add codeforces solutions folder

leetcode/lc401/notes.md

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+# C++ Bit Manipulation Reference
+
+This document contains:
+- GCC / Clang built-in bit functions
+- C++20 `<bit>` header utilities
+- C++23 additions
+
+---
+
+# Part 1 — GCC / Clang Built-in Bit Functions
+
+These are compiler-specific (GCC / Clang).
+They are fast (usually O(1)) and often map to CPU instructions.
+
+---
+
+## 1. `__builtin_popcount`
+
+Counts number of set bits (1s).
+
+### Variants
+
+```cpp
+__builtin_popcount(x)     // → int
+__builtin_popcountl(x)    // → long
+__builtin_popcountll(x)   // → long long
+```
+
+### Example
+
+```cpp
+int x = 13; // 1101
+int cnt = __builtin_popcount(x); // 3
+```
+
+---
+
+## 2. `__builtin_clz`
+
+Count Leading Zeros (from MSB).
+
+### Variants
+
+```cpp
+__builtin_clz(x)
+__builtin_clzl(x)
+__builtin_clzll(x)
+```
+
+### Example
+
+```cpp
+int x = 8; // 000...1000
+int zeros = __builtin_clz(x); // 28 (32-bit int)
+```
+
+### Notes
+
+> ⚠️ Undefined if `x == 0`
+
+```cpp
+// Highest set bit index:
+int highest = 31 - __builtin_clz(x);
+```
+
+---
+
+## 3. `__builtin_ctz`
+
+Count Trailing Zeros (from LSB).
+
+### Variants
+
+```cpp
+__builtin_ctz(x)
+__builtin_ctzl(x)
+__builtin_ctzll(x)
+```
+
+### Example
+
+```cpp
+int x = 8; // 1000
+int zeros = __builtin_ctz(x); // 3
+```
+
+> ⚠️ Undefined if `x == 0`
+
+---
+
+## 4. `__builtin_parity`
+
+Returns `1` if odd number of set bits, `0` if even.
+
+```cpp
+int x = 7; // 111
+int p = __builtin_parity(x); // 1
+```
+
+---
+
+## 5. `__builtin_ffs`
+
+Find First Set Bit (1-indexed from right). Returns `0` if input is `0`.
+
+```cpp
+int x = 10; // 1010
+int pos = __builtin_ffs(x); // 2
+```
+
+---
+
+# Part 2 — C++20 `<bit>` Header (Portable Standard)
+
+```cpp
+#include <bit>
+```
+
+> Works on **unsigned integer types** only.
+
+---
+
+## 1. `std::popcount`
+
+Counts number of set bits.
+
+```cpp
+std::popcount(x);
+```
+
+---
+
+## 2. `std::countl_zero`
+
+Count leading zeros. Safe for `x == 0` (returns bit width).
+
+```cpp
+std::countl_zero(x);
+```
+
+---
+
+## 3. `std::countl_one`
+
+Count consecutive leading ones.
+
+```cpp
+std::countl_one(x);
+```
+
+---
+
+## 4. `std::countr_zero`
+
+Count trailing zeros. Safe for `x == 0` (returns bit width).
+
+```cpp
+std::countr_zero(x);
+```
+
+---
+
+## 5. `std::countr_one`
+
+Count consecutive trailing ones.
+
+```cpp
+std::countr_one(x);
+```
+
+---
+
+## 6. `std::has_single_bit`
+
+Returns `true` if exactly one bit is set (i.e., power of 2).
+
+```cpp
+std::has_single_bit(x);
+
+// Equivalent to:
+x > 0 && (x & (x - 1)) == 0;
+```
+
+---
+
+## 7. `std::bit_width`
+
+Number of bits required to represent `x`.
+
+```cpp
+std::bit_width(x);
+
+// Equivalent to (for x > 0):
+floor(log2(x)) + 1;
+```
+
+---
+
+## 8. `std::bit_floor`
+
+Largest power of 2 ≤ `x`.
+
+```cpp
+std::bit_floor(x);
+
+// Example:
+std::bit_floor(10); // → 8
+```
+
+---
+
+## 9. `std::bit_ceil`
+
+Smallest power of 2 ≥ `x`.
+
+```cpp
+std::bit_ceil(x);
+
+// Example:
+std::bit_ceil(10); // → 16
+```
+
+---
+
+## 10. `std::rotl` — Rotate Left
+
+Circular left rotation.
+
+```cpp
+std::rotl(x, s);
+```
+
+---
+
+## 11. `std::rotr` — Rotate Right
+
+Circular right rotation.
+
+```cpp
+std::rotr(x, s);
+```
+
+---
+
+# Part 3 — C++23 Additions
+
+---
+
+## 1. `std::byteswap`
+
+Swap byte order (endianness conversion).
+
+```cpp
+std::byteswap(x);
+
+// Example:
+// 0x12345678 → 0x78563412
+```
+
+---
+
+## 2. `std::endian`
+
+Detect system byte order.
+
+```cpp
+#include <bit>
+
+if (std::endian::native == std::endian::little) {
+    // little-endian system
+}
+```
+# Applications
+A number of the form 1 << k has a one bit in position k and all other bits are zero,
+so we can use such numbers to access single bits of numbers. In particular, the
+kth bit of a number is one exactly when x & (1 << k) is not zero. The following
+code prints the bit representation of an int number x:
+```
+for (int i = 31; i >= 0; i--) {
+if (x&(1<<i)) cout << "1";
+else cout << "0";
+}
+```
+It is also possible to modify single bits of numbers using similar ideas. For
+example, the formula x | (1 << k) sets the kth bit of x to one, the formula x &
+~(1 << k) sets the kth bit of x to zero, and the formula x ^ (1 << k) inverts the
+kth bit of x.
+The formula x & (x − 1) sets the last one bit of x to zero, and the formula x &
+−x sets all the one bits to zero, except for the last one bit. The formula x | (x − 1)
+inverts all the bits after the last one bit. Also note that a positive number x is a
+power of two exactly when x & (x − 1) = 0.