-9 route did not perform exactly the order-8 search");
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return failures;
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}
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auto test_rendering() -> int {
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auto const result = renderable_result(36, known_order_8());
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std::ostringstream rendered;
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auto *const original_buffer = std::cout.rdbuf(rendered.rdbuf());
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result.output();
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std::cout.rdbuf(original_buffer);
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int failures = 0;
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std::istringstream lines(rendered.str());
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std::string line;
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std::uint64_t line_count = 0;
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while (std::getline(lines, line)) {
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++line_count;
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failures += expect(line.size() == result.length(),
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"rendered row has incorrect width");
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failures += expect(line.find('.') == std::string::npos,
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"valid solution left an unrendered cell");
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}
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failures += expect(line_count == result.length(),
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"rendered output has incorrect height");
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return failures;
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}
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auto test_small_solver() -> int {
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int failures = 0;
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for (auto const order: std::array<std::uint64_t, 2>{2, 3}) {
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auto const solution = find_solution(order);
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auto const converted = to_independent(solution);
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auto const expected_side = order * (order + 1) / 2;
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failures += expect(converted.width == expected_side &&
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converted.height == expected_side,
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"result adapter returned incorrect board dimensions");
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failures += expect(!has(validate(order, solution), "dimensions"),
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"result adapter supplied invalid validator dimensions");
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failures += expect(converted.placements.empty(),
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"solver reported a solution for an unsatisfiable order");
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}
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Results const encoded(10, {Square(23, 2)});
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auto const converted = to_independent(encoded);
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failures += expect(
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converted.width == 10 && converted.height == 10 &&
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converted.placements.size() == 1 &&
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converted.placements.front().x == 3 &&
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converted.placements.front().y == 2 &&
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converted.placements.front().side == 2,
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"result adapter did not convert encoded placement coordinates");
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return failures;
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}
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auto test_search_counters() -> int {
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SearchCounters counters;
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auto const solution = find_solution_instrumented(2, counters);
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int failures = 0;
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failures += expect(solution.squares().empty(),
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"instrumented solver changed an infeasible result");
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failures += expect(counters.search_nodes > 0 &&
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counters.loop_iterations >= counters.search_nodes,
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"instrumented solver did not count search work");
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failures += expect(counters.attempted_placements > 0 &&
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counters.backtracks > 0,
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"instrumented solver did not count placements/backtracks");
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failures += expect(counters.prune_checks == 0 &&
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counters.prune_hits == 0 &&
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counters.generated_tasks == 0 &&
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counters.completed_tasks == 0,
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"unimplemented solver counters were not zero");
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return failures;
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}
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auto test_skyline_search() -> int {
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int failures = 0;
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auto const narrowest =
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smallest_valley(std::vector<std::uint64_t>{4, 2, 2, 4, 0, 0, 0, 4});
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failures += expect(
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narrowest.x == 1 && narrowest.height == 2 && narrowest.width == 2,
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"skyline did not select the smallest-width valley");
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auto const tie =
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smallest_valley(std::vector<std::uint64_t>{4, 1, 4, 4, 2, 4});
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failures += expect(tie.x == 1 && tie.height == 1 && tie.width == 1,
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"skyline valley tie-break is not deterministic");
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SearchCounters descending_counters;
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auto const descending = search_solution_instrumented(
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8, descending_counters, CandidateOrder::descending);
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auto validation = validate(8, descending);
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failures += expect(
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validation.valid(),
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"descending skyline search returned an invalid order-8 solution:\n" +
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validation.text());
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SearchCounters direct_nine_counters;
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auto const direct_nine = search_solution_instrumented(
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9, direct_nine_counters, CandidateOrder::ascending);
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validation = validate(9, direct_nine);
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failures += expect(
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validation.valid(),
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"direct skyline search returned an invalid order-9 solution:\n" +
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validation.text());
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failures += expect(
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direct_nine_counters.search_nodes != descending_counters.search_nodes,
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"direct order-9 coverage unexpectedly reused predecessor construction");
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return failures;
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}
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auto test_solver_completion() -> int {
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int failures = 0;
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for (auto const order: std::array<std::uint64_t, 2>{1, 8}) {
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auto const solution = find_solution(order);
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auto const validation = validate(order, solution);
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failures += expect(
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validation.valid(),
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"solver returned an invalid order-" + std::to_string(order) +
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" solution:\n" + validation.text());
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}
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return failures;
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}
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}
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int main(int argc, char **argv) {
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if (argc != 2) {
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std::cerr << "usage: partridge_tests TEST-NAME\n";
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return 2;
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}
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auto const test = std::string_view(argv[1]);
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if (test == "validator") {
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return test_validator();
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}
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if (test == "construction") {
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return test_construction();
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}
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if (test == "solver-odd-route") {
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return test_odd_solver_route();
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}
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if (test == "rendering") {
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return test_rendering();
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}
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if (test == "solver-small") {
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return test_small_solver();
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}
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if (test == "solver-completion") {
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return test_solver_completion();
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}
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if (test == "search-counters") {
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return test_search_counters();
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}
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if (test == "skyline-search") {
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return test_skyline_search();
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}
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std::cerr << "unknown test: " << test << '\n';
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return 2;
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}
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