add single state space benchmark + some tests

test/bitmap.cpp

@@ -0,0 +1,74 @@
+// ReSharper disable CppLocalVariableMayBeConst
+#include "puzzle.hpp"
+
+#include <random>
+#include <catch2/catch_test_macros.hpp>
+
+TEST_CASE("bitmap_is_full all bits set", "[puzzle][board]")
+{
+    puzzle p1(5, 5);
+    puzzle p2(3, 4);
+    puzzle p3(5, 4);
+    puzzle p4(3, 7);
+    uint64_t bitmap = -1;
+
+    REQUIRE(p1.bitmap_is_full(bitmap));
+    REQUIRE(p2.bitmap_is_full(bitmap));
+    REQUIRE(p3.bitmap_is_full(bitmap));
+    REQUIRE(p4.bitmap_is_full(bitmap));
+}
+
+TEST_CASE("bitmap_is_full no bits set", "[puzzle][board]")
+{
+    puzzle p1(5, 5);
+    puzzle p2(3, 4);
+    puzzle p3(5, 4);
+    puzzle p4(3, 7);
+    uint64_t bitmap = 0;
+
+    REQUIRE_FALSE(p1.bitmap_is_full(bitmap));
+    REQUIRE_FALSE(p2.bitmap_is_full(bitmap));
+    REQUIRE_FALSE(p3.bitmap_is_full(bitmap));
+    REQUIRE_FALSE(p4.bitmap_is_full(bitmap));
+}
+
+TEST_CASE("bitmap_is_full necessary bits set", "[puzzle][board]")
+{
+    puzzle p1(5, 5);
+    puzzle p2(3, 4);
+    puzzle p3(5, 4);
+    puzzle p4(3, 7);
+
+    uint64_t bitmap1 = (1ull << 25) - 1; // 5 * 5
+    uint64_t bitmap2 = (1ull << 12) - 1;  // 3 * 4
+    uint64_t bitmap3 = (1ull << 20) - 1; // 5 * 4
+    uint64_t bitmap4 = (1ull << 21) - 1; // 3 * 7
+
+    REQUIRE(p1.bitmap_is_full(bitmap1));
+    REQUIRE(p2.bitmap_is_full(bitmap2));
+    REQUIRE(p3.bitmap_is_full(bitmap3));
+    REQUIRE(p4.bitmap_is_full(bitmap4));
+}
+
+TEST_CASE("bitmap_is_full necessary bits not set", "[puzzle][board]")
+{
+    puzzle p1(5, 5);
+    puzzle p2(3, 4);
+    puzzle p3(5, 4);
+    puzzle p4(3, 7);
+
+    uint64_t bitmap1 = (1ull << 25) - 1; // 5 * 5
+    uint64_t bitmap2 = (1ull << 12) - 1;  // 3 * 4
+    uint64_t bitmap3 = (1ull << 20) - 1; // 5 * 4
+    uint64_t bitmap4 = (1ull << 21) - 1; // 3 * 7
+
+    bitmap1 &= ~(1ull << 12);
+    bitmap2 &= ~(1ull << 6);
+    bitmap3 &= ~(1ull << 8);
+    bitmap4 &= ~(1ull << 18);
+
+    REQUIRE_FALSE(p1.bitmap_is_full(bitmap1));
+    REQUIRE_FALSE(p2.bitmap_is_full(bitmap2));
+    REQUIRE_FALSE(p3.bitmap_is_full(bitmap3));
+    REQUIRE_FALSE(p4.bitmap_is_full(bitmap4));
+}

test/bitmap_find_first_empty.cpp

@@ -0,0 +1,266 @@
+// ReSharper disable CppLocalVariableMayBeConst
+#include "puzzle.hpp"
+
+#include <random>
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/generators/catch_generators.hpp>
+
+static auto board_mask(const int w, const int h) -> uint64_t
+{
+    const int cells = w * h;
+    if (cells == 64) {
+        return ~0ULL;
+    }
+    return (1ULL << cells) - 1ULL;
+}
+
+TEST_CASE("Empty board returns (0,0)", "[puzzle][board]")
+{
+    puzzle p(5, 5);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(0ULL, x, y));
+
+    REQUIRE(x == 0);
+    REQUIRE(y == 0);
+}
+
+TEST_CASE("Full board detection respects width*height only", "[puzzle][board]")
+{
+    auto [w, h] = GENERATE(std::tuple{3, 3}, std::tuple{4, 4}, std::tuple{5, 6}, std::tuple{8, 8});
