feat: Add solution for LeetCode #1545

Author: 0xMashiro

SOLVED.md

@@ -173,6 +173,7 @@
 | 1534 | [Count Good Triplets](https://leetcode.com/problems/count-good-triplets/) | [Code](src/leetcode/problems/count-good-triplets.cpp) / [Test](test/leetcode/problems/count-good-triplets.cpp) |
 | 1536 | [Minimum Swaps to Arrange a Binary Grid](https://leetcode.com/problems/minimum-swaps-to-arrange-a-binary-grid/) | [Code](src/leetcode/problems/minimum-swaps-to-arrange-a-binary-grid.cpp) / [Test](test/leetcode/problems/minimum-swaps-to-arrange-a-binary-grid.cpp) |
 | 1544 | [Make The String Great](https://leetcode.com/problems/make-the-string-great/) | [Code](src/leetcode/problems/make-the-string-great.cpp) / [Test](test/leetcode/problems/make-the-string-great.cpp) |
+| 1545 | [Find Kth Bit in Nth Binary String](https://leetcode.com/problems/find-kth-bit-in-nth-binary-string/) | [Code](src/leetcode/problems/find-kth-bit-in-nth-binary-string.cpp) / [Test](test/leetcode/problems/find-kth-bit-in-nth-binary-string.cpp) |
 | 1550 | [Three Consecutive Odds](https://leetcode.com/problems/three-consecutive-odds/) | [Code](src/leetcode/problems/three-consecutive-odds.cpp) / [Test](test/leetcode/problems/three-consecutive-odds.cpp) |
 | 1559 | [Detect Cycles in 2D Grid](https://leetcode.com/problems/detect-cycles-in-2d-grid/) | [Code](src/leetcode/problems/detect-cycles-in-2d-grid.cpp) / [Test](test/leetcode/problems/detect-cycles-in-2d-grid.cpp) |
 | 1572 | [Matrix Diagonal Sum](https://leetcode.com/problems/matrix-diagonal-sum/) | [Code](src/leetcode/problems/matrix-diagonal-sum.cpp) / [Test](test/leetcode/problems/matrix-diagonal-sum.cpp) |

include/leetcode/problems/find-kth-bit-in-nth-binary-string.h

@@ -0,0 +1,16 @@
+#include "leetcode/core.h"
+
+namespace leetcode {
+namespace problem_1545 {
+
+using Func = std::function<char(int, int)>;
+
+class FindKthBitInNthBinaryStringSolution : public SolutionBase<Func> {
+ public:
+  char findKthBit(int n, int k);
+
+  FindKthBitInNthBinaryStringSolution();
+};
+
+}  // namespace problem_1545
+}  // namespace leetcode

src/leetcode/problems/find-kth-bit-in-nth-binary-string.cpp

@@ -0,0 +1,92 @@
+#include "leetcode/problems/find-kth-bit-in-nth-binary-string.h"
+
+namespace leetcode {
+namespace problem_1545 {
+
+/**
+ * 递归分治解法
+ * 
+ * Sₙ 的结构分析：
+ * Sₙ = Sₙ₋₁ + "1" + reverse(invert(Sₙ₋₁))
+ * 长度：len(Sₙ) = 2ⁿ - 1 = (2ⁿ⁻¹ - 1) + 1 + (2ⁿ⁻¹ - 1)
+ * 
+ * 对于第 k 位：
+ * - 如果 k == 2ⁿ⁻¹，返回 "1"
+ * - 如果 k < 2ⁿ⁻¹，在 Sₙ₋₁ 中找第 k 位
+ * - 如果 k > 2ⁿ⁻¹，在 reverse(invert(Sₙ₋₁)) 中找第 k - 2ⁿ⁻¹ 位
+ *   这等于在 invert(Sₙ₋₁) 中找倒数第 (k - 2ⁿ⁻¹) 位
+ *   即 Sₙ₋₁ 的正数第 (2ⁿ⁻¹ - (k - 2ⁿ⁻¹)) = (2ⁿ - k) 位取反
+ * 
+ * 时间复杂度: O(n)，每次递归 n 减 1
+ * 空间复杂度: O(n)，递归栈深度
+ */
+static char solution1(int n, int k) {
+  // 递归辅助函数，flip 表示当前位需要翻转的次数（0 或 1）
+  function<char(int, int, int)> dfs = [&](int n, int k, int flip) -> char {
+    if (n == 1) {
+      // S₁ = "0"
+      return flip ? '1' : '0';
+    }
+    
+    int mid = 1 << (n - 1);  // 2ⁿ⁻¹，中间位置（Sₙ 的正中间是第 2ⁿ⁻¹ 位）
+    
+    if (k == mid) {
+      // 中间位置，固定是 "1"
+      return flip ? '0' : '1';
+    } else if (k < mid) {
+      // 在左半部分 Sₙ₋₁ 中
+      return dfs(n - 1, k, flip);
+    } else {
+      // 在右半部分 reverse(invert(Sₙ₋₁)) 中
+      // 第 k 位对应于 Sₙ₋₁ 的第 (2ⁿ - k) 位取反
+      // 取反通过 flip 的奇偶性来传递
+      return dfs(n - 1, (1 << n) - k, flip ^ 1);
+    }
+  };
+  
+  return dfs(n, k, 0);
+}
+
+/**
+ * 迭代版本（避免递归开销）
+ * 时间复杂度: O(n)
+ * 空间复杂度: O(1)
+ */
+static char solution2(int n, int k) {
+  int flip = 0;
+  
+  while (n > 1) {
+    int mid = 1 << (n - 1);  // 2ⁿ⁻¹
+    
+    if (k == mid) {
+      // 中间位置，固定是 "1"
+      return flip ? '0' : '1';
+    } else if (k > mid) {
+      // 在右半部分，需要取反，并映射到对称位置
+      k = (1 << n) - k;
+      flip ^= 1;
+    }
+    // 如果在左半部分，直接继续，n 减 1
+    n--;
+  }
+  
+  // n == 1，S₁ = "0"
+  return flip ? '1' : '0';
+}
+
+FindKthBitInNthBinaryStringSolution::FindKthBitInNthBinaryStringSolution() {
+  setMetaInfo({
+    .id = 1545,
+    .title = "Find Kth Bit in Nth Binary String",
+    .url = "https://leetcode.com/problems/find-kth-bit-in-nth-binary-string/"
+  });
+  registerStrategy("Recursive", solution1);
+  registerStrategy("Iterative", solution2);
+}
+
+char FindKthBitInNthBinaryStringSolution::findKthBit(int n, int k) {
+  return getSolution()(n, k);
+}
+
+}  // namespace problem_1545
+}  // namespace leetcode

test/leetcode/problems/find-kth-bit-in-nth-binary-string.cpp

@@ -0,0 +1,70 @@
+#include "leetcode/problems/find-kth-bit-in-nth-binary-string.h"
+
+#include "gtest/gtest.h"
+
+namespace leetcode {
+namespace problem_1545 {
+
+class FindKthBitInNthBinaryStringTest : public ::testing::TestWithParam<std::string> {
+ protected:
+  void SetUp() override { solution.setStrategy(GetParam()); }
+
+  FindKthBitInNthBinaryStringSolution solution;
+};
+
+TEST_P(FindKthBitInNthBinaryStringTest, Example1) {
+  // n = 3, k = 1, S₃ = "0111001", 第1位是 "0"
+  EXPECT_EQ('0', solution.findKthBit(3, 1));
+}
+
+TEST_P(FindKthBitInNthBinaryStringTest, Example2) {
+  // n = 4, k = 11, S₄ = "011100110110001", 第11位是 "1"
+  EXPECT_EQ('1', solution.findKthBit(4, 11));
+}
+
+TEST_P(FindKthBitInNthBinaryStringTest, MiddlePosition) {
+  // 测试中间位置，应该是 "1"
+  // S₂ = "011", 中间位置 k = 2
+  EXPECT_EQ('1', solution.findKthBit(2, 2));
+  // S₃ = "0111001", 中间位置 k = 4
+  EXPECT_EQ('1', solution.findKthBit(3, 4));
+}
+
+TEST_P(FindKthBitInNthBinaryStringTest, LastPosition) {
+  // 测试最后一个位置
+  // S₂ = "011", 最后一位 k = 3 是 "1"
+  EXPECT_EQ('1', solution.findKthBit(2, 3));
+  // S₃ = "0111001", 最后一位 k = 7 是 "1"
+  EXPECT_EQ('1', solution.findKthBit(3, 7));
+}
+
+TEST_P(FindKthBitInNthBinaryStringTest, FirstPosition) {
+  // S₁ = "0", 第一位 k = 1 是 "0"
+  EXPECT_EQ('0', solution.findKthBit(1, 1));
+  // Sₙ 的第一位总是 "0"
+  EXPECT_EQ('0', solution.findKthBit(5, 1));
+  EXPECT_EQ('0', solution.findKthBit(10, 1));
+}
+
+TEST_P(FindKthBitInNthBinaryStringTest, SmallCases) {
+  // S₂ = "011"
+  EXPECT_EQ('0', solution.findKthBit(2, 1));
+  EXPECT_EQ('1', solution.findKthBit(2, 2));
+  EXPECT_EQ('1', solution.findKthBit(2, 3));
+  
+  // S₃ = "0111001"
+  EXPECT_EQ('0', solution.findKthBit(3, 1));
+  EXPECT_EQ('1', solution.findKthBit(3, 2));
+  EXPECT_EQ('1', solution.findKthBit(3, 3));
+  EXPECT_EQ('1', solution.findKthBit(3, 4));
+  EXPECT_EQ('0', solution.findKthBit(3, 5));
+  EXPECT_EQ('0', solution.findKthBit(3, 6));
+  EXPECT_EQ('1', solution.findKthBit(3, 7));
+}
+
+INSTANTIATE_TEST_SUITE_P(
+    LeetCode, FindKthBitInNthBinaryStringTest,
+    ::testing::ValuesIn(FindKthBitInNthBinaryStringSolution().getStrategyNames()));
+
+}  // namespace problem_1545
+}  // namespace leetcode