+
+    puzzle p(w, h);
+
+    uint64_t mask = board_mask(w, h);
+
+    int x = -1, y = -1;
+
+    REQUIRE_FALSE(p.bitmap_find_first_empty(mask, x, y));
+
+    // Bits outside board should not affect fullness
+    REQUIRE_FALSE(p.bitmap_find_first_empty(mask | (~mask), x, y));
+}
+
+TEST_CASE("Single empty cell at various positions", "[puzzle][board]")
+{
+    auto [w, h] = GENERATE(std::tuple{3, 3}, std::tuple{4, 4}, std::tuple{5, 5}, std::tuple{8, 8});
+
+    puzzle p(w, h);
+
+    int cells = w * h;
+
+    auto empty_index = GENERATE_COPY(values<int>({ 0, cells / 2, cells - 1}));
+
+    uint64_t bitmap = board_mask(w, h);
+    bitmap &= ~(1ULL << empty_index);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == empty_index % w);
+    REQUIRE(y == empty_index / w);
+}
+
+TEST_CASE("Bits outside board are ignored", "[puzzle][board]")
+{
+    puzzle p(3, 3); // 9 cells
+
+    uint64_t mask = board_mask(3, 3);
+
+    // Board is full
+    uint64_t bitmap = mask;
+
+    // Set extra bits outside 9 cells
+    bitmap |= (1ULL << 20);
+    bitmap |= (1ULL << 63);
+
+    int x = -1, y = -1;
+    REQUIRE_FALSE(p.bitmap_find_first_empty(bitmap, x, y));
+}
+
+TEST_CASE("First empty found in forward search branch", "[puzzle][branch]")
+{
+    puzzle p(4, 4); // 16 cells
+
+    // Only MSB (within board) set
+    uint64_t bitmap = (1ULL << 15);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == 0);
+    REQUIRE(y == 0);
+}
+
+TEST_CASE("Backward search branch finds gap before MSB cluster", "[puzzle][branch]")
+{
+    puzzle p(4, 4); // 16 cells
+
+    // Set bits 15,14,13 but leave 12 empty
+    uint64_t bitmap = (1ULL << 15) | (1ULL << 14) | (1ULL << 13);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == 0);
+    REQUIRE(y == 0);
+}
+
+TEST_CASE("Rectangular board coordinate mapping", "[puzzle][rect]")
+{
+    puzzle p(5, 3); // 15 cells
+
+    int empty_index = 11;
+
+    uint64_t bitmap = board_mask(5, 3);
+    bitmap &= ~(1ULL << empty_index);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == empty_index % 5);
+    REQUIRE(y == empty_index / 5);
+}
+
+TEST_CASE("Non-64-sized board near limit", "[puzzle][limit]")
+{
+    puzzle p(7, 8); // 56 cells
+
+    uint64_t mask = board_mask(7, 8);
+
+    // Full board should return false
+    int x = -1, y = -1;
+    REQUIRE_FALSE(p.bitmap_find_first_empty(mask, x, y));
+
+    // Clear highest valid cell
+    int empty_index = 55;
+    mask &= ~(1ULL << empty_index);
+
+    REQUIRE(p.bitmap_find_first_empty(mask, x, y));
+    REQUIRE(x == empty_index % 7);
+    REQUIRE(y == empty_index / 7);
+}
+
+// --- Oracle: find first zero bit inside board ---
+static auto oracle_find_first_empty(uint64_t bitmap, int w, int h, int& x, int& y) -> bool
+{
+    int cells = w * h;
+
+    for (int i = 0; i < cells; ++i) {
+        if ((bitmap & (1ULL << i)) == 0) {
+            x = i % w;
+            y = i / w;
+            return true;
+        }
+    }
+
+    return false;
+}
+
+TEST_CASE("Oracle validation across board sizes 3x3 to 8x8", "[puzzle][oracle]")
+{
+    auto [w, h] = GENERATE(std::tuple{3, 3}, std::tuple{4, 4}, std::tuple{5, 5}, std::tuple{6, 6}, std::tuple{7, 7},
+                           std::tuple{8, 8}, std::tuple{3, 5}, std::tuple{5, 3}, std::tuple{7, 8}, std::tuple{8, 7});
+
+    puzzle p(w, h);
+
+    uint64_t mask = board_mask(w, h);
+
+    std::mt19937_64 rng(12345);
+    std::uniform_int_distribution<uint64_t> dist(0, UINT64_MAX);
+
+    for (int iteration = 0; iteration < 200; ++iteration) {
+        uint64_t bitmap = dist(rng);
+
+        int ox = -1, oy = -1;
+        bool oracle_result = oracle_find_first_empty(bitmap, w, h, ox, oy);
+
+        int x = -1, y = -1;
+        bool result = p.bitmap_find_first_empty(bitmap, x, y);
+
+        REQUIRE(result == oracle_result);
+
+        if (result) {
+            REQUIRE(x == ox);
+            REQUIRE(y == oy);
+        }
+    }
+}
+
+TEST_CASE("Bits set outside board only behaves as empty board", "[puzzle][outside]")
+{
+    puzzle p(3, 3); // 9 cells
+
+    uint64_t bitmap = (1ULL << 40) | (1ULL << 63);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == 0);
+    REQUIRE(y == 0);
+}
+
+TEST_CASE("Last valid cell empty stresses upper bound", "[puzzle][boundary]")
+{
+    auto [w, h] = GENERATE(std::tuple{4, 4}, std::tuple{5, 6}, std::tuple{7, 8}, std::tuple{8, 8});
+
+    puzzle p(w, h);
+
+    int cells = w * h;
+    uint64_t bitmap = board_mask(w, h);
+
+    // Clear last valid bit
+    bitmap &= ~(1ULL << (cells - 1));
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    REQUIRE(x == (cells - 1) % w);
+    REQUIRE(y == (cells - 1) / w);
+}
+
+TEST_CASE("Board sizes between 33 and 63 cells", "[puzzle][midrange]")
+{
+    auto [w, h] = GENERATE(std::tuple{6, 6}, // 36
+                           std::tuple{7, 6}, // 42
+                           std::tuple{7, 7}, // 49
+                           std::tuple{8, 7}, // 56
+                           std::tuple{7, 8}  // 56
+    );
+
+    puzzle p(w, h);
+
+    int cells = w * h;
+
+    for (int index : {31, 32, cells - 2}) {
+        if (index >= cells) continue;
+
+        uint64_t bitmap = board_mask(w, h);
+        bitmap &= ~(1ULL << index);
+
+        int x = -1, y = -1;
+        REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+        REQUIRE(x == index % w);
+        REQUIRE(y == index / w);
+    }
+}
+
+TEST_CASE("Multiple holes choose lowest index", "[puzzle][multiple]")
+{
+    puzzle p(5, 5);
+
+    uint64_t bitmap = board_mask(5, 5);
+
+    // Clear several positions
+    bitmap &= ~(1ULL << 3);
+    bitmap &= ~(1ULL << 7);
+    bitmap &= ~(1ULL << 12);
+
+    int x = -1, y = -1;
+    REQUIRE(p.bitmap_find_first_empty(bitmap, x, y));
+
+    // Oracle expectation: index 3
+    REQUIRE(x == 3 % 5);
+    REQUIRE(y == 3 / 5);
+}